ELECTRONIC CIRCUITS
EE451
1
H. Chan; Mohawk College
MAIN TOPICS (2nd half)

Analog & Switching Power Supplies







Review of rectification & filtering
Review of zener diode as a voltage regulator
Transistor series shunt voltage regulators
Transistor current regulators
IC voltage regulators (e.g. 78/79XX, LM317)
Switching-mode regulators (e.g. LH1605)
Linear Integrated Circuit Applications
 BiFET & Norton op-amps, 555 timer, 8038 function
generator, active filters, etc.
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2
Power Supply Block Diagram
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3
Half-Wave Rectifier
VP  2 VS  0.7
 0.00833

Vdc  VP 1 
R L CF 

V
t
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0.0048VP
Vr 
R L CF
4
Full-Wave Rectifier
VP  0.707Vs  0.7
 0.00417

Vdc  VP 1 
R LCF 

V
t
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0.0024VP
Vr 
R L CF
5
Bridge-Type Rectifier
VP  2 Vs 1.4
 0.00417

Vdc  VP 1 
R LCF 

V
t
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0.0024VP
Vr 
R L CF
6
More Equations . . .
Rearranging the previous equations: VP = Vdc + 1.736 Vr
The ripple voltage as a percentage of the dc voltage is:
Vr
% ripple 
x100
Vdc
The diode(s) must be rated to withstand the surge current:
I surge
VP

RW
where RW is the transformer winding’s
resistance given by:
VNL  VFL
RW 
I FL
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7
Comparison of Different Types of Rectifiers



Half-wave rectifier needs only a single diode but
ripple is twice those of the other types.
Full-wave rectifier requires a centre-tapped
transformer and its output voltage is about half
those of the other types.
Bridge-type rectifier is best overall even though
it requires four diodes because the diode bridge is
often available in a single package. However, if
a single diode in the bridge is defective, the
whole package has to be replaced.
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8
Line Regulation
is a measure of the effectiveness of a voltage regulator
to maintain the output dc voltage constant despite
changes in the supply voltage.
Vo
Line regulation(m V / V ) 
Vi
Vo 100
% line regulation
x
Vi Vo
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9
Load Regulation
is a measure of the ability of a regulator to maintain a
constant dc output despite changes in the load current.
Vo
Load regulation(m V / A) 
I L
Vo 100
% load regulation
x
I L Vo
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10
Other Specifications
A common definition for voltage regulation is:
VNL  VFL
Voltageregulation(%) 
x100
VFL
The ability to reduce the output ripple voltage is:
Ripplerejection (dB)  20log
Vr (out )
Vr (in)
Vo
 or m
Source resistance of regulator is: Rs 
I L
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Zener Diode Voltage Regulator
I-V Characteristic
Circuit
IZM
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Notes on Zener Diode Regulator



VZ depends on I and temperature.
Zener diodes with rated voltage < 6 V have
negative temperature coefficient; those rated > 6
V have positive temperature coefficient.
In order to maintain a constant Vo, IZT varies in
response to a change of either IL or Vi. For
example, when RL increases, IL decreases, then
IZT has to increase to keep the current through Rs
constant. Since the voltage drop across Rs is
constant, Vo stays constant.
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13
Formulae for Zener Regulator Circuit
Rs establishes the zener bias current, IZT:
Vi  VZ Vi  VZ
Rs 

I Rs
I ZT  I L
For fixed Vi, but variable RL:
RsVZ
VZ
min. RL 

I Rs Vi  VZ
max. RL 
VZ
I L (min)
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VZ

I Rs  I ZM
14
Formulae (cont’d)
For fixed RL, but variable Vi:
RL  Rs
min .Vi 
VZ
RL
max.Vi  I R (max) Rs  VZ
where I R (max)  I ZM  I L
The output ripple voltage of the zener regulator is:
Vr ( out )
RL // RZ

