BLOCK-I
M. Sc. Previous
PAPER-IV
SOLID STATE ELECTRONICS
UNIT: I TRANSISTOR AMPLIFIER, OPERATING POINT, BIAS AND
THERMAL STABILITY
1.0
Introduction
1.1
Objectives
1.2
Transistor Biasing and Thermal Stabilization- Operating point and factors
contributing to thermal stability
1.3
Biasing technique
1.4
Collector to base bias
1.5
Self bias and Voltage Divider Bias
1.6
Stabilization against variation in V BE and B Bias compensation.
1.7
Transistor Equivalent Circuits – Y(Admittance) parameters
1.8
Hybrid Parameters
1.9
Conversion to CB to CE hybrid parameters and CB to CC hybrid parameters
1.10
R-C coupled CE amplifier and its frequency response
1.11
Low and high frequency compensation
1.12
Cascade Stages
1.13
Unit Summary
1.14
References
UNIT: II FEEDBACK CIRCUITS
2.0
Introduction
2.1
Objectives
1
2.2
Feedback in amplifiers, Principle of Feedback Amplifiers and Negative
Feedback
2.3
Gain stability effect of feedback on input and output impedances and
Distortions
2.4
Current and voltage feedback circuits
2.5
Emitter follower
2.6
Positive feedback Amplifier –Oscillator
2.7
Circuits and working of Hartley oscillator
2.8
Colpitt oscillator
2.9
Phase shift oscillator
2.10 UJT and its characteristics
2.11 UJT as relaxation oscillators
2.12 Transistor as a switch-astable multi-vibrator
2.13 Mono-stable multi-vibrators
2.14 Bi-stable multi-vibrator
2.15 Unit Summary
2.16 References
2
BLOCK – I
M. Sc. Previous
PAPER-IV
SOLID STATE ELECTRONICS
INTRODUCTON
Among the basic functions of a transistor is its amplification. For faithful
amplification (amplified magnitude of signal without any change in shape), the
following three conditions must be satisfied:
(i) The emitter-base junction should be forward biased,
(ii)The collector-base junction should be reverse biased, and
(iii)There should be proper zero signal collector current.
The proper flow of zero signal collector current (proper operating point of a
transistor) and the maintenance of proper collector-emitter voltage during the
passage of signal is known as transistor biasing.
To achieve this, bias batteries may be used or associated circuit with the transistor
may be employed. The latter method is more efficient and is frequently used. The
circuit providing the desired biasing is known as biasing circuit.
Transistor cannot be a direct substitute for a vacuum tube. A vacuum tube is a
voltage operated device in which the input voltage controls the output current or
voltage or both. This type of amplifier works best with a constant voltage source. On
the other hand, transistor is a current operated device in which the input current
controls the output current. This type of amplifier works best with a constant current
source.
3
The second difference can be made on the basis of isolation of input and the output
circuits. In transistor, these two circuits are not isolated; therefore, output circuit
parameters will affect the input circuit parameters and vice versa.
Third difference can be made with reference to the output and output impedances. In
vacuum tube circuits, both the impedances are sufficiently high, while transistor
circuits generally have a low to medium input impedance and moderate to high input
impedance. The current flowing through these impedances determines the voltage or
power gain of a transistor amplifier circuit.
The process of injecting a fraction of output energy of some device back to the input
is known as feedback in amplifiers.
The principle of feedback is probably as old as the invention of first machine but it
is only some 40 years ago that feedback has come into use in connection with
electronic circuits. It has been found very useful in reducing noise in amplifiers and
making amplifier operation stable. Depending upon whether the feedback energy
aids or opposes the input single, there are two basic types of feedback in amplifiers
viz positive feedback and negative feedback.
4
BLOCK-I
UNIT: I
TRANSISTOR AMPLIFIER, OPERATING POINT, BIAS AND THERMAL
STABILITY
Structure:
1.0
1.1
1.2
Introduction
Objectives
Transistor Biasing and Thermal Stabilization- Operating point and
factors contributing to thermal stability
1.3
Biasing technique
1.4
Collector to base bias
1.5
Self bias and Voltage Divider Bias
1.6
Stabilization against variation in VBE and B Bias compensation.
1.7
Transistor Equivalent Circuits – Y(Admittance) parameters
1.8
Hybrid Parameters
1.9
Conversion to CB to CE hybrid parameters and CB to CC hybrid
parameters
1.10
R-C coupled CE amplifier and its frequency response
1.11
Low and high frequency compensation
1.12
Cascade Stages.
1.13
Unit Summary
1.14
References
5
BLOCK-I
UNIT-I
TRANSISTOR AMPLIFIER, OPERATING POINT, BIAS AND THERMAL
STABILITY
1.0 INTRODUCTION
Among the basic functions of a transistor is its amplification. For faithful
amplification (amplified magnitude of signal without any change in shape), the
following three conditions must be satisfied:
(i) The emitter-base junction should be forward biased,
(ii)The collector-base junction should be reverse biased, and
(iii)There should be proper zero signal collector current.
The proper flow of zero signal collector current (proper operating point of a
transistor) and the maintenance of proper collector-emitter voltage during the
passage of signal is known as transistor biasing.
To achieve this, bias batteries may be used or associated circuit with the transistor
may be employed. The latter method is more efficient and is frequently used. The
circuit providing the desired biasing is known as biasing circuit.
Transistor cannot be a direct substitute for a vacuum tube. A vacuum tube is a
voltage operated device in which the input voltage controls the output current or
voltage or both. This type of amplifier works best with a constant voltage source. On
the other hand, transistor is a current operated device in which the input current
controls the output current. This type of amplifier works best with a constant current
source.
6
The second difference can be made on the basis of isolation of input and the output
circuits. In transistor, these two circuits are not isolated; therefore, output circuit
parameters will affect the input circuit parameters and vice versa.
Third difference can be made with reference to the output and output impedances. In
vacuum tube circuits, both the impedances are sufficiently high, while transistor
circuits generally have a low to medium input impedance and moderate to high input
impedance. The current flowing through these impedances determines the voltage or
power gain of a transistor amplifier circuit. There are three basic types of transistor
amplifier circuits:
(i) grounded amplifier
(ii) grounded base
(iii) grounded collector.
1.1 OBJECTIVES
When a transistor is not properly biased, it works inefficiently and produces
distortion in the output signal. Hence a transistor should be biased correctly. A
transistor is biased either with the help of battery or associating a circuit with the
transistor. The latter method is generally employed. The circuit used with the
transistor is known as biasing circuit.
In transistor biasing, when a transistor is not properly biased, it works inefficiently
and produces distortion in the output signal. In addition, amount of bias required is
important for establishing Q-point which is dictated by the mode of operation
desired. It is also desirable that the Q-point should be stable, i.e., it should not shift
its position due to temperature rise etc. Special efforts are made for this purpose.
The performance of a transistor circuit can be considered in Y parameters. Y
parameters are measured under short circuit conditions. The hybrid parameters h11
and h21 are measured with output short circuited and h12 and h22 with input open
circuited. It is convenient to short circuit the high impedance output of the capacitor
and to open circuit the low impedance input with a inductor.
7
1.2
TRANSISTOR
BIASING
AND
THERMAL
STABILIZATION-
OPERATING POINT AND FACTORS CONTRIBUTING TO THERMAL
STABILITY
The maintenance of the operating point stable is known as stabilization.
There are two factors which are responsible for shifting the operating point. Firstly,
many of the transistor parameters are markedly temperature sensitive and secondly
when a transistor is replaced by another of the same type, there is a wide spread in
the values of transistor parameters. The problem of operating point instability is not
faced in case of vacuum tubes. The reason is that the tube parameters are almost
independent of working temperature and it is also possible to manufacture tubes
with identical characteristics. So, stabilization of the operating point is necessary
due to the following reasons:
(a) Temperature dependence of Ic
(b) Individual variations and
(c) Thermal runaway.
Dependence:
(a) Temperature dependence of Ic : The instability of Ic is principally caused by the
following three sources:
(i) The collector leakage current Ico is greatly influenced by temperature changes.
The Ico doubles for every 100C rise in temperature.
(ii) Increase of  with increase of temperature.
(iii) Variation of VBE (Base to emitter voltage) with temperature. Here it should be
remembered that VCE also changes with temperature but the change is very small.
Hence IC is almost independent of VCE.
(b) Individual variations: When a transistor is replaced by another transistor of the
same type, the value of  and VBE are not exactly the same. Hence the operating
8
point is changed. So it is necessary to stabilize the operating point irrespective of
individual variations in transistor parameters.
(c) Thermal runaway. Depending upon the construction of a transistor, the collector
junction can withstand a maximum temperature. The range of temperature lies
between 600C to 1000C for Ge transistor and 1500C to 2250C for Si transistor. If the
temperature increases beyond this range then the transistor burns out. The increase
in the collector junction temperature is due to thermal runaway. When a collector
current flows in a transistor, it is heated i.e., its temperature increases. If no
stabilization is done, the collector leakage current also increases. This further
increases the transistor temperature. Consequently, there is a further increase in
collector leakage current. The action becomes cumulative and the transistor may
ultimately burn out. The self-destruction of an un-stabilized transistor is known as
thermal runaway.
The following two techniques are used for stabilization:
(1) Stabilization technique. The technique consists in the use of a resistive biasing
circuit which permits such a variation of base current IB as to maintain IC almost
constant in spite of variation of ICO,  and VBE.
(2) Compensation technique. In this technique, temperature sensitive devices such as
diodes, transistors, thermistors etc. are used. Such devices produce compensating
voltages and currents in such a way that the operating point is maintained stable.
1.3 BIASING TECHNIQUE
From the point of view of simplicity and economy, only one source of supply
(instead of two VBB and VCC) in the output circuit (i.e., VCC) is used. Some methods
are used for providing bias for a transistor.
The basic principle involved in all the methods is to obtain the required base current
(i.e., collector current) from VCC in zero signal conditions. The value of collector
load is selected in such a way that the voltage between collector and emitter should
not fall below 0.5 volt for germanium transistor and 0.7 volt for silicon transistor.
Some of the methods are as follows:
9
BASE RESISTOR METHOD
Fig. shows an NPN transistor connected in CE configuration with resistor biased. In
this method, a high resistance RB is connected between positive terminal of supply
VCC and base of the transistor. Here it should be remembered that if the transistor is
PNP, then RB is connected between negative terminal of supply VCC and base of the
transistor.
Here the required zero signal base current flows through RB and is provided by VCC.
In fig. the base-emitter junction is forward biased because the base is positive w.r.t.
emitter. By a proper selection of RB, the required zero signal base current (and hence
IC=  IB) can be made to flow.
Circuit analysis. Here we shall find the value RB such that required collector
current flows under zero signal conditions. Let IC be the required zero signal
collector current.
Considering the closed circuit ABEGA and applying the Kirchhoff's voltage law, we
have
I B RB  VBE  VCC
or
I B RB  VCC  VBE
10

RB 
VCC  VBE
IB
IB 
Further
IC

Substituting the value of IB from above eq. we get
RB
V  VBE 
 CC

IC
The value of VBE can be seen from the transistor manual. Using above eq. the value
of RB can be calculated. As VBE is generally very small as compared to VCC, hence
RB 
VCC
IC
From eq. the value of RB can be found directly. Hence this method is sometimes
called as fixed-bias method.
Stability factor S. The stability factor S is given by
S
1   
1    dI B / dI C 
In base resistor method, the base current IB is independent of collector current IC. So
the stability factor S is given by
S  1   
If  =100, then S=101. This shows that IC changes 101 times as much as any change
in ICO. Thus IC is very dependent upon ICO and hence upon temperature. The value of
S is the highest that can be obtained. Hence the circuit has very poor stability.
Example.1
Fig. shows the base bias with emitter feedback. Obtain an expression
for IC.
11
Considering the closed circuit ABEGA, and applying the Kirchoff's law, we get
VCC  I B RB  VBE  I E RE
From eq.
IB 
VCC  VBE VCC

RB
RB
So IB is independent of IC.
Now IB = IC/  and IE  IC
Substituting these values in eq. we get
VCC  RB  IC /    VBE  IC RE
VCC  VBE  IC  RE   RB /  
or

IC 
VCC  VBE
 RE   RB /   
As VBE is negligibly small as compared to VCC, hence
IC 
Example2.
VCC
 RE   RB /   
(i) A germanium transistor is to be operated at zero signal IC =1 mA.
If the collector supply VCC = 10 V, what is the value of RB is base resistor method?
Take  = 100.
(ii)
If another transistor of the same batch with  = 50 is used, what will be the
new value of zero signal IC for the same RB.
(i)
The value of RB is given by
12
RB
VCC  VBE 

IC
Here, VCC = 10V,  = 100 and IC = 1 mA. For a germanium transistor VBE = 0.3 V.
(ii)
The value of IC is given by
IC 

VCC  VBE  
RB
10  0.3 50 
9700 K 
9.7  50
9700 103 
= 0.5 mA
Fig. shows a silicon transistor with  = 100 and biased by base
Example3.
resistor method. Determine the operating point.
The Value of IC is given by
IC 
VCC  VBE  
RB
Here, VCC = 10 V, VBE = 0.7 V (Silicon transistor),
 = 100 and RB = 930 K 

IC 
10  0.7 100  1mA.
930 K 
Now VCE = VCC - ICRL
= 10 -1 mA × 4 K 
= (10-4) volt
= 6V
13

Operating point is (6V, 1mA).
1.4 COLLECTOR TO BASE BIAS
The circuit of an NPN transistor connected in CE configuration with collector to
base bias is shown in fig. This circuit is same as base bias circuit except that the base
resistor RB is returned to collector rather than to VCC supply. Using this circuit, there
is considerable improvement in the stability. If the collector current IC tends to
increase (either as a result of rise in temperature or as a result of transistor being
replaced by another of larger  ), the d.c. voltage drop across RL increase and
consequently VCE
decreases. As a result, the base current IB also reduces. This will tend to compensate
for the original increase. The compensation is never exact.
Circuit analysis. The required value of RB needed to give the zero signal current IC
can be calculated as follows:
Voltage drop across RL = (IC + IB) RE  ICRL
From the figure,
ICRL + IBRB + VBE = VCC
or
IBRB = VCC - VBE - ICRL

RB =
or
RB 
VCC  VBE  IC RL
IB
VCC  VBE  IC RL  
IC
Stability factor S. Applying KVL to the circuit of fig. we have
14
 I B  IC  RL  I B RB  VBE  VCC
or
I B  RL  RB   IC RL  VBE  VCC

IB 
VCC  VBE  I C RL
RL  RB
Since VBE is almost independent of collector current (VBE = 0.7 for Si and 0.3 V for
Ge). Then from eq. we get
dI B
RL

dI C
RL  RB
S
We know that
1 
1    dI B / dI C 

This value is smaller than 1    which is obtained for fixed-bias circuit. Thus
there is an improvement in the stability.
The circuit of fig. provides a negative feedback. This reduces the gain of the
amplifier. So the increased stability of the collector to base bias circuit is obtained at
the cost of a.c. voltage gain.
1.5 SELF BIAS VOLTAGE DIVIDER BIAS
A very commonly used biasing arrangement is self-bias or emitter bias. The circuit
arrangement is shown in fig. This is also known as universal bias stabilization
circuit. In this method two resistance R1 and R2 are connected across supply voltage
VCC and provide biasing. The emitter resistances RE provides stabilization. The
name voltage divider is derived due to the fact that resistors R 1 and R2 form a
potential divider across VCC. The resistance RE causes a voltage drop in a direction
so as to reverse-bias the emitter junction. Since the junction must be forward-biased,
the base voltage is obtained from the supply through R1-R2 network. The net
forward bias across the emitter junction is equal to Vb minus the d.c. voltage drop
across RE.
15
The improvement in the operating point stability may be explained as follows: Let
there be a rise in temperature. This causes a rise in ICO i.e. a rise in IC. Now the
current in RE increases. As a result, the voltage drop across RE increases and
consequently the base current decreases. This decreases the collector current.
Thus the presence of RE reduces the increase in IC and improves the operating point
stability. In case of amplifiers, to avoid the loss of ac signal gain (because of the
feedback caused by RE) a capacitor of large capacitance is connected across RE. The
condenser offers a very small reactance to ac signal and hence it passes through the
condenser.
Circuit Analysis. Let current I1 flows through R1. As the base current IB is very
small, the current flowing through R2 can also be taken as I1. The calculation of
collector current IC is as follows:
The current I1 flowing through R1 or R2 is given by
I1 
VCC
 R1  R2 
The voltage V2 developed across R2 is given by
Applying KVL to the base circuit, we have
V2  VBE  VE  VBE  I E RE
or
 I E  IC 
V2  VBE  IC RE
16
IC 
V2  VBE
RE
Here IC is almost independent of transistor parameters and hence good stabilization
is ensured.
The collector emitter voltage VCE can be calculated as follows:
VCE = ICRL + VCE + ICRE
VCE = VCC - IC (RL+RE)
1.6 STABILIZATION AGAINST VARIATION IN VBE AND B BIAS
COMPENSATION
So far we have studied the various biasing methods and operating point stability
provided by them. We have seen that self bias circuit provides better operating point
stability than a fixed bias circuit. In both arrangements the stabilization action
occurs due to the negative feedback improves the stability of the operating point but
at the same time it reduces the gain of the amplifier. In certain applications, the loss
in the gain becomes serious drawback and is intolerable. In such cases,
compensation techniques are used to reduce the drift of the operating point.
Sometimes for excellent bias and thermal stabilization, both stabilization as well as
compensation techniques are used. The stabilization techniques refer to the use of
resistive biasing circuits which permit IB to vary so as to keep IC relatively constant.
On the other hand, compensation techniques refer to the use of temperature-sensitive
devices such as diodes, transistors, thermistors, sensistors etc. to compensate for the
variation in currents. Here we shall discuss the following compensation techniques:
(A)
Diode compensation for instability due to VBE variation.
(B)
Diode compensation for instability due to ICO variation.
(C)
Thermistor Compensation
(D)
Sensitor compensation.
17
Diode compensation for instability due to VBE variation
For germanium transistor, changes in ICO with temperature contribute more serious
problem than for silicon transistor. On the other hand, in a silicon transistor, the
changes of VBE with temperature possesses significantly to the changes in IC. A
diode may be used as compensation element for variation in VBE or ICO. Fig. shows
the circuit of self bias stabilization technique with a diode compensation for VBE.
The Thevenin's equivalent circuit is shown in fig. The diode D used here is of the
same material and type as the transistor.
18
Hence the voltage VD across the diode has same temperature coefficient (2.5mV/deg.C) as VBE of the transistor. The diode D is forward-biased by the source
VDD and resistor RD.
Applying Kirchoff's voltage law to the base circuit of fig. we get
VTh - VBE + VD = IBRTh + RE (IB + IC)
IC   I B  1    ICO
But
From eq. we have
VTh - VBE + VD = RE IC + (RTh + RE) IB
Substituting the value of IB from eq. (2), we get
 I  1    I CO 
VTh  VBE  VD  RE I C   RTh  RE   C