Vr (in) where RZ = ac resistance
of zener diode.
RL // RZ  Rs
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Transistor Series Voltage Regulator
The simple zener regulator
can be markedly improved
by adding a transistor.
Since VBE = VZ - VL any
tendency for VL to decrease
or increase will be negated
by an increase or decrease in IE. The dc currents for the
circuit are:
Vi  VZ
VL VZ  VBE
IL 

; IR 
RL
RL
R
IL = hFEIB; IZT = IR - IB
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16
Transistor Shunt Voltage Regulator
Since VBE = VL - VZ,
any tendency for VL
to increase or decrease
will result in a
corresponding increase or decrease in IRs. This will
oppose any changes in VL because VL = Vi - IRsRs.
VL VZ  VBE
Vi  (VZ  VBE )
IL 

; I Rs 
RL
RL
RS
IE = IRs - IL = hFEIZT
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17
Op-Amp Voltage Regulators
Series
Shunt
 R2 
VZ
Vo  1 
 R3 
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Notes on Op-Amp Voltage Regulator




More flexibility possible in design of voltage
output than IC voltage regulator packages.
The essential circuit elements are: a zener
reference, a pass or shunt transistor, a sensing
circuit, and an error/amplifier circuit.
Equation indicates that Vo depends on R2, R3, and
VZ.
The shunt configuration is less efficient but R2
offers short-circuit current limiting.
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Constant Current Limiting
can be used for short-circuit or overload protection of
the series voltage regulator.
Output current
is limited to:
0.7
I L (max) 
R4
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Fold-back Current Limiting
is a better method of short-circuit protection.
VBE 2
R6
 VB 2  Vo 
(Vo  I L R4 )  Vo
R5  R6
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21
Design Equations for Fold-back Current Limiting
Maximum load current without fold-back limiting:
R5Vo  0.7( R5  R6 )
I L (max) 
R4 R6
Output voltage under current limiting condition:
0.7( R5  R6 ) RL
Vo ' 
R 4 R6  R5 RL
The short circuit current (i.e. when Vo = 0) is:
0.7( R5  R6 )
I short 
R4 R6
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22
Characteristics of Fold-back Limiting
Vo


IL
Notice that Ishort < IL(max)
and that Vo is regulated
(i.e. constant) only after
RL > a certain critical
value.
For designing purpose,
R5 + R6 = 1 k and if
Ishort and IL(max) are
specified then
07Vo
R4 
I short (Vo  0.7)  0.7 I L (max)
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23
Transistor Current Regulators
are designed to maintain a fixed current through a
load for variations in either Vi or RL.
For the BJT circuit, VEB = VZ - VRE.
Any tendency for IL to change will
cause an opposing change in VEB,
thus nullifying the perturbation.
For the JFET circuit, IL = ID = IDSS as
long as VL < VSS - VP.
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IC Voltage Regulators



There are basically two kinds of IC voltage
regulators:
 Multipin type, e.g. LM723C
 3-pin type, e.g. 78/79XX
Multipin regulators are less popular but they
provide the greatest flexibility and produce the
highest quality voltage regulation
3-pin types make regulator circuit design simple
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25
Multipin IC Voltage Regulator


The LM723 has an
equivalent circuit that
contains most of the
parts of the op-amp
voltage regulator
discussed earlier.
It has an internal voltage
reference, error
amplifier, pass transistor,
and current limiter all in
one IC package.
LM 723C Schematic
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Notes on LM723 Voltage Regulator





Can be either 14-pin DIP or 10-pin TO-100 can
May be used for either +ve or -ve, variable or
fixed regulated voltage output
Using the internal reference (7.15 V), it can
operate as a high-voltage regulator with output
from 7.15 V to about 37 V, or as a low-voltage
regulator from 2 V to 7.15 V
Max. output current with heat sink is 150 mA
Dropout voltage is 3 V (i.e. VCC > Vo(max) + 3)
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LM723 in High-Voltage Configuration
Design equations:
Vo 
Vref ( R1  R2 )
R1R2
R3 
R1  R2
External pass transistor and
current sensing added.
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R2
Rsens
0.7