or
 VTh  VBE  VD    RE IC   RTh  RE  IC  1    ICO  RTh  RE 
or
 VTh  VBE  VD   1    ICO  RTh  RE   IC   RE IC  RTh  RE 

IC 
 VTh  VBE  VD   1    I CO  RTh  RE 
RTh  1    RE
Since variation in VBE with temperature is the same as the variation in VD with
temperature, hence the quantity (VBE - VD) remains constant in eq. So the current IC
remains constant inspite of the variation in VBE. Although diode compensation for
VBE variation is not perfect yet it is effective in canceling most of the operating point
drift.
EXERCISE- 1.1
1) Name three types of transistor amplifier circuits.
2) What do you understand by stabilization of operating point?
3) What do you understand by transistor biasing? What is its need?
19
4) Draw a self-bias circuit.
5) Draw a fixed-bias circuit. Explain why the circuit is unsatisfactory if the transistor
is replaced by another of the same type.
6) What are the techniques needed for stabilization?
1.7
TRANSISTOR
EQUIVALENT
CIRCUITS-
Y
(ADMITTANCE)
PARAMETERS
The y- parameters are defined by choosing the input and output voltages V1 and V2
as independent variables and expressing the currents I1 and I2 in terms of these two
voltages. Thus,
where the I’s and V’s represent rms values of the small-signal currents and voltages.
The circuit model satisfying these equations is indicated in Fig.
20
For a given device, single transistor or cascade pair, these parameters may be
specified as explicit functions of frequency, or, as is more often the case, as graphs
of the real and imaginary parts, the conductance G and the susceptance B, versus
frequency. The data sheet of the MC 1550 gives the y-parameters measured on the
general radio 1607A immittance bridge. Typical measured values are shown. The
internal feedback factor y12 is not shown because it was found to be less than 0.001
mA/V and is neglected.
Let us consider the two-port network terminated at the output by a load admittance
YL and driven by a current source Is with source admittance Ys. The equivalent
admittance seen by the current source is Yeq = Ys + Yi.
and the output admittance is
Since y12 ~ 0, then Yi ~ y11 and YO ~ y22.
EXERCISE -1.2
1) Define the y- parameters (a) by equation (b) in words.
2) Explain y-parameters for circuit.
1.8 HYBRID PARAMETERS
21
The hybrid parameters are commonly known as h-parameters. These are generally
used to determine amplifier characteristic parameters such as voltage gain, input and
output resistances etc.
Determination and Meaning of h-parameters
Every linear circuit may be represented by a set of four h- parameters namely h11,
h12, h21 and h22. The parameters h11 and h21 may be determined by short-circuiting
the output terminal of a given circuit. On the other hand, h12 and h22 may be
determined by open- circuiting the terminals of the given circuits.
1.Determination of h11 and h21. These are determined by short- circuiting the
output terminals of a given circuit as shown in fig. A short-circuit at the output
terminals makes the voltage V2 equal to zero. We know that the input voltage is
given by the relation.
v1 = h11 = i1 + h12 v2
Substituting the value of v2 (equal to zero) in the above equation, the input voltage,
v1 = h11 i1 or h11 = v1/i1
Thus h11 may be determined from the relation v1/i1. The value of i1 is obtained by
applying a voltage at the input and then measuring the value of input current (i1).
Since h11 is the ratio of voltage to current, therefore it has the units of ohms i.e., the
same unit as that of a resistance. Similarly, we know that the output current is given
by the relation,
i1 = h21 i1 or h22 v2
Again substituting the value of v2 (equal to zero) in the above equation, the output
current:
i1 = h21 i1 or h21 = i2/i1
Thus h21 may be determined from the ration i2/i1. The values of i1 and i2 may be
obtained by applying a voltage at the input and then measuring the input current (i 1)
and output current (i2). Since h21 is the ratio of currents, therefore it has no units.
The parameter h21 is called the forward current gain of the circuit with output shortcircuited.
2.Determination of h12 and h22. These are determined by open circuiting the input
terminals of a given circuit as shown in fig (b). An open circuit, at the input
22
terminals, makes the current (i1) equal to zero. We also known that the input voltage
is given by the relation,
v1 = h11i1 + h12v2
Substitution of the value of i1 (equal to zero) in the above equation, the input
voltage,
v1 = h12v2 or h12 = v1/v2
Thus, h12 may be determined from the ratio v1/v2. The value of v1 may be obtained
by applying a voltage v2 at the output and then measuring at the input voltage (v1).
Since, h12 is a ratio of voltage, therefore it has no units. As h12 is the ratio of input
voltage (v1) to the output voltage (v2), therefore, its value is known as the reverse
voltage gain in order to distinguish it from to forward voltage gain, whose value is
equal to v2/v1.
Similarly, we know that the output current is given by the relation,
i2=h21 .i1+ h22 .v2
Again substituting the value of (equal to zero) in the above equation, the output
current,
i2=h22 .v2 or h22 = i2/v2
Thus, h22 may be determined from the ratio i2/v2. The value of current (i2) may be
obtained by applying a voltage at the output (v2) and then measuring the output with
input open. Since h22 is the ratio of current to voltage, therefore it has the units of
ohms () or Siemes (S). The parameter h22 is also called output conductance with
input open.
1.9 CONVERSION OF CB TO CE HYBRID PARAMETERS AND CB TO CC
PARAMETERS
CB to CE conversion:
Figures show the transistor connected in common-emitter (CE) configuration and
the hybrid equivalent circuit of such a transistor.
23
In a common emitter transistor configuration, the input signal is applied between the
base and emitter terminals of transistor and output appears between the collector and
emitter terminals. The input voltage (veb) and the output current (ic) are given by the
following equation:
vbe = hie . ib + hre . vce
ic = hfe . ib + vce
CB to CC hybrid parameters:
Figures show the transistor connected in a common- base (CB) configuration and its
hybrid equivalent circuit. In a common-base configuration, the input signal is
applied between emitter and base terminals and output appears between collector
and base terminals.
The input Voltage (veb) and the output current (ic) are given by the following
equations:
veb = hib . ie + hre . vcb
ie = hfh . ic + vcb
24
Approximate Conversion Formulae for h-parameters
The transistors are used in most of the circuits in common emitter configuration.
Therefore the manufacturers list only the common emitter h-parameters in their data
sheets. However, if the transistor is to be used in a configuration, other than the
common emitter, then we must use the specified conversion formulae for
determining its h-parameters. The conversion formulas for common base and
common collector configuration are as given below.
1.Conversion of formulas for common base configuration. The conversion formulas
for determining the values of h-parameters of a transistor in common base
configuration, from the common emitter h-parameter values, are as given below:
hib = hie /1+ hfe
,
hfb = -hfe /1+hfe
hrb = hie . hoe /1+ hfe
,
hob = hoe /1+hfe
2.Conversion formulae for common collector configuration. The conversion
formulae for determining the values of h-parameters of a transistor n common
collector configuration from the common emitter h-parameter value, are as given
below:
hic = hie
hfc = -(1+hfe )
,
,
hre = 1-hre ~ 1
hoc = hoe
EXERCISE- 1.3
1) What do you understand by hybrid parameters? What are their dimensions?
25
2) How will you measure h- parameters of a linear circuit?
3) Draw the h- parameter equivalent circuit of a linear circuit.
4) How are h- parameters of a transistor measured?
5) Explain (a) conversion formulae for common base configuration (b) conversion
formulae for common collector configuration.
1.10 R-C COUPLED CE AMPLIFIER AND ITS FREQUENCY RESPONSE
A cascaded arrangement of common emitter transistor stages is shown in Fig.(a) and
of common source FET stages is also shown in Fig. (b)
The output Y1 of one stage is coupled to the input X2 of the next stage via a blocking
capacitor Cb which is used to keep the dc component of the output voltage at Y1
from reaching the input X2 . Resistor Rg is from gate to ground, and the collector
(drain) circuit resistor is Rc (Rd). The source resistor Rs , the emitter resistor Re , and
the resistors R1 and R2 are used to establish the bias. The bypass capacitors, used to
prevent loss of amplification due to negative feedback, are Cz in the emitter circuit
and Cs in the source circuit. Also present are junction capacitances, to be taken into
account when we consider the high- frequency response, which is limited by their
presence.
1.11 LOW AND HIGH FREQUENCY COMPENSATION
In electrical engineering, frequency compensation is a technique used in amplifiers,
and especially in amplifiers employing negative feedback. It usually has two
primary goals: To avoid the unintentional creation of positive feedback, which will
cause the amplifier to oscillate, and to control overshoot and ringing in the
amplifier's step response. The low-frequency equivalent circuit is obtained by
neglecting all shunting capacitances and all junction capacitances by replacing
amplifier A1 by its Norton’s equivalent. For a transistor these quantities may be
expressed in terms of the CE hybrid parameters: Ri ~ hie (for small values of Rc); Ro
26
= 1/ hoe (for a current drive); and I = hfe Ib where Ib is the base signal current. The low
3-d B frequency is
This result is easy to remember since the time constants equals Cb multiplied by the
sum of the effective resistances Ro is to the left of the blocking capacitor, and Ri to
the right of Cb. For an FET amplifier, Ri = Rg >> Rd. Since Ro < Rd because Ro is Rd in
parallel with
then Ri = Rg >> Ro and
The input impedance of a transistor is much smaller than that of an FET, a coupling
capacitor is required with the transistor which is 500 times larger than that required
with the FET. Fortunately, it is possible to obtain physically small electrolytic
capacitors having such high capacitance values at the low voltages at which
transistors operate. Since the coupling capacitances required for good low-frequency
response are far larger than those obtainable in integrated form, cascade integrated
stages must be direct- coupled.
For high- frequency calculations each transistor is replaced by its small- signal
hybrid- II model. We have included a voltage source Vs with Rs = 50 and have
assumed that capacitors Cb and Cz represent short circuits for high frequency.
1.12 CASCADE STAGES
When the amplification of a single transistor is not sufficient for a particular
purpose, or when the input or output impedance is not of the correct magnitude for
the intended application two or more stages may be connected to the input of the
next stage.
To analyze such type of circuits, we make use of the general expressions for AI, Zi,
Av, Yo. It is necessary that we have available the h parameters for the specific
27
transistors used in the circuit. The h-parameters values for a specific transistor are
usually obtained from the manufacturer’s datasheet.
EXERCISES- 1.4
1) Explain in detail R-C coupled CE amplifier.
2) How is low-frequency equivalent circuit obtained?
3) What are cascade stages?
1.13 UNIT SUMMARY
(i) The proper flow of zero signal collector current (proper operating point of a
transistor) and the maintenance of proper collector-emitter voltage during the
passage of signal is known as transistor biasing.
(ii) The maintenance of the operating point stable is known as stabilization.
(iii)The hybrid parameters are commonly known as h-parameters. These are
generally used to determine amplifier characteristic parameters such as voltage gain,
input and output resistances etc.
(iv)The circuit providing the desired biasing is known as biasing circuit.
(v) The circuit used with the transistor is known as biasing circuit.
1.14 REFERENCES
(i) Electronic Devices and Circuits by Millman and Halkias, S. Chand & Company
Ltd.
(ii) Electronic Devices and Circuits an Introduction by Mottershed
(iii)Transistor Physics by Sarkar
(iv) Nashelsky – Electronic Devices & Circuit Theory (PHI) by Robert Boylested
and Louis
(v) Principles of Electronics by V.K. Mehta, S. Chand & Company Ltd.
SOLUTION
EXERCISE- 1.1
1) Refer to article 1.0, 2) Refer to article 1.2, 3) Refer to article 1.0, 4) Refer to
article 1.5, 5) Refer to article 1.3, 6) Refer to article 1.2
EXERCISE- 1.2
1) Refer to article 1.7, 2) Refer to article 1.7
28
EXERCISE- 1.3
1) Refer to article 1.8, 2) Refer to article 1.8, 3) Refer to article 1.8, 4) Refer to
article 1.8
EXERCISE- 1.4
1) Refer to article 1.10, 2) Refer to article 1.11, 3) Refer to article 1.12
BLOCK-I
UNIT: II
FEEDBACK CIRCUITS
Structure:
2.0 Introduction
29
2.1 Objectives
2.2
Feedback in amplifiers, Principle of Feedback Amplifiers and Negative
Feedback
2.3
Gain stability effect of feedback on input and output impedances and
Distortions
2.4 Current and voltage feedback circuits
2.5 Emitter follower
2.6 Positive feedback Amplifier –Oscillator
2.7 Circuits and working of Hartley oscillator
2.8 Colpitt oscillator
2.9 Phase shift oscillator
2.10 UJT and its characteristics
2.11 UJT as relaxation oscillators
2.12 Transistor as a switch-astable multi-vibrator
2.13 Mono-stable multi-vibrators
2.14 Bi-stable multi-vibrator
2.15 Unit Summary
2.16 References
BLOCK-I
UNIT: II
FEEDBACK CIRCUITS
2.0 INTRODUCTION
30
The process of injecting a fraction of output energy of some device back to the input
is known as feedback in amplifiers.
The principle of feedback is probably as old as the invention of first machine but it
is only some 40 years ago that feedback has come into use in connection with
electronic circuits. It has been found very useful in reducing noise in amplifiers and
making amplifier operation stable. Depending upon whether the feedback energy
aids or opposes the input single, there are two basic types of feedback in amplifiers
viz positive feedback and negative feedback.
2.1 OBJECTIVES
In feedback amplifiers, when the feedback voltage (or current) is so applied that it
increases the input voltage (or current) i.e., it is in phase with the input, it is called as
positive feedback or regenerative or direct feedback. Positive feedback increases the
gain of the amplifier. However, it has the disadvantage of increased distortion and
instability. So positive feedback is seldom employed in amplifiers. If the positive
feedback is sufficiently large, it leads to oscillations and hence it is used in
oscillators. When the feedback voltage is so applied that it decreases the input
voltage i.e., it is out of phase with the input, it is called as negative feedback or
degenerative feedback or inverse feedback. Negative feedback reduces the gain of
the amplifier. However, the advantage of negative feedback are: reduction in
distortion, stability in gain, increased bandwidth etc. So the negative feedback is
frequently used in amplifier circuits.
2.2 FEEDBACK IN AMPLIFIERS, PRINCIPLE OF FEEDBACK IN
AMPLIFIERS AND NEGATIVE FEEDBACK
For an ordinary amplifier i.e., without feedback, let Vo and Vi be the output voltage
and input voltage respectively. If A be the voltage gain of the amplifier, then
A = VO / Vi
The gain A is often called as open loop gain.
The principle of an amplifier with feedback is shown in fig. The amplifier has two
parts: an amplifier and a feedback circuit. Let
31
be the output voltage with
feedback and a fraction B of this voltage is applied to the input voltage. Now the
input voltage becomes (Vi +BVO) depending whether the feedback is positive or
negative. This voltage is amplified A times by the amplifier. Considering positive
feedback, we have
A(Vi +BVO) = VO
Or AVi +ABVO = VO
Or AVi = VO [1-BA]
The left hand side of eq. represents the amplifier gain A or Af with feedback i.e.,
For positive feedback
Foe negative feedback
32
Here the term BA is called as feedback factor and B as feedback ratio. The term (1+
BA) is known as loop gain and amplifier gain A with feedback is closed loop
gain(feedback loop is closed).
Negative feedback:
When the feedback energy (voltage or current) is out of phase with the input signal
and thus opposes it, it is called negative feedback. This is illustrated in Fig. as you
can see, the amplifier introduces a phase shift of 1800 into the circuit while the
feedback network is so designed that it introduces a phase shift of (i.e., 00 phase
shift). The result is that the feedback voltage Vf is 1800 out of phase with the input
signal Vin.
Negative feedback reduces the gain of the amplifier. However, the advantages of
negative feedback are: reduction is distortion, stability in gain, increased bandwidth
and improved input and output impedances. It is due to these advantages that
negative feedback is frequently employed in amplifiers.
2.3 GAIN STABILITY EFFECT OF FEEDBACK ON INPUT AND OUTPUT
IMPEDANCES AND DISTORTIONS
Consider the negative voltage feedback amplifier shown in Fig. The gain of the
amplifier without feedback is Av. Negative feedback is then applied by feeding a
fraction mv of the output voltage e0 back to amplifier input to the amplifier is the
signal voltage eg minus feedback voltage mv e0 i.e.,
33
Actual input to amplifier = e8 - mv e0
The output e0 must be equal to the input voltage e8 - mv e0 multiplied by gain Av of
the amplifier i.e.,
(e8 - mv e0) Av = e0
Av e8 - Av my e0 = e0
It may be seen that the gain of the amplifier without feedback is A v. However, when
negative voltage feedback is applied, the gain is reduced by a factor 1 + A y my. it
may be noted that negative voltage feedback does not affect the current gain of the
circuit.
(i) Gain Stability – An important advantage of negative voltage feedback is
that the resultant gain of the amplifier can be made independent of
transistor parameters or the supply voltage variations.
Avf 
Ay
1  Ay mv
For negative voltage feedback in an amplifier to be effective, the designer
deliberately makes the product Av mv much greater than unity. Therefore, in the
34
above relation, I can be neglected as compared to Av mv and the expression
becomes.
Avf 
Ay
Ay mv

1
my
It may be seen that the gain now depends only upon feedback fraction m y i.e., on the
characteristics of feedback circuit. As feedback circuit is usefully a voltage divider
(a resistive network) , therefore, it is unaffected by changes in temperature, variation
in transistor parameters and frequency, Hence, the gain of the amplifier is extremely
stable.
(ii)
Reduces non-linear distortion .
A large single stage has non linear distortion because its voltage gain changes at
various points in the cycle. The negative voltage feedback reduces the non-linear
distortion in large signal amplifiers. If can be proved mathematically that.
Dvf 
D
1  Ay mv
Where D = distortion in amplifier without feedback
Dvf = distortion in amplifier with feedback
It is clear that by applying negative voltage feedback to an amplifier, distortion is
reduced by a factor 1 + Ay mv.
(iii) Improves frequency response.
As feedback is usually obtained through a resistive net work, therefore, voltage gain
of the amplifier is independent of signal frequency. The result is that voltage gain of
the amplifier will be substantially constant over a wide range of signal frequency.
The negative voltage feedback, therefore, improves the frequency response of the
amplifier.
35
(iv) Increases circuit stability.
The output of an ordinary amplifier is easily changed due to variations in ambient
temperature, frequency and signal amplitude. This changes the gain of the amplifier,
resulting in distortion. However, by applying negative voltage feedback voltage gain
of the amplifier is stabilized or accurately fixed in value. This can be easily
explained. Suppose the output of a negative voltage feedback amplifier has
increased because of temperature change or due to some other reason. This means
more negative feedback since feedback is being given from the output. This tends to
oppose the increase in amplification and maintains it stable. The same is true should
the output voltage decrease. Consequently, the circuit stability is considerably
increased.
(v)
Increases input impedance and decreases and decreases output
impedance.
The negative voltage feedback increases the input impedance and decreases the
output impedance of amplifier. Such a change is profitable in practice as the
amplifier can then serve the purpose of impedance matching.
Input impedance.
The increase in input impedance with negative voltage feedback can be feedback
and Zm with negative feedback. Let us further assume that input current is i1.
Referring to
e8  mv e0  i1Zin
=
e8 (e8  mv e0 )  mv e0
=
(e8  mv e0 )  Av M v (e8  mv e0 )
=
{e0  Av (e8  mve0 )}
(e8  mv e0 )(1  Av M v )
36
=
OR
(i1  Zin (1  Av M v ) {e8  mv e0  i1Zin )
e8
 Zin (1  Av M v )
i1
But e8 / i1 = Zin the impedance of the amplifier with negative voltage feedback.
Zin  Zin (1  Av M v )
It is clear that by applying negative voltage feedback the input impedance of the
amplifier is increased by a factor
1  Av M v As Av M v is
much greater than
unity, therefore, input impedance is increased considerably. This is an advantage,
since the amplifier will now present less of a load to its
Output impedance.
We can show that output impedance with negative voltage feedback is given by :
Z 'out 
Where
Z 'out
Z out
1  Av M v
= Output impedance with negative voltage
feedback
37
Z 'out
= Output impedance without feedback
It is clear that by applying negative feedback, the output impedance of the amplifier
is decreased by a factor 1  Av M v . This is an added benefit of using negative voltage
feedback. With lower value of output impedance, the amplifier is much better suited
to drive low impedance loads.
Distortions:
Consider a large amplitude signal applied to a stage of an amplifier, so that the
operation of an active device (i.e., transistor) extend slightly beyond its range of
linear operation. As a result of this, the output signal is slightly distorted. Now if a
negative feedback is introduced to the amplifier stage, the voltage gain reduces. But
if the input signal is increased, by the same amount by which the gain is reduced, the
output signal amplitude remains the same (i.e., as it was without feedback). Now if
we measure the distortion in both cases, it will be found that distortion has reduced
due to feedback by a factor
(1 +  . A).
It may be noted that the input signal to the feedback amplifier may be the actual
signal available from an external source or it may be an output of an amplifier
preceding the feedback stage. To increase the input of the feedback amplifier by a
factor (1+  .A ), we can either increase the nominal gain of the pre-amplifying
stages or add a new stage. It will be interesting to know that the full benefit of the
feedback amplifier in reducing distortion, can be obtained. His can be done if the
pre-amplifying stages do not introduce any additional distortion because of the
increased output.
2.4 CURRENT AND VOLTAGE FEEDBACK CIRCUITS
Voltage and current can be feedback to the input either in series to the parallel. In
the feedback connections types, the term ―voltage‖ refers to connecting the output
voltage as input to the feedback network. The term ―current‖ refers to tapping off
some output current through the feedback network. The term ―series‖ refers to
connecting the feedback signal in series with the input signal voltage, and the term
―shunt‖ refers to connecting the feedback signal in shunt (parallel) with an input
current source.
38
It has been observed that the series feedback connections tend to increase the input
resistance, while the shunt feedback connections tend to decrease the input
resistance. Moreover, the voltage feedback will tend to decrease the output
resistance, while the current feedback tends to increase the output resistance.
(i) Voltage- series Feedback Connections
It is also called a shunt-derived series-fed feedback connection. In this, a fraction of
the output voltage is applied in series with the input voltage through the feedback
network. However, the input to the feedback network is in parallel with output of the
amplifier.
It can be shown easily that the voltage- series feedback connection increase the input
resistance and decreases the output resistance of the feedback amplifier.
(ii)Voltage- Shunt Feedback Connection
It is also called a shunt-derived shunt-fed feedback connection. In this, a fraction of
the output voltage is applied in parallel with the input voltage through the feedback
network.
It can be shown easily that the voltage- shunt feedback connection decreases both
input and output resistances of the feedback amplifier by a factor equal to (1+  .A).
(iii) Current-series Feedback Connection
It is also called a series-derived series-fed feedback connection. In this, a fraction of
the output current is converted into a proportional voltage by the feedback network
and then applied in series with the input.
It can be shown easily that the current- series feedback connection increases both the
input resistance and output resistance of the feedback amplifier by a factor equal to
(1+  .A).
(iv) Current-Shunt Feedback Connection
39
It is also called a series-derived shunt-fed feedback connection. In this, a fraction of
the output current is converted into a proportional voltage by the feedback network
and then applied in parallel with the input voltage.
It can be shown easily that the current- series feedback connection decreases the
input resistance but increases the output resistance of the feedback amplifier by a
factor equal to (1+  .A).
2.5 EMITTER FOLLOWER
It is a negative current feedback circuit. The emitter follower is a current amplifier
that has no voltage gain. Its most important characteristic is that it has high input
impedance and low output impedance this makes it an ideal circuit for impedance
matching.
Fig. shows the circuit of an emitter follower. As you can see, it differs from the
circuitry of a conventional CE amplifier by the absence of collector load and emitter
by pass capacitor. The emitter resistance RE itself acts as the load and a.c. output
voltage (Vout) is taken across RE the biasing is generally provided by voltage-divider
method or by base resistor method. The following points are worth noting about the
emitter follower:
(i)There is neither collector resistor in the circuit nor there is emitter by pass
capacitor. These are the two circuit recognition features of the emitter follower.
(ii)Since the collector is at ac ground, this circuit is also known as common collector
(CC) amplifier.
40
Operation.
The input voltage is applied between base and emitter and the resulting a.c. emitter
current produced an output voltage ie RE across the emitter resistance. This voltage
opposes the input voltage, thus providing negative feedback. Clearly it is a negative
current feedback circuit since the output voltage follows the input voltage.
Characteristics. The major characteristics of the emitter follower are:
(i)No voltage gain. In fact, the voltage gain of an emitter follower is close to 1.
(ii)Relatively high current gain and power gain.
(iii)High input impedance and low output impedance.
(iv)Input and output ac voltages are in phase.
EXERCISE- 2.1
1) What do you understand by feedback?
2) Discuss the principles of negative voltage feedback?
3) What is a feedback circuit? Explain how it provides feedback in amplifiers?
4) Describe the action of emitter follower with a neat diagram.
5) Why is voltage feedback employed in high gain amplifiers?
2.6 POSITIVE FEEDBACK AMPLIFIER-OSCILLATOR
A transistor amplifier with proper positive feedback can act as an oscillator i.e. it can
generate oscillations without any external signal source. Fig. shows a transistor
41
amplifier with positive feedback. Remember that a positive feedback amplifier is
one that produces a feedback voltage (Vf) that is in phase with the original input
signal. As you can see this condition is net in the circuit shown in fig. a phase shift
of 1800 is produced by the amplifier and a further phase shift of input i.e. feedback
voltage is in phase with the input signal.
(i)
We note that the circuit shown in is producing oscillations in the output.
However, this circuit has an input signal. This is inconsistent with our
definition of an oscillator i.e. an oscillator is a circuit that produces
oscillations without any external signal source.
(ii)
When we open the switch S of Fig. we get the circuit shown in Fig. this
means the input signal (Vin) is removed. However, Vf (which is in phase with
the original signal) is still applied to the input signal. The amplifier will be
amplified and sent to the output. The feedback network sends a portion of the
output back to the input. Therefore the amplifier receives another input cycle
and another output cycle is produced this process will continue so long as the
amplifier is turned on. Therefore, the amplifier will produces sinusoidal
output with no external no external signal source.
The following points may be noted carefully:
a) A transistor amplifier with proper positive feedback will work as an oscillator.
b) The circuit needs only a quick trigger signal to start the oscillations. Once the
oscillations have started, no external signal source is needed.
42
c) In order to get continuous undraped output from the circuit, the following
condition must be met.
My A y
where
=
1
Ay
= Voltage gain of amplifier without
feedback
My = Feedback fraction.
This relation is called Barkhausen Criterion.
2.7 CIRCUITS AND WORKING OF HARTLEY OSCILLATOR
The Hartley oscillator is similar to Colpitt's Oscillator with minor modifications.
Instead of using Tapped capacitors, two inductors L1 and L2 are placed across a
common capacitor C and the centre of the inductors is tapped as shown in Fig.
43
The tank circuit is made up of L1, L2 and C. The frequency of oscillations is
determined by the values of L1, L2 and C and is given by:
Where
LT = L1 + L2 + 2M
Here
M = mutual inductance between L1 and L2.
Note that L1 - L2 - C is also the feedback network that produces a phase shift of 1800
Circuit Operation.
When the circuit is turned on, the capacitor is charged. when this capacitor is fully
charged, it discharges through coils L1 and L2 setting up oscillations of frequency
determined by exp (i) the output voltage of the amplifier appears across L1 and
feedback voltage across L2. The voltage across L2 is 1800 out of phase with the
voltage developed across L1 (Vout) as shown in Fig. 16.14 it is easy to see that
voltage feedback (i.e., voltage across L2) to the transistor provides positive
feedback. A phase shift of 1800 is produced by L1 - L2 voltage divider. In this way,
feedback is properly phased to produce continuous un-damped oscillations.
Feedback fraction mv :In Hartley oscillator, the feedback voltage is across L2 and
output voltage is across L1.
Feedback fraction mv =
mv =
L2
L1
2.8 COLPITT’S OSCILLATOR
44
Fig. shows a Colpitt’s oscillator. It uses two capacitors and placed across a common
inductor L and the centre of the two capacitors is tapped. The tank circuit is made up
of C1, C2 and L and is given by;
Where
f 
1
2 LCT
CT 
C1C2
C1  C2
Note that C1, - C2 –L is also the feedback circuit that produces a phase shift of 1800
Circuit Operation.
When the circuit is turned on, the capacitors C1 and C2 are charged. the capacitors
discharge through L, setting up oscillations of frequency determined by exp (i) . The
output voltage of the amplifier appears across C1 and feedback voltage is developed
across C2. The Voltage across is 1800 out of phase with the voltage developed across
C1 (Vout) as shown in Fig. It is easy to see that voltage feedback (voltage across C2 )
to the transistor provides positive feedback. A phase shift of 1800 is produced by the
transistor and a further phase shift of 1800 is produced by C1 - C2 voltage divider. in
this way, feedback is properly phased to produce continuous encamped oscillation.
45
Feedback fraction my. The amount of Feedback voltage in Colpitt's oscillator
depends upon feedback fraction mv of the circuit. For this Circuit,
Feedback fraction my =
C1
C2
2.10 PHASE SHIFT OSCILLATOR
The circuit of a phase shift oscillator of a conventional single transistor amplifier
and a RC phase shift network. The phase shift network consists of three sections R 1,
C1, R2, C2 and R3 C3 At some particular frequency F0, the phase shift in each RC
section in 600 so that the total phase shift produced by the RC network is 1800. The
frequency of oscillations is given by:
f0 
Where
1
2 RC 6
R1  R2  R3  R
C1  C2  C3  C
46
Circuit operation.
When the circuit is switched on, it produces oscillations of frequency determined.
The output E0 of the amplifier is feedback to RC feedback network. This network
produces a phase shift of 1800 and a voltage Ei appears at its output which is applied
to the transistor amplifier.
Obviously, the feedback fraction m = Ei / E0. The feedback phase is correct. A phase
shift of 1800 is produced by the transistor amplifier. A further phase shift of 1800 is
produced by the RC network. As a result, the phase shift around the entire loop is
3600.
Advantages:
(i)
It does not require transformers or inductors.
(ii) It can be used to produce very low frequencies.
(iii) The circuit provides good frequency stability
Disadvantages:
(i)It is difficult for the circuit to start oscillations as the feedback is generally small.
(ii)The circuit gives small output.
EXERCISE- 2.2
1) What is the need of an oscillator? Discuss the advantages of oscillators?
2) Explain phase shift oscillator in detail.
3) With a neat diagram, explain the action of Hartley and Colpitt’s oscillator.
4) Why is amplifier circuit necessary in an oscillator?
2.11 UJT AND ITS CHARACTERISTICS
47
A uni-junction transistor (abbreviated as UJT) is a three terminal semiconductor
switching device. This device has a unique characteristic that when it is triggered,
the emitter current increases regenerative until it is limited by emitter power supply.
Due to this characteristic, the uni-junction transistor can be employed in a variety of
applications e.g. switching, pulse generator, saw-tooth generator etc.
Construction.
Fig. shows the basic structure of a uni-junction transistor. It consists of an n-type
silicon
bar with an electrical connection on each end. The leads to these connections are
called base-leads base-one
B1 and base two B2. Part way along the bar between the two bases, nearer to B2 than
B1 a p-n Junction is formed between a p -type emitter and the bar. The lead to this
junction is called the emitter lead E. Fig. shows the symbol of uni-junction
transistor. Note that emitter is shown closer to B2 than B1. The following points are
worth noting:
(i)Since the device has one p-n junction and three leads, it is commonly called a unijunction transistor (uni means single).
(ii)With only one p-n-junction, the device is really a form of diode. Because the two
base terminals are taken from one section of the diode, this device is also called
double-based diode.
48
(iii)The emitter is heavily doped having many holes. The n region, however, is
lightly doped. For this reason, the resistance between the base terminals is very high
(5 to 10 K  ) when emitter head is open.
Characteristics of UJT
The characteristics of UJT are:
(i) In cut- off region, VE increases from zero, slight leakage current flows from
terminal to the emitter. This current is due to minority carriers in reverse biased
diodes.
(ii) Above a certain value of VE forward IE begins to flow, increasing until the peak
voltage VP and current IP are reached at point P.
(iii) After the peak point P, an attempt to increase VE is followed by a sudden
increase in emitter current IE with a corresponding decrease in VE. This is a negative
resistance portion of the curve because with increase in IE , VE decreases. The
device, therefore, has a negative resistance region which is stable enough to be used
with a great deal of reliability in many areas, e.g. trigger circuits, saw-tooth
generators, timing circuits.
49
(iv) The negative portion of the curve lasts until the valley point V is reached with
valley point voltage VV and valley point current IV. After the valley point, the device
is driven to saturation.
2.11 UJT AS RELAXATION OSCILLATOR
The applications of UJT transistors are:
(i) UJT relaxation oscillator
(ii) Over- voltage detector
Fig. shows UJT relaxation oscillator where the discharging of a capacitor through
UJT can develop a saw tooth output. When battery VBB is turned on, the capacitor C
charges through resistor R1. During the charging period, the voltage across the
capacitor rises in an exponential manner until it reaches the peak – point voltage. At
this instant of time, the UJT switches to its low resistance conducting mode and the
capacitor is discharged between E and B1. As the capacitor voltage flays back to
zero, the emitter ceases to conduct and the UJT is switched off. The Next cycle then
begins, allowing the capacitor C to charge again. The frequency of the output sawtooth wave can be varied by changing the value of R1 since this controls the time
constant R1 C of the capacitor charging circuit.
The time period and hence the frequency of the saw-tooth wave can be calculated as
follows. Assuming that the capacitor is initially uncharged, the voltage, VC across
the capacitor prior to break down is given by:
=
(1 - e-t/R 1C)
R1C
=
Charging time constant of resistor capacitor circuit
t
=
time from the commencement of waveform.
where VC
50
The discharge of the capacitor occurs when Vc is equal to the peak point voltage
 VBB i.e.
VBB  VBB (1  e 
1t / R1C
)
OR
  1 e 
OR
e
OR
t  R1 C log e
1t / R1C
1t / R1C
Time period , t
 1 
1
1 
 2.3R1 C log10
Frequency of saw tooth wave,
f 
1
1 
1
Hz
t in sec onds
EXERCISE- 2.3
1) Explain the construction and working of UJT.
2) Describe some characteristics of UJT.
3) Write a brief note on UJT relaxation oscillator.
2.12 TRANSISTOR AS A SWITCH - ASTABLE MULTI-VIBRATOR
A multi-vibrator which generates square waves of its own, i.e. without any external
triggering pulse is known as an astable or free running multi-vibrator.
The astable multi-vibrator has no stable state. It switches back and forth from one
state to the other, remaining in each state for a time determined by circuit constants.
In other words, as first one transistor conducts (i.e. ON state) and the other stays in
the OFF state for some time. After this period of time, the second transistor is
automatically turned ON and the first transistor is turned OFF. Thus the
51
multivibrator will generate a square wave output of its own. The width of the square
wave and its frequency will depend upon the circuit constants.
Circuit details.
Fig. shows the circuit of a typical transistor astable multi-vibrator using two
identical transistors Q1 and Q2. The circuit essentially consists of two symmetrical
CE amplifier stages, each providing a feedback to the other. Thus collector load of
the two stages are equal i.e. R1 = R4 and the biasing resistors are also equal i.e. R2 =
R3. The output of transistor Q1 is coupled to the input of Q2 through C1 while the
output of Q2 is fed to the input of Q1 through C2. The square wave output can be
taken from Q1or Q2.
Operation
When VCC is applied, collector currents start flowing in Q1 and Q2. In addition the
coupling capacitors C1 and C2 also start charging up. As the characteristics of no two
transistors (i.e.
VBB )
are exactly alike, therefore, one transistor say Q1, will
52
conduct more rapidly than the other. The rising collector current in Q1 drives its
collector more and more positive. The increasing positive output at point A is
applied to the base of transistor Q2 through C1. This establishes a reverse bias on Q2
and its collector current start decreasing. As the collector of Q2 is connected to the
base of Q1 through C2 therefore, base of Q1 becomes more negative i.e. Q1 is more
forward biased. This further increases the collector current in Q1 and causes a further
decrease of collector current in Q2. This series of actions is repeated until the circuit
drives Q1 to saturation and Q2 to cut off. These actions occur very rapidly and may
be considered practically instantaneous. The output of Q1 (ON state) is
approximately zero and that of Q2 (OFF sate) is approximately VCC. This is shown
by ab in Fig.
When Q1 is at saturation and Q2 is cut off, the full voltage VCC appears across R1 and
voltage across R4 will be zero. The charges developed across C1 and C2 are
sufficient to maintain the saturation and cut off conditions at Q1 and Q2 respectively.
This condition is represented by time interval bc in Fig. However, the capacitors will
not retain the charges indefinitely but will discharge through their respective
circuits. As C1 discharges, the base bias at Q2 becomes less positive and at a time
determined by R2 and C1 forward bias is re-established at Q2. This causes the
collector current to start in Q2. The increasing positive potential at collector of Q2 is
applied to the base of Q1 through the capacitor C2. Hence the base of Q1 sends a
negative voltage to the base of Q2 through C1 thereby causing further increase in the
collector current of Q2 with this set of actions taking place, Q2 is quickly driven to
saturation and Q1 to cut off. This condition is represented by cd in Fig. The period of
time during which Q2 remains at saturation and Q1 at cut off is determined by C2 and
R3 .
On or Off time.
The time for which either transistor remains ON or OFF is given by :
ON time for Q1 (or OFF time for Q2) is
T1 = 0.694R2C1
OFF time for Q1 (or ON time for Q2)
53
T2 = 0.694R3C2
Total time period of the square wave is
T = T1 + T2 = 0.694 (R2C1+R3C2)
As R2 = R3 = R and C1 = C2 = c,
T = 0.694 (RC + RC) = 1.4 RC seconds
Frequency of the square wave is
f 
1 0.7