I max
Choose R1 + R2 = 10 k,
and Cc = 100 pF.
To make Vo variable,
replace R1 with a pot.28
LM723 in Low-Voltage Configuration
I L (max)
R 4 Vo  0.7(R 4  R 5 )

R 5 R sens
I short
R sens
With external pass transistor
and foldback current limiting
R 2 Vref
Vo 
R1  R 2
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0.7(R 4  R 5 )

R 5 R sens
0.7Vo

Ishort (Vo  0.7)  0.7I L (max)
Under foldback condition:
0.7R L (R 4  R 5 )
Vo ' 
R 5 R sens  R 4 R L
29
Three-Terminal Fixed Voltage Regulators







Less flexible, but simple to use
Come in standard TO-3 (20 W) or TO-220 (15
W) transistor packages
78/79XX series regulators are commonly
available with 5, 6, 8, 12, 15, 18, or 24 V output
Max. output current with heat sink is 1 A
Built-in thermal shutdown protection
3-V dropout voltage; max. input of 37 V
Regulators with lower dropout, higher in/output,
and better regulation are available.
30
H. Chan; Mohawk College
Basic Circuits With 78/79XX Regulators


Both the 78XX and 79XX regulators can be used to
provide +ve or -ve output voltages
C1 and C2 are generally optional. C1 is used to cancel any
inductance present, and C2 improves the transient
response. If used, they should preferably be either 1 mF
tantalum type or 0.1 mF mica type capacitors.
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Dual-Polarity Output with 78/79XX Regulators
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78XX Regulator with Pass Transistor




0.7
R1 
I max
0.7
R2 
I R2
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
Q1 starts to conduct
when VR2 = 0.7 V.
R2 is typically chosen so
that max. IR2 is 0.1 A.
Power dissipation of Q1
is P = (Vi - Vo)IL.
Q2 is for current limiting
protection. It conducts
when VR1 = 0.7 V.
Q2 must be able to pass
max. 1 A; but note that
max. VCE2 is only 1.4 V.
33
78XX Floating Regulator


Vo  Vreg
 Vreg

 
 I Q  R2
 R1

or
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It is used to obtain an
output > the Vreg value
up to a max.of 37 V.
R1 is chosen so that
R1  0.1 Vreg/IQ, where
IQ is the quiescent
current of the regulator.
R2 
R1 (Vo  Vreg )
Vreg  I Q R1
34
3-Terminal Variable Regulator

The floating regulator could be made into a
variable regulator by replacing R2 with a pot.
However, there are several disadvantages:
 Minimum output voltage is Vreg instead of 0 V.
 IQ is relatively large and varies from chip to chip.
 Power dissipation in R2 can in some cases be quite
large resulting in bulky and expensive equipment.

A variety of 3-terminal variable regulators are
available, e.g. LM317 (for +ve output) or LM
337 (for -ve output).
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Basic LM317 Variable Regulator Circuits
(a)
Circuit with capacitors
to improve performance
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(b)
Circuit with protective
diodes
36
Notes on Basic LM317 Circuits



The function of C1 and C2 is similar to those used
in the 78/79XX fixed regulators.
C3 is used to improve ripple rejection.
Protective diodes in circuit (b) are required for
high-current/high-voltage applications.
Vo  Vref
R2 
where Vref = 1.25 V, and Iadj is
 Vref

 
 I adj  R2 the current flowing into the adj.
 R1

terminal (typically 50 mA).
R1 (Vo  Vref )
Vref  I adj R1
R1 = Vref /IL(min), where IL(min)
is typically 10 mA.
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Other LM317 Regulator Circuits
Circuit with pass transistor
and current limiting
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Circuit to give 0V min.
output voltage
38
Block Diagram of Switch-Mode Regulator
It converts an unregulated dc input to a regulated dc
output. Switching regulators are often referred to as
dc to dc converters.
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39
Comparing Switch-Mode to Linear Regulators
Advantages:




70-90% efficiency (about double that of linear ones)
can make output voltage > input voltage, if desired
can invert the input voltage
considerable weight and size reductions, especially at
high output power
Disadvantages:
 More complex circuitry
 Potential EMI problems unless good shielding, lowloss ferrite cores and chokes are used
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40
General Notes on Switch-Mode Regulator
The duty cycle of the series transistor (power switch) determines
the average dc output of the regulator. A circuit to control the
duty cycle is the pulse-width modulator shown below:
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General Notes cont’d . . .




The error amplifier compares a sample of the regulator
Vo to an internal Vref. The difference or error voltage is
amplified and applied to a modulator where it is
compared to a triangle waveform. The result is an output
pulse whose width is proportional to the error voltage.
Darlington transistors and TMOS FETs with fT of at least
4 MHz are often used. TMOS FETs are more efficient.
A fast-recovery rectifier, or a Schottky barrier diode
(sometimes referred to as a catch diode) is used to direct
current into the inductor.
For proper switch-mode operation, current must always
be present in the inductor.
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42
Step-Down or Buck Converter



When the transistor is turned ON, VL is initially high but
falls exponentially while IL increases to charge C.
When the transistor turns OFF, VL reverses in polarity to
maintain the direction of current flow. IL decreases but
its path is now through the forward-biased diode, D.
Duty cycle is adjusted according to the level of Vo.
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43
V & I Waveforms for Buck Regulator
PWM
output
VL
IL
Vo
Normal
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Low Vo
High Vo
44
Equations for Buck Regulator
Vo
ton
ton


Vi ton  toff
T
Selecting IL = 0.4Io where Io
is the max. dc output current:
2.5Vo (Vi  Vo )
L
I oVi f osc
0.05I o
0.01768I o
C
or
V pp f osc
Vrms f osc
where V is the ripple voltage
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45
Notes on Operation of Buck Regulator



When IL = 0.4Io was selected, the average
minimum current, Imin, that must be maintained
in L for proper regulator operation is 0.2Io.
If IL is chosen to be 4% instead of 40% of Io,
the 2.5 factor in the equation for L becomes 25
and Imin becomes 0.02Io.
L and C are both proportional to 1/fosc; hence, the
higher fosc is the smaller L and C become. But
for predictable operation and less audible noise,
fosc is usually between 50kHz to 100 kHz.
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46
Step-Up, Flyback, or Boost Regulator


Assuming steady-state conditions, when the transistor is
turned ON, L reacts against Vin. D is reverse-biased and
C supplies the load current.
When the transistor is OFF, VL reverses polarity causing
current to flow through D and charges C. Note that Vout
is > Vin because VL adds on to Vin.
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47
Equations for Boost Regulator
Vo  Vi ton

Vo
T
Assuming IL = 0.4Io:
2.5Vi (Vo  Vi )
L
I oVo2 f osc
2
(Vo  Vi ) I o
0.3536(Vo  Vi ) I o
C
or
f oscVo V pp
f oscVo Vrms
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48
Voltage-Inverting or Buck-Boost Regulator



Vo can be either step-up or step-down and its polarity is
opposite to input.
During ON period, Vin is across L, and D is reversebiased.
During OFF period, VL reverses polarity causing current
to flow through C and D.
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49
Equations for Buck-Boost Regulator
Vo
ton

Vi  Vo T
For IL = 0.4Io:
2.5ViVo
L
I o (Vo  Vi ) f osc
I oVo
0.3536I oVo
C
or
Vpp (Vi  Vo ) f osc
Vrms (Vi  Vo ) f osc
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50
Basic Push-Pull Power Converter
Operates as a class D power amplifier. Output rectifier converts
the square-wave to dc. Each transistor must withstand 2xVin plus
voltage spikes.
51
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Basic Half-Bridge Power Converter
Each transistor “sees” approx. Vin. Full flux reversal in the
transformer and capacitors across DS prevent voltage spikes.
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52
Basic Full-Bridge Power Converter
Either Q1 & Q3 or Q2 & Q4 are turned ON simultaneously.
Ideal for high power applications.
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53
Single-Package Switch-Mode Regulator