Hz
T RC
It may be noted that in these expressions, R is in ohms and C in farad.
2.13 MONOSTABLE MULTIVIBRATOR
A multi-vibrator in which one transistor is always conducting (i.e. in the ON state)
and the other is non-conducting (i.e. in the OFF state) is called a mono-stable multivibrator.
A mono-stable multi-vibrator has only one state stable. In other words, if one
transistor is conducting and the other is non-conducting, the circuit will remain in
this position. It is only with the application of external pulse that the circuit will
interchange the states. However, after a certain time the circuit will automatically
switch back to the original stable state and remains there until another pulse is
applied. Thus a mono-stable multi-vibrator cannot generate square waves of its own
like an astable multi-vibrator. Only external pulse will cause it to generate the square
wave.
Circuit Details. Fig. shows the circuit of a transistor mono-stable multi-vibrator. It
consists of two similar transistors Q1 and Q2 with equal collector loads i.e. R1 – R4.
The values of VBB and R5 are such as to reverse bias Q1 and keep it at cut off. The
pulse is given through C2 to obtain the square wave. Again output can be taken from
Q1 or Q2.
54
Operation.
With the circuit arrangement shown, Q1 is at cut off and Q2 is at saturation. This is
the stable state for the circuit and it will continue to stay in this state until a
triggering pulse is applied at C2. When a negative pulse of short duration and
sufficient magnitude is applied to the base of Q1 through C2 the transistor Q1 starts
conducting and positive potential is established at its collector. The positive
potential at the collector of Q1 is coupled to the base of Q2 through capacitor C1.
This decreases the forward bias on Q2 and its collector current decreases. The
increasing negative potential on the collector of Q2 is applied to the base of Q1
through R3. This further increases the forward bias on Q1 and hence its collector
current. With this set of actions taking place, Q1 is quickly driven to saturation and
Q2 cut off.
With Q1 at saturation and Q2 at cut off, the circuit will come back to the original
stage (i.e. Q2 at saturation and Q1 at cut off) after some time as explained in the
following discussion. The capacitor C1 (Charged to approximately VCC) discharges
through the path R2 VCC Q1. As C1 discharges it sends a voltage to the base of Q2 to
make it less positive. This goes on until a point is reached when forward bias is reestablished on Q2 and collector starts to flow in Q2. The step by step events already
explained occur and Q2 is quickly driven to saturation and Q1 to cut off. This is the
stable state for the circuit and it remains in this condition until another pulse causes
the circuit to switch over the states.
55
2.14 BISTABLE MULTIVIBRATOR
A multi-vibrator which has both the states stable is called a bi-stable multi-vibrator.
The bi-stable multi-vibrator has both the states stable. It will remain in whichever
state it happens to be until a trigger pulse causes it to switch to the other state. For
instance, suppose at any particular instant, transistor Q1 is conducting and transistor
Q2 is at cut off. If left to itself, the bi-stable multi-vibrator will stay in this position
forever. However, if an external pulse is applied to the circuit in such a way that Q 1
is cut off and Q2 is turned on, the circuit will stay in the new position. Another
trigger pulse is then required to switch the circuit back to its original state.
Circuit details.
The circuit of a typical transistor bi-stable multi-vibrator consists of two identical
CE amplifier stages with output of one fed to the input of the other. The feedback is
coupled through resistors (R2R3) shunted by capacitors C1 and C2. The main purpose
of capacitors C1 and C2 is to improve the switching characteristics of the circuit by
passing the high frequency components of the square wave. This allows fast rise and
fall time and hence distortion less square wave output. The output can be taken
across either transistor.
Operation.
When VCC is applied, one transistor will start conducting slightly ahead of the other
due to some difference in the characteristics of the transistors. This will drive one
transistor to saturation and the other to cut off in a manner described for the circuit
will stay in this condition. In order to switch the multi-vibrator to its other state, a
trigger pulse must be applied. A negative pulse applied to the base of Q1 through C3
will cut it off or a positive pulse applied to the base of Q2 through C4 will cause it to
conduct.
Suppose a negative pulse of sufficient magnitude is applied to the base of Q1
through C3. This will reduce the forward bias on Q1 and cause a decrease in its
collector current and an increase in collector voltage. The rising collector voltage is
coupled to the base of Q2 where it forward biases the base-emitter junction of Q2.
56
This will cause an increase in its collector current and decrease in collector voltage.
The decreasing collector voltage is applied to the base of Q1 where it further reverse
biases the base – emitter junction of Q1 to cut off. The circuit will now remain stable
in this state until a negative trigger pulse at Q2 (or a positive trigger pulse at Q1)
changes this state.
EXERCISE- 2.4
1) What is a multi-vibrator? Explain the principle on which it works?
2) With a neat sketch, explain the working of (i) a-stable multi- vibrator (ii) monostable multi-vibrator (iii) bi-stable multi- vibrator.
3) What is the basic difference between the three types of multi- vibrators?
2.15 UNIT SUMMARY
(i) The process of injecting a fraction of output energy of some device back to the
input is known as feedback in amplifiers.
(ii) When the feedback energy (voltage or current) is out of phase with the input
signal and thus opposes it, it is called negative feedback.
(iii)The advantages of negative feedback are: highly stabilized gain, reduction in
non-linear distortion, increased bandwidth i.e., improved frequency response,
increased circuit stability, less amplitude distortion etc.
(iv)The emitter follower is a current amplifier that has no voltage gain.
(v)A transistor amplifier with proper positive feedback can act as an oscillator i.e. it
can generate oscillations without any external signal source.
(vi)A uni-junction transistor (abbreviated as UJT) is a three terminal semiconductor
switching device. This device has a unique characteristic that when it is triggered,
the emitter current increases regenerative until it is limited by emitter power supply.
(vii)A multi-vibrator which generates square waves of its own i.e. without any
external triggering pulse is known as an actable or free running multi-vibrator.
57
(viii)A multi-vibrator which has both the states stable is called a bi-stable multivibrator.
2.16 REFERENCES
1)Electronic Devices and Circuits by Millman and Halkias, S. Chand & Company
Ltd.
2)Electronic Devices and Circuits an Introduction by Mottershed
3)Transistor Physics by Sarkar
4)Nashelsky – Electronic Devices & Circuit Theory (PHI) by Robert Boylested and
Louis
5)Principles of Electronics by V.K. Mehta, S. Chand & Company Ltd.
SOLUTION
EXERCISE- 2.1
1) Refer to article 2.0, 2) Refer to article 2.2, 3) Refer to article 2.2, 4) Refer to
article 2.5, 5) Refer to article 2.4
EXERCISE- 2.2
1) Refer to article 2.6, 2) Refer to article 2.10, 3) Refer to article 2.7 & 2.8, 4) Refer
to article 2.3
EXERCISE- 2.3
1) Refer to article 2.11, 2) Refer to article 2.11, 3) Refer to article 2.11
EXERCISE- 2.4
1) Refer to article 2.12, 2) Refer to article 2.12, 2.13& 2.14, 3) Refer to article
2.12,2.13 &2.14
58
BLOCK-II
M. Sc. Previous
PAPER-IV
SOLID STATE ELECTRONICS
UNIT: III
OPERATIONAL AMPLIFIER
Structure:
3.0
Introduction
3.1
Objectives
3.2 Differential amplifier circuits and working of operational amplifier and
Circuit Symbol of an OP-AMP
3.3
Inverting and non-inverting OP-AMP amplifiers
3.4
Use of 741 IC as adder
3.5
Subtractor
3.6
Differentiator
3.7
Integrator
3.8
OP-AMP as constant current source
3.9
Comparator
3.10 Square wave generator
3.11 Triangular wave generator
3.12 Unit Summary
3.13 References
UNIT:IV
VOLTAGE MULTIPLIER CIRCUITS
Structure:
4.0
Introduction
59
4.1
Objectives
4.2
Voltage multipliers circuits
4.3
Wave shaping circuits
4.4
Clipping Circuits
4.5
Clamping Circuits
4.6
Differentiating and Integrating circuits
4.7 Voltage regulated power supply and Regulation Sensitivity and Stability
Factors
4.8
Unit Summary
4.9
References
60
BLOCK-II
M. Sc. Previous
PAPER-IV
SOLID STATE ELECTRONICS
INTRODUCTION
The operational amplifier is a direct-coupled, high gain, negative feedback
amplifier. They are made with different internal configurations in linear ICs.
The operational amplifier is a complete amplifier. Furthermore, it is designed in
such a way that external components like resistors, capacitors, etc. can be connected
to its terminals. So the external characteristics can be changed. Due to this reason,
the amplifier may fit to a particular application. The widespread applications of
operational amplifiers are due to the use of negative feedback. We know that the
performance of an amplifier with feedback solely controlled and determined by
feedback elements only and is independent of the elements of the amplifier. As the
feedback elements are generally passive hence the operation can be made very stable
and predictable in performance.
A voltage multiplier is an electrical circuit that converts AC electrical power from a
lower voltage to a higher DC voltage by means of capacitors and diodes combined
into a network.
61
BLOCK-II
UNIT: III
OPERATIONAL AMPLIFIER
Structure:
3.0
Introduction
3.1
Objectives
3.2 Differential amplifier circuits and working of operational amplifier and
Circuit Symbol of an OP-AMP
3.3
Inverting and non-inverting OP-AMP amplifiers
3.4
Use of 741 IC as adder
3.5
Subtractor
3.6
Differentiator
3.7
Integrator
3.8
OP-AMP as constant current source
3.9
Comparator
3.10 Square wave generator
3.11 Triangular wave generator
3.12 Unit Summary
3.13 References
62
BLOCK-II
UNIT: III
OPERATIONAL AMPLIFIER
3.0 INTRODUCTION
The operational amplifier is a direct-coupled, high gain, negative feedback
amplifier. They are made with different internal configurations in linear ICs.
The operational amplifier is a complete amplifier. Furthermore, it is designed in
such a way that external components like resistors, capacitors, etc. can be connected
to its terminals. So the external characteristics can be changed. Due to this reason,
the amplifier may fit to a particular application. The widespread applications of
operational amplifiers are due to the use of negative feedback. We know that the
performance of an amplifier with feedback solely controlled and determined by
feedback elements only and is independent of the elements of the amplifier. As the
feedback elements are generally passive hence the operation can be made very stable
and predictable in performance.
3.1 OBJECTIVES
The term operational amplifier was originally used for the d.c. amplifiers which
perform mathematical operations as summation, subtraction, integration and
differentiation in analog computers. Now-a-days, the operational amplifiers are put
to a variety of other uses e.g. voltage regulators, in instrumentation and control
63
system, phase shift and oscillator circuits, pulse generators, square wave generator,
comparator, analog to digital and digital to analog, converters, scale changer, analog
computer and in many others. Although the scope of operational amplifier is much
wider even the name OP-AMP continues.
Operational amplifiers are used as comparator, pulse generator, square wave
generator, Schmitt trigger etc. These days OP-AMP use integrated circuit
technology and is referred to as basic linear or analogue integrated circuit. They
possess all the merits of monolithic integrated circuits, e.g., small size, low cost,
high reliability, low offset voltage and current and temperature tracking properties.
3.2 DIFFERENTIAL AMPLIFIER CIRCUITS AND WORKING OF
OPERATIONAL AMPLIFIER AND CIRCUIT SYMBOL OF AN OP-AMP
Standard triangular symbol is generally used for an OP-AMP. The early operational
amplifier had only one input and one output terminal. The output was always
inverted with respect to the input. The OP-AMPs now available are usually of
differential type with two input terminals and a single output
terminal. It is understood that all voltages are with respect to ground and hence the
ground lines is not usually shown.
The input terminals are marked with minus (-) and plus (+) signs. Terminals a
(marked-) is called as inverting input terminal. The negative sign indicates that a
signal applied at the terminal will appear amplified but in phase inverted (opposite
polarity) at terminal c. Similarly, the terminal b (marked +) is called as noninverting
input terminal. Here the positive sign indicates that a signal applied at the terminal b
will appear amplified but in phase (same polarity) at the terminal c. It should be
64
clearly understood that minus and plus signs do not mean that the voltages V1 and
V2 are negative and positive respectively. Moreover, it does not mean that the
negative voltage is applied at terminal and positive voltage is applied at terminal b.
The output voltage is directly proportional to the input voltage which is difference
V1 and V2 thus VoV1. The constant of proportionality is the gain of the amplifier
which is denoted by A. When no resistor or capacitor is connected from output
terminal to any one of the input terminals (No feedback), the OP-AMP is said to be
in open-loop condition. Here the word open signifies that feedback path or loop is
open.
CHARACTERISTICS OF AN IDEAL OP-AMP
Ideal OP-AMP has the following characteristics:
(i)An infinite voltage gain.
(ii)An infinite bandwidth.
(iii)The resistance measured between inverting and non-inverting terminals is input
resistance. Infinite input resistance mean that input current is zero i.e., the amplifier
is a voltage controlled device.
(iv)Zero output resistance. Zero output resistance means that Vo is independent of
the load resistance connected across the output.
(v)Perfect balance. The output is zero (Vo=0) when equal voltages (V1 = V2)
are applied at the two input terminals.
A practical OP-AMP is, however, non-ideal.
OPERATIONAL AMPLIFIER STAGES
Fig. shows the block diagram of a typical OP-AMP.
65
It consists of two differential amplifiers followed by level shifter and an output
stage.
Input stage. The input stage is a dual-input, balanced output differential amplifier.
The function of differential amplifier is to provide most of the voltage gain to OPAMP. It also provides high resistance to OP-AMP.
Intermediate stage. The intermediate stage is a dual input, unbalanced output
differential amplifier. This is driven by the output of first stage and is used to
provide some additional gain. There is a direct coupling between the first two stages.
So the d.c. level at the output of intermediate stage is well above the ground level.
This is undesirable.
Level shifting stage. The level shifter (level translator) circuit is used after
intermediate stage. Usually this is an emitter follower using constant current source.
The function of level shifter is to shift the d.c. level at the output of intermediate
stage downwards to zero volt with respect to ground.
Output stage. The output stage is generally push-pull or complementary symmetry
push-pull amplifier. Its function is to increase large output voltage swing capability,
large output current swing capability of the amplifier and to provide low output
resistance.
EQUIVALENT CIRCUIT OF OP-AMP
The equivalent circuit of an OP-AMP is shown. V1 is the voltage at the inverting
terminal and V2 is the voltage at the non-inverting terminal. Vid is the difference of
66
two input voltages i.e. (V2-V1). Ri is the input resistance which appears between the
inverting and non-inverting input terminals.
Ro is the output resistance which is Thevenin equivalent resistance looking back into
the output terminal of OP-AMP. The voltage source A Vid is an equivalent Thevenin
voltage source. The output voltage is directly proportional to the algebraic difference
between the two input voltages.
OPERATIONAL AMPLIFIER PARAMETERS
Few commonly used electrical parameters of OP-AMP are defined as follows
(1) Input offset voltage. When the input is OV, the output of OP-AMP should be
zero. But in actual operation, there is some offset voltage at the output. The input
offset voltage is defined as the voltage that must be applied between the two input
terminals of an OP-AMP to nullify the output. Typically it lies in the range. 1 mV to
5mV. The smaller the value of input offset voltage, the better is the input terminal
matched.
(2) Input offset current. An output offset voltage will also result due to any
difference in dc bias current at both inputs. The reason is that the two input
transistors are never exactly matched. Each has a slightly different current. The input
offset current is the difference between the two input currents. The input offset
current typically lies in the range 20nA to 60nA. The smaller the input offset
current, the better is the OP-AMP's performance.
(3) Input bias current. The input bias current is the average of the currents that
flow into the inverting and non-inverting input terminals of an OP-AMP. The
smaller the input bias current, the smaller is the possible unbalance.
67
(4) Input offset voltage drift. It is the ratio of the change of input offset voltage to
the change in temperature.
(5) Input offset current drift. It is the ratio of the change of input offset current to
the change in temperature.
(6) Input resistance. This is the differential input resistance that can be measured at
either of the input terminal with the other terminal connected to ground. The OPAMP having bipolar input stage has an input resistance in the range of 100K  to
1M  . Usually, the voltage gain is large enough. Hence, the input resistance has
little effect on the circuit performance.
(7) Output resistance. It is the resistance measured between the output terminal of
the OP-AMP and the ground. This is of the order of 40 to 100  . This resistance
does not significantly affect the closed-loop performance of the OP-AMP.
(8) Slew rate (SR). It is defined as the maximum rate of change of output voltage
per unit of time and is expressed in volts per microseconds, i.e.,
Slew rate indicates how rapidly the output of OP-AMP can change in response to
change in input frequency.
EXERCISE- 3.1
1) What is an OP-AMP?
2) What are the uses of an OP- AMP? Also give equivalent circuits of an OP-AMP?
3) What are the characteristics of an OP-AMP?
4) Define the terms:
(i) input off- set voltage and current
(ii) slew rate.
3.3 INVERTING AND NON-INVERTING OP-AMP AMPLIFIERS
68
(a) Differential amplifier.
The open loop differential amplifier is shown in fig. Here V1 and V2 are signals
applied to inverting and non- inverting terminals respectively. V1 and V2 may be
either a.c. or d.c., as OP-AMP can amplify both types of signals. Here source
resistances are not considered because they are negligibly small in comparison with
the very high input resistance of OP-AMP. As the OP-AMP amplifies the difference
between two input signals and hence this configuration is called as differential
amplifier. The output voltage is given by
Vo = AVid = A (V2-V1)
where A is large signal voltage gain or open-loop gain.
The common mode rejection ratio is defined as |Ad /Ac | where Ad = ½ (A1 – A2) and
Ac = (A1 + A2).
(b) Inverting amplifier
In this configuration, the input signal is applied to the inverting input terminal as
shown in fig. The non-inverting terminals is grounded i.e., V1 = 0. The output is
given by
69
Vo = AVid = A (V2-V1)
= -AV1
( V2 = 0)
The negative sign indicates that the output voltage is out of phase with respect to
input i.e., output voltage is 1080 out of phase with respect to input. Thus in inverting
amplifier, the input is amplified by gain. A with change is polarity. Hence, the name
is given 'inverting amplifier'.
(c)Non-Inverting amplifier
In this configuration, the input signal is applied to the non-inverting input terminal
of OP-AMP. The inverting input terminal is grounded.
The output voltage is given by
Vo = AVid
= A(V2-V1)
= AV2
( V1 = 0)
This shows that output voltage is gain A times the input voltage V2 and is in phase
with the input. As in non-inverting amplifier, the input signals is amplified by gain
A without change in polarity and hence named as 'non-inverting amplifier'.
INVERTING OP-AMP (NEGATIVE SCALER)
Fig. shows the basic inverting amplifier with an input resistance R1 and a feedback
resistor Rf. In this mode of operation, the positive input terminal of the amplifier is
grounded and the input signal is applied to the negative input terminal.
70
Note that V1 may be a dc voltage or an ac signal within the bandwidth of the
amplifier. It is obvious from the figure that the feedback currents are algebraically
added at point G. So this point is called as summing point. When input voltage v1 is
applied at the input terminal, the point G attains some positive potential. Now there
exists a output voltage vo. Due to negative feedback, a fraction of the output voltage
with phase inverted is fed back to point G, although not connected to ground, but is
held virtually at ground potential irrespective of the magnitudes of the potentials v1
and vo. The voltage at point G will become exactly zero when negative feedback
voltage is exactly equal to positive voltage produced by v1.
Gain. The current i1 flowing through point G is given by
Similarly,
At point G,
The ratio of output voltage v0 and input voltage v1 is known as the gain of the
amplifier. Hence the gain of inverting amplifier is given by
71
Thus the voltage gain is equal to the ratio of feedback resistance Rf to the input
resistance R1. The negative signifies that output voltage is inverted with respect to
input voltage.
Input resistance. The input resistance of the whole amplifier is defined as the ratio
of voltage v1 to the input current.
Thus
Here Rin refers to the voltage amplifier and not to the OP-AMP which has an infinite
input impedance.
Negative scalar. Here we shall show that OP-AMP works as a negative scalar. We
denote the ratio of Rf/R1 by K1 a real constant. Now from eq.
vo = -Kv1
Eq. shows that the input voltage scale has been multiplied by a factor - K to give the
output voltage scale. Thus the circuit can act as scalar changer. In scalar changer, the
precision resistors are used to get the accurate value of scalar factor K.
Unity gain amplifier. The output of basic OP-AMP is given by
Rf
vo

v1
R1
If Rf = R1, then
Av 
vo
R
  1  1
v1
R1
So, the circuit provides a unity voltage gain with 1800 phase inversion.
NON-INVERTING AMPLIFIER (POSITIVE SCALER)
72
The circuit of non-inverting amplifier is shown in fig.
Here the input voltage v2 is applied to the no inverting terminal and hence the name
non-inverting amplifier. The potential of point G is also v2 since the gain of OPAMP is infinite. The polarity of vo is the same as that of v2. The voltage across R1 is
v2 and across Rf is (vo-v2).
Gain. The values of currents i1 and i2 are given as
i1 
v v
v2
and i2  o 2
R1
Rf
Applying Kirchhoff's first law at point G, we get
(-i1) + i2 = 0

v2 vo  v2

0
R1
Rf
or
1
vo v2 v2
1
 
 v2  
R R
R f R1 R f
f
 1
or
 R1  R f
vo
 v2 
 RR
Rf
 1 f
or
vo R1  R f  R f 

 1 

R2
R1
R1 

or
 R 
A  1  f 
R1 

73






So the gain is one plus the ratio of two resistances Rf and R1. Here the output voltage
is in phase with input voltage. This circuit offers a high input impedance and low
output impedance.
Voltage follower. It R1 is infinite, then Av = 1 i.e. vo = v2.
Thus the output voltage follows the input voltage i.e., OP-AMP circuit acts as the
voltage follower.
 R
Positive scalar. Here vo/v2 = 1   f
  R1

  K

vo = Kv2
So the amplifier acts as positive scalar.
The amplifier is used when we require an output which is equal to input multiplied
by a positive constant. As the circuit has high input impedance and low output
impedance, this is generally used as impedance matching device between high
impedance source and low impedance load.
EXERCISE- 3.2
1) Explain inverting and non- inverting amplifiers.
2) Define common mode rejection ratio.
3.4 USE OF 741 IC AS ADDER
The most useful of the OP-AMP circuits used in analog computers is the summing
amplifier circuit. Fig. shows a three input summing circuit. This circuit provides a
means of algebraically summing three-input voltages, each multiplied by a constant
gain factor. In the circuit G is a virtual ground and the output voltage is phase
inverted.
74
As G is virtual ground, the different currents are given by
i1 
v
v
v1
v
, i2  2 , i3  3 andi   o
R1
R2
R3
Rf
Applying Kirchhoff's current distribution law at point G, we get
i1 + i2 + i3 - i = 0
or
v1 v2 v3 vo
  
0
R1 R2 R3 R f
or
R
R 
R
v0    f v1  f v2  f v3 
R2
R3 
 R1
or
vo    K1v1  K2v2  K3v3 
If R1 = R2 = R3 = R and Rf/R = K, then
vo   K  v1  v2  v3  
Rf
R
v1  v2  v3 
Thus the output voltage is proportional to the algebraic sum of three input voltages.
Again if Rf =R, we have
vo   v1  v2  v3 
In this case, the output voltage vo is numerically equal to the algebraic sum of the
input voltages. Hence the name summing or adder amplifier.
If Rf = R/3, then
vo   1/ 3 v1  v2  v3 
In this case, the output is equal to the average of the three inputs.
75
3.5 SUBTRACTOR
Fig. shows the circuit of the subtractor. The function of the subtractor is to provide
an output which is equal to the difference of two input signals or proportional to the
difference of two input signals. Here one signal is applied at the inverting terminal
while the second signal is applied at the non-inverting terminal of an OP-AMP.
Let (vo) and (vo)2 be the output voltages produced by input voltages v1 and v2
respectively. Now
 vo 1  

 vo 2  1 

Rf
R1
v1
Rf 
Rf
v2
 v2 
R1 
R1
Since Rf >> R1 ,i.e., Rf / R1 >>1.
According to superposition theorem
vo   vo 1   vo 2
Above Eq. shows that output voltage is proportional to the difference of two input
voltages.
76
If Rf = R1, then from eq,we get
vo = (v2-v1)
Thus the output voltage is equal to the difference of two input voltages.
3.6 DIFFERENTIATOR
The function of the differentiator is to given an output voltage which is proportional
to the rate of change of the input voltage. The circuit of a differentiator (fig.) is the
same as that of an inverting OP-AMP except that the input resistance R1 is replaced
by a capacitor. When we feed linearly increasing the
voltage to the differentiator, we get a constant d.c. output. So it is an inverse
mathematical operation to that of an integrator.
Assuming that G is at ground potential, we can write for capacitor
v1 

q
, where q = charge on capacitor
C
dv1 1 dq i
dq

 wherei 
dt C dt C
dt
Again
Substituting the value of i from above eq.’s we get
vo  CR
dv1
dt
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This Eq. shows that the output voltage vo is equal to a constant -CR times the time
derivative of the input voltage V1.
3.7 INTEGRATOR
The circuit of integrator is shown in fig. This circuit produces an output voltage
which is proportional to the time integral of the input voltage. Due to this reason this
is known as integrator. The integrator is an inverting OP-AMP in which feedback
resistor Rf has been replaced by a capacitor C. Feedback through the capacitor forces
a virtual ground to exist at the inverting input terminal. Now the voltage across the
condenser is simply the output voltage vo.
The capacitive impedance Xc can be expressed as
Xc 
1
1

jC sC
Where s = j = Laplace notation.
i1 
v1
R1
and
i2 
vo
  sCvo
Xc
At point G,
i1  i2
From the figure,
78
Above Eq. can be rewritten in time domain as
vo (t ) 
1
v1 (t ) dt
R1C 
Above Eq. shows that the output is the integral of the input with an inversion and
scale multiplier of 1/RC. When a step voltage is applied at the input terminal, the
output voltage is a ramp or linearly changing voltage. Integrators are used in ramp or
sweep generators, in filters, analog computers etc.
3.8 OP-AMP AS CONSTANT CURRENT SOURCE
In any device, when the output current is proportional to the input signal voltage, the
device is termed as voltage to current converter. The circuit of voltage to current
converter is shown in fig. Here the resistance Rf is replaced by a load resistance RL.
The circuit is used in analog to digital converter.
Let the current flowing through RL be iL. Hence
iL 
v1
R1
Thus the current iL is independent of the load resistance RL and is proportional to the
input voltage v1.
Differentiating Circuit
79
A circuit in which output voltage is directly proportional to the derivative of the
input is known as a differentiating circuit.
Output 
d
(Input)
dt
A differentiating circuit is a simple RC series circuit with output taken across the
resistor R. The circuit is suitability designed so that output is proportional to the
derivative of the input. Thus if a d.c. or constant input is applied to such a circuit,
the output will be zero. It is because the derivative of a constant is zero.
Fig. shows a typical differentiating circuit. The output across R will be the
derivative of the input. It is important to note that merely using voltage across R
does not make the circuit a differentiator; it is also necessary to set the proper circuit
values. In order to achieve good differentiation, the following two conditions should
be satisfied:
(i)
The time constant RC of the circuit should be much smaller than the time
period of the input wave.
(ii)
The value of XC should be 10 or more times larger than R at the operating
frequency.
Fulfilled these conditions, the output across R in fig. will be the derivative of the
input. Let ei be the input alternating voltage and let i be the resulting
alternating current. The charge q on the capacitor at any instant is
q = Cec
80
dq d
d
  q    Cec 
dt dt
dt
Now
i
or
i C
d
 ec 
dt
Since the capacitive reactance is very much larger than R, the input voltage can be
considered equal to the capacitor voltage with negligible error i.e. ec = ei
iC

Output voltage,
d
 ei 
dt
eo= iR
 RC

d
 ei 
dt

d
 ei 
dt
( RCis cons tan t )
Output voltage 
d
(Input)
dt
Output waveforms. The output waveform from a differentiating circuit depends
upon the time constant and shape of the input wave. Three important cases will be
considered.
EXERCISE-3.3
1) Explain the following (i) adder (ii) subtractor (iii) differentiator (iv)integrator.
3.9 COMPARATOR
In electronics, a comparator is a device that compares two voltages or currents and
switches its output to indicate which is larger. It is used in Analog-to-digital
converter (ADCs). An operational amplifier (OP-AMP) has a well balanced
difference input and a very high gain. This parallels the characteristics of
81
comparators and can be substituted in applications with low-performance
requirements.
In theory, a standard OP-AMP operating in open-loop configuration (without
negative feedback) may be used as a low-performance comparator. When the noninverting input (V+) is at a higher voltage than the inverting input (V-), the high gain
of the OP-AMP causes the output to saturate at the highest positive voltage it can
output. When the non-inverting input (V+) drops below the inverting input (V-), the
output saturates at the most negative voltage it can output. The OP-AMP's output
voltage is limited by the supply voltage. An OP-AMP operating in a linear mode
with negative feedback, using a balanced, split-voltage power supply, (powered by ±
VS) its transfer function is typically written as: Vout = Ao(V1 − V2). However, this
equation may not be applicable to a comparator circuit which is non-linear and
operates open-loop (no negative feedback).
In practice, using an operational amplifier as a comparator presents several
disadvantages as compared to using a dedicated comparator: OP-AMPs are designed
to operate in the linear mode with negative feedback. Hence, an OP-AMP typically
has a lengthy recovery time from saturation. Almost all OP-AMPs have an internal
compensation capacitor which imposes slew rate limitations for high frequency
signals. Consequently an OP-AMP makes a sloppy comparator with propagation
delays that can be as slow as tens of microseconds.
1.Since OP-AMP do not have any internal hysteresis an external hysteresis network
is always necessary for slow moving input signals.
2.The quiescent current specification of an OP-AMP is valid only when the
feedback is active. Some OP-AMPs show an increased quiescent current when the
inputs are not equal.
3.A comparator is designed to produce well limited output voltages that easily
interface with digital logic. Compatibility with digital logic must be verified while
using an OP-AMP as a comparator.
4.Some multiple-section OP-AMP may exhibit extreme channel-channel interaction
when used as comparators.
5.Many OP-AMP have back to back diodes between their inputs. OP-AMP inputs
usually follow each other so this is fine. But comparator inputs are not usually the
same. The diodes can cause unexpected current through inputs.
3.10 SQUARE WAVE GENERATOR.
82
When the input fed to a differentiating circuit is a square wave, output will consist
of sharp narrow pulses as shown in Fig. During the OC part of input wave, its
amplitude changes abruptly and hence the differentiated wave will be a sharp narrow
pulse as shown in Fig. However, during the constant part CB of the input, the output
will be zero because the derivative of a constant is zero.
Let us look at the physical explanation of this behaviour of the circuit. Since time
constant RC of the circuit is very small w.r.t. time period of input wave and Xc >> R,
the capacitor will become fully charged during the early part of each half-cycle of
the input wave. During the remainder part of the half cycle, the output of the circuit
will be zero because the capacitor voltage (ec) neutralises the input voltage and there
can be no current flow through R. Thus we shall get sharp pulse at the output during
the start of each half-cycle of input wave while for the remainder part of the halfcycle of input wave, the output will be zero. In this way, a symmetrical output wave
with sharp positive and negative peaks is produced. Such pulses are used in many
ways in electronic circuits e.g. in television transmitters and receivers, in multi
vibrators to initiate action etc.
3.11 TRIANGULAR WAVE GENERATOR.
When the input fed to a differentiating circuit is a triangular wave, the output will
be a rectangular wave as shown in Fig. During the period OA of the input wave, its
amplitude changes at a constant rate and, therefore, the differentiated wave has a
constant value for each constant rate of change. During the period AB of the input
wave, the change is less abrupt so that the output will be a very narrow pulse of
83
rectangular form. Thus when a triangular wave is fed to a differentiating circuit, the
output consists of a succession of rectangular waves of equal or unequal depending
upon the shape of the input wave.
When input is a sine wave. A sine wave input becomes a cosine wave and a cosine
wave input becomes an inverted sine wave at the output.
(i)
The time constant RC of the circuit should be very large as compared to the
time period of the input wave.
(ii)
The value of R should be 10 or more times larger than XC.
Let ei be the input alternating voltage and let i be the resulting alternating current.
Since R is very large is compared to capacitive reactance XC of the capacitor, it is
reasonable to assume that voltage across R (i.e. eR) is equal to the input voltage i.e.
ei = eR
i
Now
eR ei

R R
The charge q on the capacitor at any instant is
q   i dt
Output voltage,
eo 
q  i dt

C
C
84
ei

 R dt
C
ei 

i  
R

=
1
ei dt
RC 
  ei dt
RC is cons tan t 

Output voltage   Input Voltage
EXERCISE- 3.4
1) What is a comparator?
2) Explain square wave generator & triangular wave generator.
3.12 UNIT SUMMARY
(i) The operational amplifier is a direct-coupled, high gain, negative feedback
amplifier. They are made with different internal configurations in linear ICs.
(ii) Slew rate (SR) is defined as the maximum rate of change of output voltage per
unit of time and is expressed in volts per microseconds, i.e.,
(iii) Inverting Operational Amplifier works as a negative scalar.
(iv) A circuit in which output voltage is directly proportional to the derivative of the
input is known as a differentiating circuit.
(v)A comparator is a device that compares two voltages or currents and switches its
output to indicate which is larger. It is used in Analog-to-digital converter.
3.13 REFERENCES
85
1)Operational Amplifiers by Clayton
2)Electronic Devices and Circuits by Millman and Halkias (S. Chand & Company
Ltd.)
3)Electronic Devices and Circuits an Introduction by Mottershed
4)Transistor Physics by Sarkar
5)Electronic Devices and Circuits by Sanjeev Gupta (Dhanpat Rai Publications)
6)A Textbook of Electronic Devices and Circuits by R.S. Sedha (S. Chand &
Company Ltd.)
SOLUTION
EXERCISE- 3.1
1) Refer to article 3.0, 2) Refer to article 3.0, 3) Refer to article 3.1, 4) Refer to
article 3.2
EXERCISE- 3.2
1) Refer to article 3.3, 2) Refer to article 3.3
EXERCISE- 3.3
1) Refer to article 3.4, 3.5, 3.6 & 3.7
EXERCISE- 3.4
1) Refer to article 3.9, 2) Refer to article 3.10, 3.11
BLOCK-II
86
UNIT: IV
VOLTAGE MULTIPLIER CIRCUITS
Structure:
4.0
Introduction
4.1
Objectives
4.2
Voltage multipliers circuits
4.3
Wave shaping circuits
4.4
Clipping Circuits
4.5
Clamping Circuits
4.6
Differentiating and Integrating circuits
4.7 Voltage regulated power supply and Regulation Sensitivity and Stability
Factors
4.8
Unit Summary
4.9
References
BLOCK-II
87
UNIT:IV
VOLTAGE MULTIPLIER CIRCUITS
4.0 INTRODUCTION
A voltage multiplier is an electrical circuit that converts AC electrical power from a
lower voltage to a higher DC voltage by means of capacitors and diodes combined
into a network.
4.1 OBJECTIVES
Voltage multipliers can be used to generate bias voltages ranging from a few volts
for electronic appliances, to millions of volts for purposes such as high-energy
physics experiments and lightning safety testing.
4.2 VOLTAGE MULTIPLIER CIRCUITS
Assuming that the peak voltage of the AC source is +Us we can describe the
(simplified) working of the cascade as follows:
1. Negative peak (−Us): The C1 capacitor is charged through diode D1 to
0 V(potential difference between left and right plate of the capacitor is Us)
2. Positive peak (+Us): the potential of C1 adds with that of the source, thus
charging C2 to 2Us through D2
3. Negative peak: potential of C1 drops to 0 V thus allowing C3 to be charged
through D3 to 2Us.
4. Positive peak: potential of C1 rises to 2Us (analogously to step 2), also
charging C4 to 2Us. The output voltage (the sum of voltages under C2 and
C4) raises till 4Us.
88
In reality more cycles are required for C4 to reach the full voltage. Each additional
stage of two diodes and two capacitors increases the output voltage by twice the
peak AC supply voltage.
EXERCISE4.1
1) What is a voltage multiplier?
2) What is the use of voltage multiplier?
4.3 WAVE SHAPING CIRCUITS
Electronic circuits used to create or modify specified time-varying electrical voltage
or current waveforms using combinations of active electronic devices, such as
transistors or analog or digital integrated circuits, and resistors, capacitors, and
inductors. Most wave-shaping circuits are used to generate periodic waveforms.
The common periodic waveforms include the square wave, the sine and rectified
sine waves, the saw tooth and triangular waves, and the periodic arbitrary wave. The
arbitrary wave can be made to conform to any shape during the duration of one
period. This shape then is followed for each successive cycle.
A number of traditional electronic and electromechanical circuits are used to
generate these waveforms. Sine-wave generators and LC, RC, and beat-frequency
oscillators are used to generate sine waves; rectifiers, consisting of diode
combinations interposed between sine-wave sources and resistive loads, produce
rectified sine waves; multivibrators can generate square waves; electronic
integrating circuits operating on square waves create triangular waves; and
electronic relaxation oscillators can produce saw tooth waves.
In many applications, generation of these standard waveforms is now implemented
using digital circuits. Digital logic or microprocessors generate a sequence of
numbers which represent the desired waveform mathematically. These numerical
values then are converted to continuous-time waveforms by passing them through a
digital-to-analog converter. Digital waveform generation methods have the ability to
generate waveforms of arbitrary shape, a capability lacking in the traditional
approaches.
4.4 CLIPPING CIRCUITS
The circuit with which the waveform is shaped by removing (or clipping) a portion
of the applied wave is known as a Clipping circuit.
89
Clippers find extensive use in radar, digital and other electronic systems. Although
several clipping circuits have been developed to change the wave shape, we shall
confine our attention to diode clippers. These clippers can remove signal voltages
above or below a specified level. The important diode clippers are (i) positive
clipper (ii) biased clipper (iii) combination clipper.
(i) Positive clipper. A positive clipper is that which removes the positive half-cycles
of the input voltage. Fig. shows the typical circuit of a circuit of a positive clipper
using a diode. As shown, the output voltage has all the positive half-cycle removed
or clipped off.
The circuit action is as follows. During the positive half cycle of the input voltage,
the diode is forward biased and conducts heavily. Therefore, the voltage across the
diode (which behaves as a short) and hence across the load RL is zero. Hence output
voltage during positive half-cycle is zero.
During the negative half-cycle of the input voltage, the diode is reverse biased and
behave as an open. In this condition, the circuit behaves as a voltage divider with an
output given by:
Output voltage = 
RL
Vm
R  RL
Generally, RL is much greater than R.

Output voltage = - Vm
It may be noted that if it is desired to remove the negative half-cycle of the input, the
only thing to be done is to reverse the polarities of the diode in the circuit shown in
Fig. Such a clipper is then called a negative clipper.
(ii) Biased clipper. Sometimes it is desired to remove a small portion of positive or
negative half-cycle of the signal voltage. For this purpose, biased clipper is used.
90
Fig. shows the circuit of a biased clipper using a diode with a battery of V volts.
With the polarities of battery shown, a portion of each positive half-cycle will be
clipped. However, the negative half-cycle will appear as such across the load. Such a
clipper is called biased positive clipper.
The circuit action is as follows. The diode will conduct heavily so long as input
voltage is greater than +V. When input voltage is greater than +V, the diode behave
as a short and the output equals +V. The output will stay at +V so long as the input
voltage is greater than +V. During the period the input voltage is less than +V, the
diode is reverse biased and behaves as an open. Therefore, most of the input voltage
appears across the output. In this way, the biased positive clipper removes input
voltage above +V.
During the negative half-cycle of the input voltage, the diode remain reverse biased.
Therefore, almost entire negative half-cycle appears across the load.
If it is desired to clip a portion of negative half-cycles of input voltage, the only
thing to be done is to reverse the polarities of diode or battery. Such a circuit is then
called a biased negative clipper.
(iii) Combination clipper. It is a combination of biased positive and negative
clippers. With a combination clipper, a portion of both positive and negative halfcycle of input voltage can be removed or clipped as shown in Fig.
91
The circuit action is as follows. When positive input voltage is greater than +V1,
diode D1 conducts heavily while diode D2 remains reverse biased. Therefore, a
voltage +V1 appears across the load. This output stays at +V1 so long as the input
voltage exceeds +V1. On the other hand, during the negative half-cycle, the diode D2
will conduct heavily and the output stays at -V2 so long as the input voltage is
greater than -V2. Note that +V1 and -V2 are less than +Vm respectively.
Between +V1 and -V2 neither diode is on. Therefore, in this condition, most of the
input voltage appears across the load. It is interesting to note that this clipping
circuit can give square wave output if Vm is much greater than clipping levels.
Applications of Clippers: Clippers are used to perform 1) Changing the shape of a
waveform 2)Circuit transient protection.
4.5 CLAMPING CIRCUITS
A circuit that places either the positive or negative peak of a signal at a desired d.c.
level is known as a Clamping circuit.
A clamping circuit (or a clamper) essentially adds a d.c. component to the signal.
Fig. shows the key idea behind clamping. The input signal is a sine wave having a
peak-to-peak value of 10V. The clamper adds the d.c. component and pushes the
signal upwards so that the negative peaks fall on the zero level. As you can see, the
waveform now has peak values of + 10V and 0V.
It may be seen that the shape of the original signal has not changed; only there is
vertical shift in the signal. Such a clamper is called a positive clamper. The negative
92
clamper does the reverse i.e. it pushes the signal downwards so that the positive
peaks fall on the zero level.
The following points may be noted carefully.
(i) The clamping circuit does not change the peak-to-peak or r.m.s. value of the
waveform. Thus referring to Fig. above, the input wave form and clamped output
have the same peak-to-peak value i.e., 10V in this case. If you measure the input
voltage and clamped output with an a.c. voltmeter, the readings will be the same.
(ii)
A clamping circuit changes the peak and average values of a waveform. This
point needs explanation. Thus in the above circuit, it is easy to see that input
waveform has a peak value of 5V and average value over a cycle is zero. The
clamped output varies between 10V and 0V. Therefore, the peak value of clamped
output is 10V and average value is 5V. Hence we arrive at a very important
conclusion that a clamper changes the peak value as well as the average value of a
waveform.
The operation of a clamper is based on the principle that charging time of a
capacitor is made very small as compared to its discharging time.
Positive clamper
The input signal of a positive clamper is assumed to be a square wave with time
period T. The clamped output is obtained across RL. The circuit design incorporates
two main features. Firstly, the values of C and RL are so selected that time constant is
very large. This means the voltage across the capacitor will not discharge during the
interval the diode is non conducting.
During the negative half cycle of the input signal, the diode is forward biased and
during the positive half cycle of the input signal, the diode is reverse biased.
The resulting waveform is shown in fig. and Vout = 2V.
93
Negative clamper
The clamped output of negative clamper is taken across RL.
During the positive half cycle of the input signal, the diode is forward biased and
during the negative half cycle of the input signal, the diode is reverse biased.
94
The resulting waveform shown in fig. and Vout = -2V.
EXERCISE- 4.2
1) What is clipper?
2) Describe (i) positive clipper (ii) biased clipper (iii) combination clipper.
95
3) What do you understand by clamping circuit?
4) Explain the action of positive clamper and negative clamper?
4.6 DIFFERENTIATING AND INTEGRATING CIRCUITS
By introducing electrical reactance into the feedback loops of OP-AMP
amplifier circuits, we can cause the output to respond to changes in the input voltage
over time. Drawing their names from their respective calculus functions,
the integrator produces a voltage output proportional to the product (multiplication)
of the input voltage and time; and the differentiator (not to be confused
with differential) produces a voltage output proportional to the input voltage's rate of
change.
Capacitance can be defined as the measure of a capacitor's opposition to changes in
voltage. The greater the capacitance, the more the opposition. Capacitors oppose
voltage change by creating current in the circuit: that is, they either charge or
discharge in response to a change in applied voltage. So, the more capacitance a
capacitor has, the greater its charge or discharge current will be for any given rate of
voltage change across it. The equation for this is:
The dv/dt fraction is a calculus expression representing the rate of voltage change
over time. If the DC supply in the above circuit were steadily increased from a
voltage of 15 volts to a voltage of 16 volts over a time span of 1 hour, the current
through the capacitor would most likely be very small, because of the very low rate
of voltage change (dv/dt = 1 volt / 3600 seconds). However, if we steadily increased
the DC supply from 15 volts to 16 volts over a shorter time span of 1 second, the
rate of voltage change would be much higher, and thus the charging current would
be much higher (3600 times higher, to be exact). Same amount of change in voltage,
but vastly different rates of change, resulting in vastly different amounts of current
in the circuit.
To put some definite numbers to this formula, if the voltage across a 47 µF capacitor
was changing at a linear rate of 3 volts per second, the current "through" the
capacitor would be (47 µF)(3 V/s) = 141 µA.
We can build an OP-AMP circuit which measures change in voltage by measuring
current through a capacitor and outputs a voltage proportional to that current.
96
EXERCISE- 4.3
1) Explain differentiating and integrating circuits.
4.7 VOLTAGE REGULATED POWER SUPPLY REGULATION
SENSITIVITY AND STABILITY FACTORS
A voltage regulator is an electrical regulator designed to automatically maintain a
constant voltage level. A voltage regulator may be a simple "feed-forward" design or
may include negative feedback control loops. It may use an
electromechanical mechanism, or electronic components. Depending on the design,
it may be used to regulate one or more a.c. or d.c. voltages.
Electric voltage regulators: A simple voltage regulator can be made from a resistor
in series with a diode (or series of diodes). Due to the logarithmic shape of diode V-I
curves, the voltage across the diode changes only slightly due to changes in current
drawn. When precise voltage control is not important, this design may work fine.
Feedback voltage regulators operate by comparing the actual output voltage to some
fixed reference voltage. Any difference is amplified and used to control the
regulation element in such a way as to reduce the voltage error. This forms
a negative feedback control loop; increasing the open-loop gain tends to increase
regulation accuracy but reduce stability (avoidance of oscillation, or ringing during
step changes). There will also be a trade-off between stability and the speed of the
response to changes. If the output voltage is too low (perhaps due to input voltage
reducing or load current increasing), the regulation element is commanded, up to a
point, to produce a higher output voltage–by dropping less of the input voltage (for
linear series regulators and buck switching regulators), or to draw input current for
longer periods (boost-type switching regulators); if the output voltage is too high,
the regulation element will normally be commanded to produce a lower voltage.
However, many regulators have over-current protection, so that they will entirely
stop sourcing current (or limit the current in some way) if the output current is too
high, and some regulators may also shut down if the input voltage is outside a given
range.
97
Regulator with an operational amplifier
The stability of the output voltage can be significantly increased by using
an operational amplifier.
In this case, the operational amplifier drives the transistor with more current if the
voltage at its inverting input drops below the output of the voltage reference at the
non-inverting input. Using the voltage divider (R1, R2 and R3) allows choice of the
arbitrary
output voltage between Uzand Uin.
Voltage Stabilizers: Many simple DC power supplies regulate the voltage using
a shunt
regulator such as a zener diode, avalanche breakdown diode, or voltage regulator
tube.
Each of these devices begins conducting at a specified voltage and will conduct as
much current as required to hold its terminal voltage to that specified voltage. The
power supply is designed to only supply a maximum amount of current that is within
the safe operating capability of the shunt regulating device (commonly, by using a
series resistor). In shunt regulators, the voltage reference is also the regulating
device.
If the stabilizer must provide more power, the shunt regulator output is only used to
provide the standard voltage reference for the electronic device, known as
the voltage stabilizer. The voltage stabilizer is the electronic device, able to deliver
much larger currents on demand.
EXERCISE- 4.4
98
1) What is a voltage regulator?
2) Explain in detail the action of voltage regulator.
3) What do you understand by voltage stabilizer?
4.8 UNIT SUMMARY
(i) The operational amplifier is a direct-coupled, high gain, negative feedback
amplifier. They are made with different internal configurations in linear ICs.
(ii) Slew rate (SR) is defined as the maximum rate of change of output voltage per
unit of time and is expressed in volts per microseconds, i.e.,
(iii) Inverting Operational Amplifier works as a negative scalar.
(iv) A circuit in which output voltage is directly proportional to the derivative of the
input is known as a differentiating circuit.
(v)A comparator is a device that compares two voltages or currents and switches its
output to indicate which is larger. It is used in Analog-to-digital converter.
(vi) A voltage multiplier is an electrical circuit that converts AC electric power from
a lower voltage to a higher DC voltage by means of capacitors and diodes combined
into a network.
(vii)Wave- shaping circuits are used to generate periodic waveforms.
(viii) The circuit with which the waveform is shaped by removing (or clipping) a
portion of the applied wave is known as clipping circuit.
(ix) A circuit that places either the positive or negative peak of a signal at a desired
d.c. level is known as a clamping circuit.
(x) A voltage regulator or an electrical regulator designed to automatically maintain
a constant voltage level.
4.9 REFERENCES
1)Operational Amplifiers by Clayton
99
2)Electronic Devices and Circuits by Millman and Halkias (S. Chand & Company
Ltd.)
3)Electronic Devices and Circuits an Introduction by Mottershed
4)Transistor Physics by Sarkar
5)Electronic Devices and Circuits by Sanjeev Gupta (Dhanpat Rai Publications)
6)A Textbook of Electronic Devices and Circuits by R.S. Sedha (S. Chand &
Company Ltd.)
SOLUTION
EXERCISE- 4.1
1) Refer to article 4.0, 2) Refer to article 4.1
EXERCISE- 4.2
1) Refer to article 4.4, 2) Refer to article 4.4, 3) Refer to article 4.4, 4) Refer to
article 4.5
EXERCISE- 4.3
1) Refer to article 4.6
EXERCISE- 4.4
1) Refer to article 4.7, 2) Refer to article 4.7, 3) Refer to article 4.7
100
BLOCK-III
M.Sc. Previous
PAPER-IV
SOLID STATE ELECTRONICS
UNIT:V
COMMUNICATION ELECTRONICS
Structure:
5.0
Introduction
5.1
Objectives
5.2
Modulation and Types of modulation analysis and production of AM and FM
wave Generation DSB/SC modulation of AM waves
5.3
Demodulation of AM waves Generation of DSBSC waves and Coherent
detection of DSB/SC waves
5.4
SSB modulation
5.5
Generation and detection of SSB waves
5.6
Vestigial sideband modulation
5.7
Frequencies division multiplexing
5.8
Unit Summary
5.9
References
UNIT:VI
ELECTRONIC DEVICES
Structure:
6.0
Introduction
6.1
Objectives
101
6.2
Electronic devices: JFET, MOSFET AND MESFET
6.3
Structure & working of their characteristics under different conditions
6.4
Microwave devices tunnel diode and Gunn diode
6.5
Impatt diode and parametric devices
6.6
Unit Summary
6.7
References
UNIT: VII
PHOTONIC DEVICES
Structure:
7.0
Introduction
7.1
Objectives
7.2
Radiotive and non- radiotive transmitter
7.3
LDR
7.4
Photodiode Detectors
7.5
Solar cells
7.6
LED diode lasers condition for population inversion light contentment factor
7.7
Threshold current for lasing
7.8
Unit Summary
7.9
References
102
BLOCK-III
UNIT: V
COMMUNICATION ELECTRONICS
5.0 INTRODUCTION
For the transmission of message to distant parts of the globe, sound waves are first
converted into electrical signals with the help of microphone. To release this audio
signal into space, antenna is employed for effective radiation of energy. But the
frequency of audio signal is always quite low and consequently, it cannot be fed as
such to the antenna for communication. Therefore, before applying the audio signal
to the antenna, a process is performed in which the audio signal is superimposed on
a high frequency wave, called carrier wave. In this process, as mentioned, a separate
high frequency wave is needed because we cannot change any of the characteristics,
e.g., amplitude, frequency and phase of the audio signal as it would amount to a
change in the message to be communicated. But the amplitude, of frequency or
phase of the high frequency wave is modified in accordance with the audio signal,
so that the resultant wave inherits the frequency of modulated wave is quite high,
effective radiation from antenna takes place.
5.1 OBJECTIVES
The purpose of modulation is to alter the frequency level of intelligence. There are
two main reasons for this alteration in frequency level:
(i)At high frequencies, the intelligence practically can be transmitted by radiation.
(ii)Different messages having different frequency levels can be transmitted
simultaneously without any interference.
5.2 MODULATION AND TYPES OF MODULATION ANALYSIS AND
PRODUCTION OF AM AND FM WAVE AND GENERATION DSB/SC
MODULATION OF AM WAVES
Modulation is defined as a process by which a high frequency carrier is made to
vary in some manner as function of the instantaneous value of message to be
transmitted.
The most common type of modulation is amplitude modulation, phase modulation
and frequency modulation.
103
Consider the following waveform which represents a high frequency sinusoidal
carrier of frequency ωe
e (t)  A (t )  cos e   (t )
Basically, there are three parameters which may be varied as function of the
message to be transmitted. (i)The first choice would be to let the amplitude A(t) vary
as the function of the message, i.e., the modulating signal. This choice is certainly
feasible and is given the name amplitude modulation.
(ii)The second choice would be to let the phase vary which conveys the message.
Again, this is also done and is denoted by the term phase modulation.
(iii)Lastly, if the derivative of
with respect to time is assumed to vary, resulting
in frequency variations, the modulation process is called frequency modulation.
Amplitude modulation is often referred as linear modulation. Phase and frequency
modulation belongs to the general class of non-linear modulation popularly referred
as angle modulation or exponential modulation.
Amplitude Modulation
When amplitude of a sinusoidal signal is varied in accordance with the amplitude of
the message signal the sinusoidal signal is said to be amplitude modulated or A.M.
Let the carrier and modulated signals be represented respectively by
Vc (t)= Ac cos (ωc t + )
104
Vm (t)= Am cos (ωm t)
Where Ac is amplitude of carrier
is the initial face angle of the carrier
Am is the amplitude of modulating signal
ωc is angular frequency of the carrier
ωm is angular frequency of the modulating signal
The Am signal is then represented by
v(t) = Ac ( 1+ m cos ωm t) cos ωc t
The deviation in amplitude from the carrier amplitude is controlled by the constant
m.
Power of an A.M. can be determined by the equation by the equation
From the equation v(t) = Ac ( 1+ m cos ωm t) cos ωc t
= Ac cos ωc t + Ac m cos ωm t cos ωc t
= Ac cos ωc t + Ac m (cos ωm t cos ωc t)
From
2 cos A cos B = cos (A+B) + cos (A-B), above equation can be written as
v(t) = Ac cos ωc t+ m/2[(Ac (cos (ωc+ ωm )t+ Ac cos (ωc - ωm ) t]
The first term represents the carrier signal with amplitude Ac. The second term
represents for sinusoidal signals.
The sideband having frequency higher (ωc+ ωm ) than that of the carrier is called
upper sideband. The sideband having frequency lower (ωc - ωm ) than that of the
carrier is called upper sideband.
Generation of FM waves
A wave whose frequency is varied in proportion to the instantaneous amplitude of
the information wave is frequency modulation. The result of this encoding or
105
modulation process is a complex modulated wave whose instantaneous frequency is
a function of the amplitude of the modulating wave and differs from the frequency
of the carrier from instant to instant as the amplitude of the modulating wave varies.
Let the modulation signal Vm (t) be sinusoidal of frequency and a amplitude, then
this signal is represented by the equation Vm (t)= Am cos (ωm t).
And ωt (t) = ωc + k Am cos ωm t
= ωc + ω cos ωm t, where ω = k Am and
f = k Am /2
The instantaneous frequency deviation is ω cos ωm t which is proportional to the
magnitude of modulating signal Am cos (ωm t). This shows instantaneous frequency
lines in the range fc + f to fc - f.
Comparison between frequency modulation and Amplitude Modulation
Frequency Modulation:
(i) There is a substantial reduction in interference effects. That is, noise can be easily
minimized in f.m. systems. The presence of the noise at the receiver input in
addition to the desired signal tends to alter the input voltage both in instantaneous
amplitude and instantaneous phase. In frequency modulation system, amplitude
variations can be eliminated by slicing them with the help of limiter, so that always
constant amplitude is applied to the discriminator.
(ii) No restriction is placed on the modulation index. The instantaneous frequency
deviation is proportional to the instantaneous magnitude of the modulating signal.
(iii)The average power in frequency modulated wave is the same as that contained in
the unmodulated wave.
Amplitude Modulation:
(i) In this type of modulation, alternation of the amplitude of the desired signal by
the noise at the receiver input severely affects the response and amounts to marked
distortion.
106
(ii) In amplitude modulation, use of an excessively large modulating signal may
result in distortion because of over modulation. Modulation index can have a
maximum value unity for distortion-less modulation.
(iii) The average power in modulated wave is greater than that contained in
unmodulated wave. This added power is provided by the modulating source.
GENERATION DSB/SC MODULATION OF AM WAVES
Generation of Amplitude Modulation-DSB/SC
AM-DSB/SC is an abbreviation of amplitude-modulated, double-sideband,
suppressed carrier. As shown in Fig., let us assume F(f) to be the Fourier transform
of the information or modulation source, em(t). Then X(f) shown in Fig (b) will
represent the translated spectrum, that is, the spectrum of e(t) cos ωct. The receiver
accomplishes frequency conversion of X(f) by multiplying e(t) cos ωct by cos ωct.
The resulting spectrum is denoted by Y(f), in Fig. Recovery of em(t) may now be
accomplished by filtering
as indicated by dotted lines in Fig. The actual system which accomplishes this is
shown in Fig. The disadvantage of this system is the necessity of knowing cos ωct at
the receiver. This method of detection is called synchronous detection since the
detector
107
must have a carrier wave that is in synchronism with that used at the transmitter. The
synchronism may be accomplished by transmitting a pilot carrier.
The system performance of AM-DSB/SC is identical to AM-DSB (described in the
preceding article) except for the power wasted by the carrier ; that is, if an AM-DSB
and an AM-DSB/SC system have equal power in the sidebands, then the output
signal-to-noise ratios are equal. If an AM-DSB and an AM-DSB/SC system have the
same total transmitted powers, then the output signal-to-noise ratios differ by a
factor of three, that is,
This difference can be explained by noting that for equal powers the AM-DSB
system only has 1/3rd of the signal power of the AM-DSB/SC system. For AM/DSB,
1.5 watts transmitted means 1.0 watts in the carrier and 0.5 watts in the side bands.
Hence the transmitted sideband powers differ by a factor of three and we would
therefore expect the output signal-to-noise ratio to differ by the same factor.
Demodulation is the act of extracting the original information-bearing signal from a
modulated carrier wave. A demodulator is an electronic circuit (or computer
108
program in a software defined radio) that is used to recover the information content
from the modulated carrier wave.
Demodulation of AM waves: An AM signal encodes the information onto the carrier
wave by varying its amplitude in direct sympathy with the analogue signal to be
sent. There are two methods used to demodulate AM signals.
AM-DSB has the advantage that it does not require synchronous detection as in the
case of AM/DSB/SC and AM-SSB to be studied in subsequent articles. As shown in
Fig AM-DSB/SC has information contained in both the amplitude and phase
considering em(t) sinusoidal. Synchronous (often referred as coherent) detection is
necessary to extract the information in phase and amplitude. Since em(t) changes
sign, it causes the carrier to change phase.
Hence we modulate by a source that does not change sign. This can be achieved by
adding a bias component to em(t) positive and then modulate. This is shown in Fig.
As we already know this type of modulation is known as AM-SSB.
It may be mentioned here that the Fourier transform of [K+em(t)] cos ωc(t) is
identical to the AM-DBS system except that now we have a carrier component at fc.
109
The detection problem is, however, completely different, because now all the
information is in the amplitude and an amplitude-sensitive device may be used to
recover em(t). Thus the advantage of AM-DSB is the case with which reception
occurs. The disadvantage is the large amount of power wasted in the carrier
components.
EXERCISE- 5.1
1) What is modulation? Why is modulation necessary in communication system?
2) Explain amplitude modulation. Derive the voltage equation of an AM wave.
3) What do you understand by sideband?
4) What do you understand by frequency modulation? Explain its advantages over
amplitude modulation.
5) Explain with diagram the generation of DSB/SC modulation of A.M. waves.
5.3 DEMODULATION OF AM WAVES AND GENERATION &
COHERENT DETECTION OF DSB/SC (DOUBLE-SIDEBAND) WAVES
The envelope detector is a very simple method of demodulation. It consists of
a rectifier (anything that will pass current in one direction only), and a low-pass
filter. The rectifier may be in the form of a single diode, or may be more complex.
Many natural substances exhibit this rectification behavior, which is why it was the
earliest modulation and demodulation technique used in radio. The filter is usually
a RC low-pass type, but the filter function can sometimes be achieved by relying on
the limited frequency response of the circuitry following the rectifier. The crystal
set exploits the simplicity of AM modulation to produce a receiver with very few
parts, using the crystal as the rectifier, and the limited frequency response of the
headphones as the filter.
The product detector multiplies the incoming signal by the signal of a local
oscillator with the same frequency and phase as the carrier of the incoming signal.
After filtering the original audio signal will result. This method will decode both
AM and SSB, although if the phase cannot be determined a more complex setup is
required.
110
An AM signal can be rectified without requiring a coherent demodulator. For
example, the signal can be passed through an envelope detector (a diode rectifier and
a low-pass filter). The output will follow the same curve as the
input baseband signal. There are forms of AM in which the carrier is reduced or
suppressed entirely, which require coherent demodulation.
5.4 SSB MODULATION
AM-SSB is an abbreviation for amplitude modulation single sideband. Instead of
transmitting the total spectrum about fc, that is both sidebands, only one sideband is
transmitted. This system is shown in Fig. The advantages of this system over AMDSB/SC are that the required channel bandwidth is reduced by a factor of ½. The
disadvantage of this system is the same as that of AM-DSB-SC that is this also
requires synchronous detection with the recent developments of atomic clocks as
frequency standards it has become possible to eliminate the pilot carriers. However,
as already explained, AM-DSB does not require synchronous detection.
Let us now consider an AM-SSB system with emphasis on system performance. Let
us first consider a simplified means of producing an AM-SSB wave. Shown in Fig is
the phase-shift method of generating SSB wave.
Thus es(t) represents a single sideband at f=fc=fm. Assuming as the transmitted wave
the total transmitted power will be
Em 2
Pt 
2
111
and all this power is useful signal power; that is, it is all in the sideband.
Next consider the simplified AMSSB receiver shown in Fig. Let the input to the
multiplier circuit be the AM-SSB signal + noise. Representing the noise as a finite
number of discrete components, we have
ein  Em cos (c  m ) t 
(2k  1) f

 fc 
2

fm / f
 2
k 1
n
cos 2

t

It may be mentioned here that only noise terms cover one sideband since the
amplifier need only half a bandwidth of fm. After mixing, we have
e2 (t )  E m cos ( c   m ) t cos  et 
f m / f
 2
k 1
n
(2k  1)  f 

cos 2  f c 
 t cos ct
2

Assuming the filter to pass only those terms having frequencies less than fm, we get
e0 (t ) 
Em
cos mt 
2
fm / f

k 1
 (2k  1)  f 
n cos 2 

2

The first term represents desired signal, thus
S0 
Em 2
8
The second term represents noise. Each discrete component has a mean-square value
n2/2, and there is fm/-f of them. Thus,
Since the noise at the input to the mixer is 2ηfm, we have
112
N0 
Nm
4
Using Eqs. we get
S0
P
S
 t  in
N 0 2nf m Nin
Thus the pre-detection and post detection signal-to-noise are equal.
Advantages of Single Side Band Modulation:
(i) Bandwidth is SSB transmission is half than in double-side band system e.g.
bandwidth occupied by one radio telephone channel is reduced to half i.e. only 3kc/s
instead of 6kc/s.
(ii) In SSB system, no carrier is transmitted and therefore possibility of interference
with other channels is avoided.
(iii)The improvement in signal to noise ratio is from 10 to 12 db at the receiver
output over that in double sideband system.
(iv) SSB system eliminates the possibility of distortion due to selective fading.
(v)SSB system provides an improvement in signal to noise of at least 9 dbs.
Disadvantages of Single Side Band transmission:
(i) The transmitter and receiver become more complex and performance required is
of high standard.
(ii) For demodulation process, carrier is inserted at the receiver. The frequency of
this reinserted carrier must be within 15 c/s of the suppressed carrier frequency in
each case of speech and 4c/s in case of music. Such a requirement complicates the
demodulating process; because to meet it, this is necessary to transmit a pilot signal
or the carrier voltage itself at a very low level for synchronizing the receiver
oscillator frequency. This signal has to be filtered at the receiver with the use of
highly selective filters, amplified and then either reinserted to provide the carrier or
is used to control the carrier frequency produced by the local oscillator. Design of
these highly selective filters is thus involved in SSB receiver. This complexity
contributes to an addition in cost.
Applications of Single Side band Transmission:
Because of complexity and cost of SSB receiver, this system is not used for
commercial broadcasting. It finds use in other fields such as:
(i) Police wireless communication
113
(ii) SSB telegraph system
(iii) Point-to-Point radio telephone communication
(iv) In V.H.F. and U.H.F. communications
5.5 GENERATION AND DETECTION OF SSB WAVES
There are two methods for production of SSB signals. First method is based on the
frequency-domain description of the SSB signal which suggests that the SSB signal
can be obtained from the corresponding DSB/SC through proper filtering. This
method is called frequency discrimination method or filter method. Second method
is based on the time domain description of the SSB signal and generally requires 90o
phase shift networks for the modulating and carrier signals. This method is called
phase discriminator method or phase shift method. Third method makes use of
product modulators (balanced modulator) and low pass filter and is applicable to
modulating signals having a finite energy gap near zero frequency. Since this
method was devised by Weaver is known as Weavers method or third method. We
will now discuss these three methods in detail.
(i) Filter method.
This method simply involves in the generation of a DSB/SC signal for the given
carrier signal and the given
modulating signal and then filtering out the undesired sideband. The method looks
fairly simple; but the filtering will present serious problem when the highest
frequency of the lower sideband (LSB) is very near to the lower frequency of the
upper sideband (USB) that is when the frequency separation between LSB and USB
is too small. The separation is twice the minimum frequency in the modulating
signals x(t). Thus if a tuned circuit is used as a band pass filter to reject one of the
114
sidebands, the Q of the tuned circuit is determined by the carrier frequency fc and the
value of the lowest modulating signal frequency.
When the required carrier frequency is high and the modulating signal effect is very
low, filtering of one of the sidebands would become virtually impossible. To solve
this problem repeated filtering is used.
(ii) Phase shift method.
This method uses two identical product modulators and two quadrature (90o) phaseshift networks, one of which is for the carrier frequency and the other is for the
modulating signal. For successful operation, it is necessary that for the product
modulators to be identical, phase shifts to be precisely 90o and for the phase shifter,
for the modulating signal, to have a flat amplitude response over the modulating
signal frequency range.
The two inputs to one of the modulators are the modulating signal x(t) and the
carrier signal vc(t) while the two inputs to the other product modulator are the 90o
phase-shifted x(t) the 90o phase shifted vc(t). The sum and difference of the two
outputs of the product modulators, represent the individual sidebands.
Any deviation from the flat amplitude response of 90o phase-shifter for the
modulating signal, will result in the appearance of the undesired sideband. This can
be avoided by using two phase-shifters, instead of one, for the modulating signal.
The phase shifts introduced by these phase shifters can now be functions of
frequency but in such a way that the difference between the phase shifts at all
115
frequencies over the modulating signal frequency range, is equal to 90o while three
amplitude responses are identical (not necessarily flat).
EXERCISE- 5.2
1) Give a brief note on demodulation of AM waves.
2) What is SSB modulation?
3) Discuss a suitable method of generating an SSB signal.
4) What are the advantages and disadvantages of SSB modulation?
5) Explain methods for production of SSB signals.
5.6 VESTIGIAL SIDE BAND MODULATION (VSB)
It is an abbreviation of vestigial sideband. Consider a modulating signal of large
band width having significant low frequency content. Principal examples are
television, video, facsimile, and high speed data signals. Practical SSB systems have
poor low frequency response. On the other hand, DSB work quite well for low
message frequencies but transmission bandwidth is twice that of SSB. Thus a
compromise modulation scheme is desired which s VSB.
VSB is derived by filtering DSB (or AM) in such a fashion that one sideband is
passed almost completely while just a trace, or vestige, of the other sideband is
included. The key to VSB is the sideband filter, typical transfer function is shown in
Fig.
Fig. VSB filter characteristics
116
While the exact shape of the response is not crucial, it must have odd symmetry
about the carrier frequency and a relative response of ½ at the point. Therefore,
taking the upper side band case,
H ( f )  u ( f  f c )  H  ( f  f c )  u ( f  f c )  H  ( f  f c )
H  ( f )    ( f )
where
and
H ( f )  0
f 
as shown in Fig.
Fig. VSB modulator
The VSB sideband filter is thus a practical sideband filter with transition width 2,
and a VSC modulator takes the form of SSB modulator shown in Fig. If carrier
suppression is not wanted, the balanced modulator is replaced by an AM modulator.
Because the width of the partial sideband is one-half the filter transition width, the
transmission bandwidth is
1  W    W
VSB and SSB spectra are quite similar, particularly when (((W, which is often true.
The similarities exist in the time domain as well, and we can write xc(t) as


1
Ac  xc (t ) cos et  x' (t )  x (t ) sin et
2
where the quadrature component consists of x’ (t) plus
xc 

x (t )  j 2  H  ( f )  ( f ) e j  t df

117

If << W, VSB approximates SSB and x(t)= 0 : conversely for large (, VSB
approximate DSB. The transmitted power is not easy to determine but depends on
the vestige width .
Frequency and Phase Modulation
Frequency modulation and phase modulation are normally abbreviated as FM and
PM respectively. They belong to the general class of angle modulation (or
exponential modulation). Phase modulation and frequency modulation are not
essentially different in the sense that variation in the phase of a carrier is
accompanied by a corresponding change in frequency. This is because of the
relationship between phase  and frequency ω of the carrier that is

d
dt
As shown in fig, if a carrier has been angle modulated, it will be impossible to
determine whether PM and FM had been used. Therefore, the term FM and PM are
only used to indicate which parameters of the carrier are made to vary as function of
the modulating signal em (t). Since the carrier waveforms for PM and FM are very
similar, the methods of producing and detecting those waveforms must have a great
deal in common. Fig. illustrates the basic difference between the two.
Fig. shows some form of phase modulation will be achieved. However, it will be
very complex and non-linear form having no practical use. Yet it suggests two
identical frequencies, (i.e. one source for both with a phase-shifting network in one
of the channel).
118
The carrier of the amplitude-modulated signal has been removed so that only the
two sidebands are added to the unmodulated voltage. This has been accomplished by
the balanced modulator and the addition takes place in the combining network. As
can be seen the resultant of the two sideband voltages will always be in quadrature
with the carrier voltage. Moreover as the modulation increases, so will be phase
deviation, and hence phase modulation has been obtained. Thus the resultant voltage
coming from the combining network is phase modulated, but there is also a little
amplitude modulation present. The AM can be removed by an amplitude limiter.
Since frequency-modulation is what we want, the modulatory voltage have to be
equalized before it enters the balanced modulator. As we know PM may be changed
into FM by prior boosting of the modulation. A simple RL equalizer shown in Fig.
can be used.
The most convenient operating frequency for the crystal oscillator and phase
modulator is in the vicinity of 1 MHz. Since transmitting frequencies are normally
much higher than this, frequency multiplies are used.
Frequency Discriminator
A frequency discriminator is a device which produces an output voltage proportional
to the input-frequency. The discriminator is usually tuned about a given frequency,
say the difference frequency in this case, and the output voltage is proportional to
the deviation of the input frequency from this point. One type of such discriminator
circuit is shown. The upper and lower turned circuits T1 and T2, tuned above and
below the centre frequency f0, respectively. The voltage e1 and e2 are shown as
function of input frequency. Since e0 = e1 + e2, the total output signal is linear about
f0 if T1 and T2 are properly tuned and adjusted.
119
If the difference between the carrier and the standard falls as f0 then no output is
produced by the discriminator. Should the oscillator change, thus causing the
transmitted carrier to change the difference frequency will also change and will be
something other than f0. Consequently, on output will be created from the
discriminator. This output will be in the form of a d. c. voltage and is used to control
the bias on the reactance tube circuit and restore the proper carrier frequency. When
the transmitter is modulated the discriminator output will consist of a d.c.
component (if correction is necessary) plus a.c. component. Filtering must be used
to remove a.c. component.
The receiver is similar to that used in a conventional AM-DSB system except for
bandwidth requirements of the amplifiers and the use of frequency instead of an
amplitude sensitive detector. If the carrier has been phase modulated, the output
from the detector must be integrated to recover the modulating voltage. The detector
is shown in Fig. Its gain vs frequency characteristic is shown in Fig.
Bandwidth Requirements
Because of the similarity between PM and FM, only FM bandwidth requirement will
be discussed here. FM is produced by varying the instantaneous frequency of the
carrier to be modulated the instantaneous deviation being directly proportional to the
instantaneous value of the message or modulating wave. If the frequency of the
carrier is to be a function of em(t), then the carrier phase is a function of
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Thus we may write
where K has the units of radians per volt per second.
Considering a modulating signal to be sinusoidal, we have
and the FM wave may be expressed as
Here KEm represents the maximum frequency deviation of the carrier. Let
where mf is termed the modulation index for an FM. Eq. then becomes,
es (s)  Ee cos (e t  m f sin m t )
cos (mf sin ωmt) and sin (mf sin ωmt) may be expanded in terms of Bessel’s function
as follows:
Substituting these values in Eq. we have
121
It is seen that each pair of side-bands is proceeded by J coefficients. These are
Bessel’s functions of the first kind and of the order denoted by the subscript, with
the arguments mf. Jn (mf) may be shown to be a solution of an equation of the form
d2y
dy
 mf
 (m f 2  n 2 ) y  0
d mf 2
d fm
The solution, i.e., the formula for the Bessel function, is
(m f ) 2
5.7 FREQUENCIES DIVISION MULTIPLEXING
FDM is the technique used to divide the bandwidth available in a physical medium
into a number of smaller independent logical channels with each channel having a
small bandwidth. The method of using a number of carrier frequencies each of
which is modulated by an independent speech signal is in fact frequency division
multiplexing.
When many channels are multiplexed together, 400Hz is allocated to each channel
to keep them well separated. First the voice channels are raised in frequency, each
by a different amount. Then they can be combined, because no two channels how
occupy the same portion of the spectrum. Notice that even though there are gaps
(guard bands) between the channels, there is some overlap between adjacent
channels, because the filters do not have sharp edges. This overlap means that a
strong spike at the edge of one channel will be felt in the adjacent one as nonthermal noise.
122
Frequency-division multiplexing works best with low-speed devices. The frequency
division multiplexing schemes used around the world are to some degree
standardized. A wide spread standard is 12 400-Hz each voice channels ( 300Hz for
user, plus two guard bands of 500Hz each) multiplexed into the 60 to 108 KHz
band. Many carriers offer a 48 to 56 kbps leased line service to customers, based on
the group. Other standards upto 230000 voice channels also exist.
Example:
The allocated spectrum is about 1MHz, roughly 500 to 1500 KHz. Different
(stations, each operating in a portion of the spectrum with the inter-channel
separation great enough to prevent interference. This system is an example of
frequency division multiplexing.
Advantages of FDM
1. Here user can be added to the system by simply adding another pair of transmitter
modulator and receiver demodulators.
2.FDM system support full duplex information flow which is required by most of
application.
3.Noise problem for analog communication has lesser effect.
Disadvantages of FDM
1.In FDM system, the initial cost is high. This may include the cable between the
two ends and the associated connectors for the cable.
2.In FDM system, a problem for one user can sometimes affect others.
3.In FDM system, each user requires a precise carrier frequency.
EXERCISE- 5.3
1) Discuss with a diagram the communication system with a VSB.
2) What is frequency division multiplexing (FDM)?
3) Discuss its advantages and disadvantages.
5.8 UNIT SUMMARY
(i) Frequency modulation is produced when the instantaneous frequency of carrier is
varied in accordance with the modulating signal, while the amplitude of the carrier
remains constant.
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(ii)AM-SSB is an abbreviation for amplitude modulation single sideband.
(iii)FDM is the technique used to divide the bandwidth available in a physical
medium into a number of smaller independent logical channels with each channel
having a small bandwidth.
(iv) Frequency modulation and phase modulation are normally abbreviated as FM
and PM respectively.
(v) A frequency discriminator is a device which produces an output voltage
proportional to the input-frequency.
5.9 REFERENCES
1)Electronic Devices and Circuits by Millman and Halkias, S. Chand & Company
Ltd.
2)Electronic Devices and Circuits an Introduction by Mottershed
3)Transistor Physics by Sarkar
4)Operational Amplifiers by Clayton
5)Nashelsky – Electronic Devices and Circuit Theory by Robert Boylested and
Louis
SOLUTION
EXERCISE- 5.1
1) Refer to article 5.1& 5.2, 2) Refer to article 5.2, 3) Refer to article 5.2, 4) Refer to
article 5.2
EXERCISE- 5.2
1) Refer to article 5.3, 2) Refer to article 5.4, 3) Refer to article 5.5, 4) Refer to
article 5.4, 5) Refer to article 5.5
EXERCISE- 5.3
1) Refer to article 5.6, 2) Refer to article 5.7, 3) Refer to article 5.7
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BLOCK-III
UNIT-VI
ELECTRONIC DEVICES
6.0 INTRODUCTION
An electronic device is any physical entity in an electronic system used to affect the
electrons or their associated fields in a desired manner consistent with the intended
function of the electronic system. Components may be packaged singly or in more
complex groups as integrated circuits. Some common electronic components
are capacitors, inductors, resistors, diodes, transistors, etc. Components are often
categorized as active (e.g. transistors and thermistors) or passive (e.g. resistors and
capacitors).
6.1 OBJECTIVES
Components are generally intended to be connected together, usually by being
soldered to a printed circuit board (PCB), to create an electronic circuit with a
particular function (for example amplifier, radio receiver, or oscillator).
6.2 ELECTRONIC DEVICES: JFET, MOSFET AND MESFET
Field - Effect Transistor
There are two main types of field - effect transistors:
1. Junction field - effect transistor (JFET).
2. Metal Oxide semiconductor field -effect transistor (MOSFET)
Junction field - effect Transistor
The Junction field - effect transistors (JFET's) can be divided depending upon their
structure into the following two categories:
1. N-channel JFET and
2. P-channel JFET.
The basic construction of an N-channel JFET is as shown in figure. It consists of an
N-type Semiconductor bar with two p-type heavily doped regions diffused on
125
opposite sides of its middle part and the P-type regions from two PN junctions. The
space between the junctions (i.e., N-type region) is called a channel. Both the P-type
regions are connected internally and single wire is taken out in the form of a
terminal called the gate (G). The electrical connections (called ohmic contacts) are
made to both ends of the N-Type semiconductor and are taken out in the form of two
terminals called drain (D) and Source (S). The Drain (D) is a terminal through which
electrons leave the semiconductor bar and source (S) is a terminal through which the
electrons enter the semiconductor.
Whenever a voltage is applied across the drain and source terminals, a current flows
through the N-channel. The current consists of only one type of carriers (i.e.,
electrons). Therefore the field-effect transistor (FET) is called a unipolar device.
This distinguishes a FET from a BJT (i.e., a bipolar junction transistor) where the
current consists of the flow of both the electrons and holes.
MOSFETs
The MOSFETS is an abbreviation for metal-oxide semiconductor field-effect
transistor. Like JEET, the MOSFT has a source, gate and drain. However, unlike
JFET, the gate of a MOSFET is insulated from the channel. Because of this, the
MOSFET is sometimes known as IGFET which stands for insulated-gate field effect transistor. Other names used for MOSFET are MISFET (metal-insulatorsemiconductor field -effect transistor) and MOST (metal - oxide semiconductor
Transistor). There are two basic types of MOSFETs; depletion type and
enhancement- type MOSFETs.
Depletion- Type MOSFET
126
Figure shows the basic structure of an N- channel depletion type MOSFET. It
consists of a conducting bar of N-type material with an insulated gate on the left and
P-region on the right. Free electrons can flow from source to drain through the Ntype material. The P-region is called substrate. It physically reduces the conducting
path to a narrow channel. A thin layer of silicon dioxide is deposited on the left side
of the channel. This layer insulates the gate form the channel. Because of this, a
negligible gate current flows even when the gate voltage is positive. It will be
interesting to know that a PN junction, which exists in a JFET, has been eliminated
in the MOSFET.
The basic construction of a depletion-type P-channel MOSFET is similar to that of
N-channel except that the conducting bar is of P-type material and the substrate is of
N-type material.
Enhancement- type MOSFET
The enhancement-type MOSFET has no depletion mode it operates only in
enhancement mode. It differs in construction from the depletion-type MOSFET in
the sense that it has no physical channel
MESFETS (METAL SEMICONDUCTOR FIELD EFFECT TRANSISTORS)
These are unipolar microwave transistors that have several advantages compared to
bipolar microwave transistors. They have higher efficiency, fmax’ operation
frequencies, input impedances and lower noise figures. In fact these are replacing
bipolar transistors and even parametric amplifiers (to be discussed later) in several
applications such as radars. Although junction FET’s (JFETs) and insulated gate
127
FETs (GFET’s) are also suitable for microwave amplification and oscillation,
MESFETs with silicon and gallium arsenide (GaAs) are very popular. GaAs
MESFETs due to their higher mobility (6 times larger than silicon) larger peak drift
velocity (2
times
larger
than
Si),
smaller
parasitic
resistances,
larger
transconductances and smaller transit time are almost always preferred. They use
metal semiconductor schottky junction for the gate contact and hence the name
MESFET.
6.3 STRUCTURE, WORKING AND THEIR CHARACTERISTICS UNDER
DIFFERENT CONDITIONS
Construction of MESFET:
The schematic diagram of a GaAs MESFET along with its symbol is shown in Fig.
It uses inter-digitated structure. A moderately doped n type GaAs epitaxial layer is
grown on a high resistivity, semi-insulating GaAs substrate. The two ohmic contacts
for source and drain are made on the top of epitaxial layer using Au-Ge, Au-Te or
Au-Te-Ge alloys. In between these two contacts another contact made of metal
aluminium semiconductor schottky junction is added that is called the gate.
Operation
The MESFET operates with drain at positive potential with respect to source and the
gate is reverse biased so that the majority-carriers (the electrons) flow in the n type
epitaxial layer from the source. This creates depletion layer (completely depleted of
carrier-electrons) in the channel and gradually pinches off. The cross-section of
128
current flow in the n-layer gets constricted due to insulating nature of the depletion
region (i.e., the gain controls the current flow from the drain to the source).
As the reverse bias between the source and gate is increased, the height of the charge
depletion region also increases. The non-pinched off region now has lesser channel
height increasing channel resistance. Thus the drain current I sub ds is modulated by
the gate voltage Vgs. The VI characteristics Vds vs Ids for various values of Vgs are
as shown in Fig.
It is clearly seen that the drain current Ids is completely controlled by the field effect
of the gate voltage Vgs (hence the name FET). Pinch off occurs when the Ids
increases continuously and the ohmic voltage drop between source and channel
reverse biases the function. When the channel is pinched off Ids remains almost
constant even if Vds is increased. The pinch off voltage is the gate reverse that
removes all the free charges from the channel and is given by the relation.
Characteristics of JFET
We known that a family (or a set) of curves which relate device current and voltages
are knows as characteristics curves. Following are the two important characteristics
of a JFET.
1.
V-I or drain characteristics. These curves given relationship between the drain
current (ID) and drain-to-source voltage (VDS) for different values of gate-tosource voltage (VGS).
129
2.
Transfer Characteristics. These curves given relationship between drain current
(ID) and gate-to-source voltage (VGS) for different values of drain-to-source
(VDS) voltage.
Drain Characteristics
These curves may be obtained by using the circuit arrangement shown in figure.
First of all, we adjust the gate-to-source voltage (VGS) to zero Volt. Then increase
the drain-to-source voltage (VDS) in small suitable steps and record the
corresponding values of drain current (ID) attach step. Now if we plot a graph with
drain-to-source voltage along the horizontal axis and drain current along the vertical
axis, we shall obtain a curve marked VGS =0 and in a similar procedure may be used
to obtain curves for different values of gate-to-sources voltage.
Transfer Characteristics
These are also called transonductance curves, which give us the relationship
between drain current (ID) and gate-to-source voltage (VGS) for a constant value of
130
drain-to-source voltage (VDS). The transfer characteristics may be obtained by
adjusting the drain-to-source voltage to some suitable value and increase the gate-tosource voltage in small suitable steps. Now records the corresponding values of
drain current at each step. If we plot a graph with gate-to-source voltage (VGS) along
the horizontal axis and the drain current (ID) along the vertical axis, we shall obtain a
curve as shown in figure A similar procedure may be used to obtain curves at
different values of gate-to-source voltage.
Drain Characteristic of Depletion - Type MOSFET.
Figure shows the drain characteristic for the N-channel depletion - type MOSFET in
the common source configuration. These curves are plotted for both negative and
positive values of gate-to-source voltage (VGS). The curves shown above the curve
for VGS =0 have a positive zero whereas those below it have a negative value of V GS.
When VGS is zero and negative, the MOSFET operates in the depletion-mode. On
the other hand, if VGS is zero and positive, the MOSFET operates in the
enhancement- mode.
It may be noted that the drain characteristics of depletion-type MOSFET's are
131
similar to that of JFET. The only difference is that JFET does not operate for
positive values of gate-to-source voltage. (VGS).
Transfer characteristics of Depletion - type MOSFET
Figure shows the transfer characteristic (also called transconductance curve) for an
N-channel depletion-type MOSFET. It may be noted form this curve that the region
AB of the characteristic is similar to that of JFET. But here, this curve extends for
the positive values of gate-to-source voltage similar to that of JFET. But here, this
curve extends for the positive values of gate-to-source voltage (VGS) also. The value
IDSS represents the current form drain-to-source with VGS =0. The drain current at
any point along the transfer characteristic (i.e., the curve ABC) is given by the
relation,
ID = IDSS [1-VGS /VGS (off)]2
It may be noted that even if VGS = 0, the device has a drain current equal to IDSS.
Due to this fact, it is called normally - ON MOSFET.
Drain Characteristics for Enhancement - type MOSFET
Figure shows the drain characteristics for N-Channel enhancement-type MOSFET.
It may be noted form this fig., that when the gate-to-source voltage (VGS) is less than
threshold voltage, VGS(th), there is no drain current. However, in actual practice, an
extremely small value of drain current does flow through the MOSFET. This current
flow is due to the presence of thermally generated electrons in the P-type substrate.
When the value of VGS is kept above VGS(th), a significant drain current flows, where
VGS(th) is threshold voltage.
132
The values of drain current increase with the increase in gate-to-source voltage. It is
because of the fact that the width of inversion layer widens for increased values of
VGS and therefore allows more number of free electrons to pass through it. The drain
current reaches its saturation value above a certain value of drain-to-source voltage
(VDS).
Transfer characteristic of Enhancement-type MOSFET.
In this, there is no drain current when the gate-to-source voltage, VGS = 0. However,
if VGS is increased above the threshold voltage, VGS(th), the drain current increases
rapidly. The drain current at any point along the curve is given by the relation,
ID = K [VGS - VGS(th)]2
where K is a constant, whose value depends on the type of MOSFET. It value can be
determined form the data sheet by taking specified value of drain current called
ID(ON) at the given value of VGS and then substituting these values in the above
equation. Incidentally, may be noted that enhancement-type MOSFET does not have
an IDSS parameter like JFET and depletion-type MOSFET.
Applications of MESFET
GaAs MESFETs due to their excellent performance characteristics have found a
number of microwave applications
1. As front end low noise amplifier of microwave receivers in both radar and
communications
2. As power amplifiers for output stage of microwave links
133
3. As driver amplifiers for high power transmitters
4. As output amplifiers in narrow band troposcatter links or in broad band
generators
5. As power oscillators
6. Dual gate MESFETs can be used for harmonic frequency multiplication up
to K band.
EXERCISE- 6.1
1) Explain the construction and working of JFET.
2) Briefly describe some characteristics of JFET.
3) Explain the construction and working of MOSFET.
6.4 MICROWAVE DEVICES
Solid state microwave devices can be classified:
1.Based on their electrical behavior
2.Based on their construction.
DEPENDENCE:
1.Based on electrical behavior we have:
(a)Non-linear resistance type: eg varistors (variable resistances)
(b)Non-linear reactance type: eg varactors (variable reactors)
(c)Negative resistance type: eg Tunnel diode, Impatt diode, Gunn diode.
(d)Controllable impedance type: eg PIN diode.
Based on construction we have:
(a)Point contact diodes
(b)Schottky barrier diodes
(c)Metal oxide semiconductor devices (MOS)
134
(d)Metal insulation devices.
The above solid state diodes have many applications, viz. amplification, detection
down conversion, up conversion, modulation, switching, limiting, power generation,
phase shifting etc. In this chapter we shall study principle of operation,
constructional details, performance parameters, circuits and applications of some of
the important semiconductor devices.
TUNNEL DIODE (ESAKI DIODE)
Tunnel diode is a specially made p-n junction device which exhibits negative
resistance over part of the forward bias characteristic. It’ has extremely heavy
doping on both sides of the majority and an abrupt transition from the p-side to the
n-side. The tunneling effect is a majority carrier effect and is consequently very fast.
The tunnel diode is useful for oscillation useful for amplification purposes. Because
of the thin junction and short transit time, it is also useful for microwave
applications in fast switching circuits.
Volt-amp Characteristics of a Tunnel Diode
The volt-ampere characteristics of a tunnel diode
Ip’ Vp = Peak point parameters
Iv’ Vv = Valley point parameters
Peak point to valley point –negative resistance
135
The tunnel effect controls the current at very low values of forward bias where the
normal or the infection current is very small as shown in Fig. The mechanism of
tunneling is purely a quantum mechanical phenomenon. An electron on one side of
the barrier will have a certain probability of leaking through the barrier if barrier is
very thin. If both p and n type materials of a junction are heavily doped, the
depletion region becomes very narrow; as narrow as of the order of 100 Ǻ.
GUNN DIODE
The construction of a Gunn diode can be understood with the help of the following
diagram and its typical characteristics are given below.
Typical Characteristics
It typically uses a 10-12 V supply with typical bias current of 250 mA giving a
continuous wave power of 25 m W in the X -band.
1. CW power
: 25m W to 250 m W X band (5-15 GHz).
100 mW at 18--26.5 GHz.
40 mW at 26.5-40 GHz.
2. Pulsed power
: 5W(5-12GHz).
3. Efficiency 2% to 12% (at 1.5 W CW to 5 m W CW)
136
Applications of Gunn Diode:
1.In Radar transmitters (police Radar, CW Doppler Radar).
2.Pulsed Gunn diode oscillators used in transponders for air traffic (ATC) control
and in industry telemetry systems.
3.Broadband linear amplifier (replacing TWT's).
4.Fast combinational and sequential logic circuits.
5.Low and medium power oscillator in microwave receivers.
6.As pump sources in par amp.
Gunn diodes have an advantage over IMPATT diodes in that they have lesser noise.
The disadvantage of Gunn diode is that it is very temperature dependent 0.5-3
MHz/0C change. Well designed devices have 50 kHz/0C for a range of -400C to +
700C.
6.5 IMPATT DIODE AND PARAMETRIC DEVICES
IMPATT DIODE
Any device which exhibits negative resistance for dc will also exhibit it for ac i.e., If
an ac voltage is applied current will rise when voltage falls at an ac rate. Hence
negative resistance can also be defined as that property of a device which causes the
current through it to be 1800 out of phase with the voltage across it. Thus is the kind
of negative resistance exhibited by IMPATT diode i.e., If we show voltage and
137
current have a 1800 phase difference, then negative resistance in IMPATT diode is
proved.
A combination of delay involved in generating avalanche current multiplication
together with delay due to transit time through a different space provides the
necessary 1800 phase difference between applied voltage and the resulting current in
an IMPATT diode.
As shown in Fig. IMPATT is a diode, the junction being between the p+ and n
layers.
An extremely high voltage gradient (400 kV/cm) is applied to the IMPATT diode
eventually resulting in a very high current. A normal diode would very quickly
breakdown under these. conditions but IMPATT is constructed such that it will
withstand these conditions repeatedly. Such a high potential gradient back biasing
the diode causes a flow of minority carriers across the junction.
Fig
Let us consider application of a RF ac voltage superimposed on top of the high dc
voltage. Increased velocity of electrons and holes result in additional electrons and
holes by knocking them out of the crystal structure by so called Impact ionization.
These additional carriers continue the process at the junction and it now snowballs
into an avalanche. If the original dc field was just at the threshold of allowing this
situation to develop, this voltage will be exceeded during the whole of the RF
138
positive cycle and the avalanche current multiplication will be taking place during
this entire time. Since it is a multiplication process avalanche is not instantaneous.
This process infact takes a time such that the current pulse maximum at the junction
occurs at the instant when RF voltage across the diode is zero and going negative. A
900 phase shift or phase difference between voltage and current has then been
achieved.
The current pulse as shown in Fig. is situated at the junction. It does not stay there
but moves towards the cathode due to applied reverse bias at a drift velocity
dependant on the presence of high dc field.
The time taken by the pulse to reach the cathode depends on this velocity and on
the thickness of the highly doped ‘n+' (charges) layer.
The thickness is adjusted such that time taken for current pulse to move from V =
0 position to V = negative maximum of RF cycle is exactly 900. Hence voltage and
current are 1800 out of phase and a dynamic RF negative resistance has been proved
to exist. Hence IMPATT diode is useful both as an oscillator and as an amplifier.
The Resonant frequency of IMPATT diode is given by
f 
where,
Vd
2L
Vd = Carrier drift velocity.
139
L = Length of the drift space charge region.
The efficiency η of IMPATT diode is given by
 Pac  Va

P
dc
  Vd

 Ia 
 
 Id 
Where,
Pac = ac power
Pdc = dc power
Va and Ia = ac voltage and current
Vd and Id = dc voltage and current
Application of IMPATT diode
IMPATT diodes are used as microwave oscillators such as (i) microwave generators
(ii) modulated output oscillators (iii) receiver local oscillators and (iv) par amp
pumps. IMPATT diodes are also suitable for negative resistance amplification. High
Q IMPATTS are used in Intrusion alarm network, police radar and low power
microwave transmitter whereas low Q IMPATTS are useful in FM (frequency
modulated) telecommunication transmitters and CW (continuous wave) Doppler
radar transmitter.
PARAMETRIC AMPLIFIERS
A parametric amplifier is one that uses a non-linear reactance (capacitive or
inductive) or a time varying reactance for its amplification (rather than resistance as
in a normal amplifier). In fact, parametric devices basically depend on the possibility
of increasing the energy of the signal at one frequency by supplying energy at some
other frequency. Consider the simple tank circuit in which we can separate the plates
of the capacitor used, mechanically. Assume that prior to the time t = 0, the circuit
has been energized so that the voltage 'V' and charge 'Q' on the capacitance are
varying sinusoid ally.
We know that,
140
V
  A
Q
, C 0 r
C
d
where the symbols have their usual meanings.
To obtain amplification, capacitor plates are pulled apart when the charge and the
voltage are at their maximum. Because of the electric field between the plates, it
requires an expenditure of energy (mechanical energy) to pull the plates apart. This
mechanical energy appears as additional electric energy stored in the capacitor and
manifests itself as an abrupt increase in the voltage as shown in the Fig. [because Q
= CV, as Q is constant, a decrease in C will result in an increase in V]. The voltage
and the charge continue the oscillations towards zero. At zero voltage, the
capacitance plates are brought back to their original separation and this requires no
expenditure of energy as the electric field is also zero now. The voltage and charge
now swing to their wave maximum at which plates are pulled apart once again and
the process can be continued at each maximum and minimum of voltage and hence a
signal builds up i.e., each time the plates are pulled apart, energy is added to the
signal.
If the plates are separated each time by the same extent, the amplitude of the
voltage would build up to infinity. However as amplitude builds up, it requires more
and more force to separate the plates so that ultimately the force required would also
be infinite. With only finite force available the amplitude builds up asymptotically to
a finite value only, when the energy added per separation just equals to the energy
dissipated.
141
It is to be noted that in the present case energy is added twice per cycle i.e., the
circuit is pumped at twice the signal frequency. There are many cases wherein it is
desirable to pump at a frequency other than twice the signal frequency, for example
a convertor.
VARACTOR DIODES
The term varactor is a shortened form of variable reactor, referring to the voltage
variable capacitance of a reverse biased junction. They have non-linearity of
capacitance which is fast enough to follow microwaves.
Varactor diode is the
most widely used active element in a parametric amplifier. Parametric amplifier is a
low noise amplifier because no resistance is involved in the amplifying process.
As already said, varactor diode is a semiconductor device in which the junction
capacitance can be varied as a function of the reverse voltage (bias) of the diode
(Fig.). Losses in this non-linear element will be almost negligible. The junction
capacitance depends on the applied voltage and junction design. In some cases a
junction with fixed reverse bias may be used as a capacitance of a fixed value. The
VI characteristics of a typical varactor diode is shown in Fig. Commonly used
schematic symbols are shown in Fig.
Fig. Junction Capacitance vs V
We know that,
142
C j  Vr n
where,
Cj
= junction capacitance
Vr
= reverse bias voltage
n
= a parameter that decides the type of junction.
where, S1
= the first fourier component of the time dependent elastance
(reciprocal of capacitance).
  2f
Also
Q
S1 
f cv
f
1 
C1 C jv
where, 0.17 < Г < 0.25 for most varactor junctions.
Г
= 0.17 for graded junction
= 0.25 for step junction
Cjv
= Junction capacitance at the operating bias.
Note that when the varactor is under dynamic condition i.e., when the junction
capacitance varies because of the applied voltage (as in FM modulation) and
f 
frequency

2 the capacitance value varies as the instantaneous value of the
signal and hence it is taken as the time dependant non-linear capacitance.
Applications of Varactor Diodes
They have several applications like:
143
1.Harmonic generation
2.Microwave frequency multiplication (up conversion)
3.Low noise amplification (parametric amplifier)
4.Pulse generation and pulse shaping.
5.Tuning stage of a radio receiver (replacing the bulky variable plate capacitor)
6.Active filters.
7.Switching circuits and modulation of a microwave signal.
SCHOTTKY BARRIER DIODE (SBD)
It is a simple metal semiconductor interface exhibiting a non- linear impedance and
is basically an extension of the point contact diode. When the diodes are forward
biased current flows because of majority carriers from semiconductor into the metal.
Minority carriers are virtually absent compared with p-n junction diodes, These
diodes have very less reverse recovery times and almost nil storage capacitance,
Silicon is most commonly used although GaAs finds use at higher frequencies.
SBD’s have their main applications in microwave detection and mixing. Available
SBD’s have frequency range up to 100 GHz and noise figures of 4 dB at 2 GHz and
15 dB at 100 GHz. At still higher frequencies (1000 GHz to 2000 GHz), point
contact diodes have an edge over SBD’s because of their lower shunt capacitance.
They can be used as both varactors and varistors over a wide frequency range.
Construction
A SBD consists of a metal base on which a silicon pellet is mounted. A spring
loaded wire with a sharp point makes contact with the polished surface of the semiconductor pellet. The other connections are made as shown in Fig. Such construction
can be easily mounted into coaxial or wave guide lines. They are noisier above 10
GHz.
144
Fig. Construction of a Schottky barrier diode
Operation
Since there is a contact between a semiconductor and a metal in a SBD, It results in
a potential barrier at the interface. The I-V and C- V characteristics being similar to
those of p-n junctions with lower break down voltage and also due to extremely high
electron number densities, the depletion region on the metal side is very small.
When the contact is made, electrons in the conduction band of the semiconductor,
which were at a higher energy level flow into the metal (n type metal interface is
considered). This depletion of electrons builds up a positive space charge in the
semiconductor and an electric field opposes further flow. This leads to the creation
of barrier at the interface which is due to the differences in the work functions of the
two materials. In a SBD’s the n-type semiconductor width is assumed to be wider
than the barrier region width, w. In most barrier types, the n-type semiconductor
width is narrower than the barrier width.
Under forward bias the barrier height is reduced. Electrons will be infected into the
metal with an approximately exponential V-I characteristic. Under reverse bias, the
barrier height is increased and the electron infection almost ceases.
Applications
1.Low noise mixer: Schottky barrier diodes are increasingly being used as a load
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noise mixer replacing tunnel diodes and varactors, due to their low cost, simplicity
and reliability noise figures of 4 to 5 dB are common.
2.Balanced mixer in a CW Radar.
3.Microwave detectors.
TRAPATT DIODE
It is derived from the IMPATT diode and is closely related to it. It is a high
efficiency microwave generator capable of operating from several hundred MHz to
several GHz. The basic operation of the oscillator is a semiconductor p-n junction
diode reverse biased to current densities well in excess of those encountered in
normal avalanche operation.
It is typically p+ - n - n+ Si or GaAs structure.
Fig. Schematic arrangement of TRAPATT diode
Operation
A high field avalanche zone propagates through the diode and fills the depletion
region with a dense plasma of electrons and holes that become trapped in the low
field region behind the zone.
In Fig. AB shows charging, BC shows plasma formation, DE shows B plasma
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extraction, EF shows residual extraction, and FG shows charging.
EXERCISE- 6.2
1) Give the names of some microwave devices .What are their applications?
2) Explain tunnel diode with Volt-amp characteristics.
3) What are the advantages of Gunn diode over Impatt diode?
4) What are the applications of Impatt Diode?
5) What is a varactor diode? What are its applications?
6) Write a short note on Schottky Barrier diode and Trapatt diode.
6.6 UNIT SUMMARY
(i)An electronic device is any physical entity in an electronic system used to affect
the electrons or their associated fields in a desired manner consistent with the
intended function of the electronic system.
(ii) The MOSFETS is an abbreviation for metal-oxide semiconductor field-effect
transistor.
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(iii) MESFETS (Metal Semiconductor Field Effect Transistors) are unipolar
microwave transistors that have several advantages compared to bipolar microwave
transistors.
(iv) Tunnel diode is a specially made p-n junction device which exhibits negative
resistance over part of the forward bias characteristic.
(v)A parametric amplifier is one that uses a non-linear reactance (capacitive or
inductive) or a time varying reactance for its amplification (rather than resistance as
in a normal amplifier).
(vi) Schottky Barrier Diode (SBD) is a simple metal semiconductor interface
exhibiting a non- linear impedance and is basically an extension of the point contact
diode.
6.7 REFERENCES
1) A Textbook of Electronic Devices and Circuits by R.S. Sedha, S. Chand &
Company
2) Electronic Devices and Circuits by Millman and Halkias, S. Chand & Company
Ltd.
3) Electronic Devices and Circuits an Introduction by Mottershed
4) Transistor Physics by Sarkar
5) Principles of Electronics by V.K. Mehta, S. Chand & Company Ltd.
6) Electronic Devices and Circuits by Sanjeev Gupta, Dhanpat Rai Publications.
SOLUTION
EXERCISE- 6.1
1) Refer to article 6.3, 2) Refer to article 6.3, 3) Refer to article 6.3
EXERCISE- 6.2
1) Refer to article 6.4, 2) Refer to article 6.4, 3) Refer to article 6.4, 4) Refer to
article 6.5, 5) Refer to article 6.5, 6) Refer to article 6.5
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BLOCK-III
UNIT: VII
PHOTONIC DEVICES
7.0 INTRODUCTION
The science of photonics includes
the
eneration, emission, transmission,
modulation, signal processing, switching, amplification, detection and sensing of
light. The term photonics thereby emphasizes that photons are neither particles nor
waves — they are different in that they have both particle and wave nature.
7.1 OBJECTIVES
Study of Photonic Devices covers all technical applications of light over the
whole spectrum from ultraviolet over the visible to the near-, mid- and far-infrared.
Most applications, however, are in the range of the visible and near infrared light.
7.2 RADIOTIVES AND NON-RADIOTIVE TRANSMITTERS
In electronics and telecommunications a transmitter or radio
transmitter is
an electronic device which, with the aid of an antenna, produces radio waves. The
transmitter itself generates a radio frequency alternating current, which is applied to
the antenna. When excited by this alternating current, the antenna radiates radio
waves. In addition to their use in broadcasting, transmitters are necessary component
parts of many electronic devices that communicate by radio, such as cell
phones and Bluetooth enabled devices, garage door openers, two-way radios in
aircraft,
ships,
and
spacecraft, radar sets,
and
navigational
beacons.
The
term transmitter is usually limited to equipment that generates radio waves for
communication purposes;
or radiolocation,
such
as radar and
navigational
transmitters. Generators of radio waves for heating or industrial purposes, such
as microwave ovens or diathermy equipment, are not usually called transmitters even
though they often have similar circuits.
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7.3 LDR
A photo-resistor, light dependent resistor (LDR) or cadmium sulphide (CdS) cell is
a resistor whose resistance decreases with increasing incident light intensity. It can
also be referred to as a photoconductor.
A photo-resistor is made of a high resistance semiconductor. If light falling on the
device is of high enough frequency, photons absorbed by the semiconductor give
bound electrons enough energy to jump into the conduction band. The resulting free
electron (and its whole partner) conduct electricity, thereby lowering resistance.
A photoelectric device can be either intrinsic or extrinsic. An intrinsic
semiconductor has its own charge carriers and is not an efficient semiconductor, e.g.
silicon. In intrinsic devices the only available electrons are in the valence band, and
hence the photon must have enough energy to excite the electron across the
entire band gap. Extrinsic devices have impurities, also called dopants, added whose
ground state energy is closer to the conduction band; since the electrons do not have
as far to jump, lower energy photons (i.e., longer wavelengths and lower
frequencies) are sufficient to trigger the device. If a sample of silicon has some of its
atoms replaced by phosphorus atoms (impurities), there will be extra electrons
available for conduction. This is an example of an extrinsic semiconductor.
7.4 PHOTODIODE DETECTORS
A photodiode detector consists of a small PIN photodiode, integrally coupled to a
scintillation crystal, often CsI(Tl). As a standard rule, a charge sensitive preamplifier
is incorporated in the assembly.
The intrinsic noise of the photodiode/preamplifier combination prohibits the use of
large scintillation crystals for detection of low energy (< 1 MeV) gamma-rays. This
noise determines the lowest energy that can be detected with the device. CsI(Tl)
crystals of 1 cm3 coupled to 10x10 mm2 PIN photodiodes can be used down to 40
keV; for larger crystals (e.g. for 2x2x2.5 cm3 coupled to 18x18 mm2 diodes), this
energy is about 70 keV.
CsI(Tl) crystals do not crack or cleave and photodiodes are shock resistant. Many
configurations are possible. The noise level and energy resolution of the detector
depend very much on the crystal/diode configuration. Contact SCIONIX for your
specific requirement. The noise of photodiode scintillation detectors increases with
temperature. Above 50 o C these instruments are not advised.
150
An important application of photodiode detectors is in physics research for the
detection of charged particles. A thin silicon detector is placed in front of a CsI(Tl)
crystal read out with a photodiode to perform an E / E measurement.
Application





Photodiode scintillation detectors can be used e.g. in applications where:
No high voltage is available or desired (medical applications)
Stable gain is essential (long term environmental monitoring)
High magnetic fields are present (physics research)
A rugged detector is required.
7.5 SOLAR CELLS
The Solar Cells are semiconductor junction devices which are used for
converting optical radiation (Sunlight) into electrical energy. The generated
electric voltage is proportional to the intensity of incident light. Due to their
capability of generating voltage, they are called as photovoltaic cells. A solar
151
cell is a P-N Junction device with no voltage applied directly across the junction.
This converts photon power into electric power and delivers this power to land.
Design requirements of solar cell: Following points are to be considered while
constructing a solar cell:
1. A large area junction should be located near the surface of the device. This is
usually done by construction planar junction by diffusion or ion implantation.
2. The surface is to be coated with appropriate materials to reduce reflection
and to decrease surface recombination.
3. To obtain large photo voltage, heavy doping is required. But too heavy
doping may reduce the lifetime of the device.
4. Series resistance of the device should be very small so that power is not lost
due to ohmic losses.
5. Special design is required for contact.
Figure shows the construction of a solar cell. The cell is a P-N junction diode
with appropriately doped semiconductors. The top P-type layer is made very thin
so that the light radiation may penetrate to fall on junction. The doping levels of
P -doped semiconductor is very high. Every effort is made to ensure that the
surface area perpendicular to sun 9is maximum. P-type material is surrounded by
a nickel planted ring which serves as the positive terminal of the cell. A metallic
contact at the bottom of N-type material acts as the negative terminal. The
Circuit symbol of the cell is shown.
Working
When a photon of light energy collides with the valence electron either in P-type
material or N-type material, it imparts sufficient energy to leave its parent atom.
152
As a result, free electrons and holes are generated on each side of the junction. In
P-type material, the newly generated electrons are minority carriers. These
electrons move freely across the junction with no applied bias. Similarly, in Ntype material, the newly generated holes are minority carriers. These holes move
freely across the junction with no applied bias. The result is an increase in
minority carrier flow. In this way, depletion region potential causes the photon
current to flow through the external load.
Applications
The solar cells have a variety of applications. Few of them are:
(I) In portable exposure meters.
(II) in space satellites.
(III)In low resistance relays for ON and OFF operations.
(IV)Multiple-unit silicon solar cells with controlled spectral response
characteristics act as photovoltaic devices in infra-red region of spectrum. So, it
can be used as infra-red detectors.
Open-Circuit Output Voltage Characteristics
Figure shows a P-N junction solar cell with a resistive load R. When no bias is
applied to junction, an electric field E exists in the space charge. Let us consider
that radiations are allowed to incident on the cell. Now electron-hope pairs are
created in the space charge. They swept out and produce photocurrent IL in
reverse biased direction. This current produces a voltage drop across load and
diode becomes effectively forward biased. As a result, the magnitude of electric
field E decreases. The corresponding forward bias current IF is in a direction
opposite to photocurrent IL. The resultant current is decided by the relative
magnitude of the two component currents. Therefore, net P-N junction current I
is given by.
Where IS is reverse saturation current of P-N junction.
The main parameters on V-I characteristics of solar cells are the forward voltage
at zero current (VOC) and the reverse current at zero bias (ISC).Both of these are
153
induced by the photo-generated excess carriers. Together, the two quantities
determine the maximum power available from the solar cell.
When light is falling on a solar cell, the terminal voltage is determined by the
load resistance it is driving. Therefore, there are two limiting cases of interest:
1. The sort-circuit condition occurs when R=O so that V=O. Then I=ISC=IL.
2. The open-circuit condition occurs when R. The net current (I) is zero
and the voltage produced is the open-circuit voltage. The photocurrent is just
balanced by the forward- biased junction current (IL = IF).
We will now discuss these two limiting cases in some moral details.
When sunlight falls on an unbiased P-N junction, electron-hole pairs are
generated in the depletion region as shown in.
The newly generated electron-hole pairs are collected at the two ends of the
depletion width under the influence of high electric field present across the
depletion width. This gives rise to open circuit voltage VOC.
Short-Circuit Current
The three most important parameters of solar cell are the short-circuit current I
the open-circuit voltage V and fill factor (FF). Fig. shows the V-I characteristics
of a solar cell.
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On the vertical axis, V=0 anywhere and hence represents a short circuit
conditions. The current at this intersection is called as short circuit current. The
short circuit current is represented by ISC. Under open circuit condition Id is
known as open circuited voltage will result. This is known as open Circuited
voltage and is represented by VOC. The term fill factor is used to define the
power extraction efficiency of the cell. The fill factor is an important figure of
merit in solar cell design. Now, we define a parameter called the fill factor (FF)
as
(FF) lies in the range 0.7-0.8 for well designed solar cell.
EXERCISE- 7.1
1) Explain some photonic devices.
2) What is LDR? Expalin its working.
3) What are photo diode detectors? Explain with diagram.
4) What are the applications of photo diode detectors?
5) Explain working of solar cell with the help of diagram.
6) Give V-I characteristics of solar cell.
7) What is fill factor?
7.6 LED
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A light-emitting diode (LED) is a semiconductor light source. LEDs are used as
indicator lamps in many devices, and are increasingly used for lighting.
Introduced as a practical electronic component in 1962, early LEDs emitted lowintensity red light, but modern versions are available across
the visible, ultraviolet and infrared wavelengths, with very high brightness.
When a light-emitting diode is forward biased (switched on), electrons are able
to recombine with electron holes within the device, releasing energy in the form
of photons. This effect is called electroluminescence and the color of the light
(corresponding to the energy of the photon) is determined by the energy gap of
the semiconductor. An LED is often small in area (less than 1 mm2), and
integrated optical components may be used to shape its radiation pattern. LEDs
present many advantages over incandescent light sources including lower energy
consumption, longer lifetime, improved robustness, smaller size, faster
switching, and greater durability and reliability. LEDs powerful enough for room
lighting are relatively expensive and require more precise current and heat
management than compact fluorescent lamp sources of comparable output.
Light-emitting diodes are used in applications as diverse as replacements
for aviation lighting, automotive lighting (particularly brake lamps, turn signals
and indicators) as well as in traffic signals. The compact size, the possibility of
narrow bandwidth, switching speed, and extreme reliability of LEDs has allowed
new text and video displays and sensors to be developed, while their high
switching rates are also useful in advanced communications
technology. Infrared LEDs are also used in the remote control units of many
commercial products including televisions, DVD players, and other domestic
appliances.
7.7 THRESHOLD CURRENT FOR LASING
The lasing threshold is the lowest excitation level at which a laser's output is
dominated by stimulated emission rather than by spontaneous emission. Below
the threshold, the laser's output power rises slowly with increasing excitation.
Above threshold, the slope of power vs. excitation is orders of
magnitude greater. The line-width of the laser's emission also becomes orders of
magnitude smaller above the threshold than it is below. Above the threshold, the
laser is said to be lasing. The term "lasing" is a back formation from "laser,"
which is an acronym, not an agent noun.
Theory
156
The lasing threshold is reached when the optical gain of the laser medium is
exactly balanced by the sum of all the losses experienced by light in one round
trip of the laser's optical cavity. This can be expressed, assuming steady-state
operation, as
.
Here R1 and R2 are the mirror (power) reflectivity, l is the length of the gain
medium,
is the round-trip threshold power gain, and exp (
− 2αl) is the round trip power loss. Note that α > 0. This equation separates the
losses in a laser into localized losses due to the mirrors, over which the
experimenter has control, and distributed losses such as absorption and
scattering. The experimenter typically has little control over the distributed
losses.
The optical loss is nearly constant for any particular laser (α = α0), especially
close to threshold. Under this assumption the threshold condition can be
rearranged as
.
Since R1R2 < 1, both terms on the right side are positive, hence both terms
increase the required threshold gain parameter. This means that minimizing the
gain parameter gthreshold requires low distributed losses and high reflectivity
mirrors. The appearance of l in the denominator suggests that the required
threshold gain would be decreased by lengthening the gain medium, but this is
not generally the case. The dependence on l is more complicated
because α0 generally increases with l due to diffraction losses.
EXERCISE- 7.2
1) What is LED? Write its applications.
2) Write a short note on Threshold current for lasing.
7.8 UNIT SUMMARY
(i) A photo-resistor, light dependent resistor (LDR) or cadmium sulphide (CdS)
cell is a resistor whose resistance decreases with increasing incident light intensity.
It can also be referred to as a photoconductor.
(ii) The Solar Cells are semiconductor junction devices which are used for
157
converting optical radiation (Sunlight) into electrical energy.
(iii) A light-emitting diode (LED) is a semiconductor light source. A light-emitting
diode (LED) is a semiconductor light source.
7.9 REFERENCES
1) A Textbook of Electronic Devices and Circuits by R.S. Sedha, S. Chand &
Company
2) Electronic Devices and Circuits by Millman and Halkias, S. Chand & Company
Ltd.
3) Electronic Devices and Circuits an Introduction by Mottershed
4) Transistor Physics by Sarkar
5) Principles of Electronics by V.K. Mehta, S. Chand & Company Ltd.
6) Electronic Devices and Circuits by Sanjeev Gupta, Dhanpat Rai Publications.
SOLUTION
EXERCISE- 7.1
1) Refer to article 7.2, 2) Refer to article 7.3, 3) Refer to article 7.4, 4) Refer to
article 7.4, 5) Refer to article 7.5, 6) Refer to article 7.5, 7) Refer to article 7.5
EXERCISE- 7.3
1) Refer to article 7.6, 2) Refer to article 7.7
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