The LH1605 is a 5A step-down switching regulator.
Vo is adjustable from 3 to 30 V by using a pot. for R1.
In the circuit above, Q1 turns ON when voltage across
Rsens is 0.7 V. Q2 then turns ON shorting Vref to ground
and driving Vo to zero. .
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54
Equations for LH1605 Switching Regulator
Vo  2.5  0.00125R1 or
R1  800Vo  2000
With IL = 0.4Io:
1
CT 
40000f osc
2.5Vo (Vi  Vo )
L
I oVi f osc
0.01768I o
0.05I o
C
or
Vrms f osc
V pp f osc
Rsens
0.7

I max
Typically, CF = CC = 10 mF; RB = 10 k
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55
BiFET IC Operational Amplifier
Advantages of TL081 vs bipolar op-amp (LM741):







higher input impedance (typically 1012 )
wider unity-gain bandwidth (3 MHz)
higher slew rate (13 V/ms typical)
lower offset current (5 pA)
lower bias current (30 pA)
lower power consumption (1.4 mA supply current)
All other parameters are comparable to bipolar
op-amps.
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56
Frequency Compensation



Most op-amps contain a small internal
compensating capacitor (15 to 30 pF) for
ensuring stability at the expense of bandwidth.
For a specific application requiring a wider
bandwidth, an uncompensated op-amp, such as
the TL080, may be chosen with a small external
compensating capacitor.
Two commonly used methods are: conventional
compensation and feed-forward compensation.
The latter method can increase the BW 5 to 10 x.
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57
Circuits for Frequency Compensation
Conventional
C1 is typ.10 to 20 pF
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Feed-forward
C1 is typ. 100 to 150 pF
58
Response With Frequency Compensation
Av
With feed-forward
compensation
Increase
in BW
With normal
compensation
1k
10k
100k
Hz
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1M
10M
f
59
Astable Multivibrator or Relaxation Oscillator
Circuit
Output waveform
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60
Equations for Astable Multivibrator
VUT
 Vsat R2
 Vsat R2

; VLT 
R1  R2
R1  R2
 R1  2 R2  where
Assuming

|+Vsat| = |-Vsat| T  t1  t 2  2 ln

R1
  = RfC
If R2 is chosen to be 0.86R1, then T = 2RfC and
1
f 
2R f C
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61
Monostable (One-Shot) Multivibrator
Circuit
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Waveforms
62
Notes on Monostable Multivibrator



Stable state: vo = +Vsat, VC = 0.6 V
Transition to timing state: apply a -ve input pulse such
that |Vip| > |VUT|; vo = -Vsat. Best to select RiCi 
0.1RfC.
Timing state: C charges negatively from 0.6 V through
Rf. Width of timing pulse is: t  R C ln | Vsat | 0.6 
p
f
 | V | V 
LT 
 sat
If we pick R2 = R1/5, then tp = RfC/5.
Recovery state: vo = +Vsat; circuit is not ready for retriggering
until VC = 0.6 V. The recovery time  tp. To speed up the
recovery time, RD (= 0.1Rf) & CD can be added.

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63
Norton or Current-Mode Op-Amp



Simplified circuit

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Amplifies I (= I- - I+)
between the inputs.
Q3 and D1 form a
current mirror (ICQ3 
ID1). In practice, two
matched transistors are
used; the 1st transistor
connected as a diode.
Current into base of Q1
IB1 = I.
Note that VB  0.7 for
both Q1 & Q2.
64
Notes on LM3900 Op-Amp






Comes in a standard 14-pin DIP quad package.
Can operate from a single supply (4 to 32 V) or
dual supplies (±2 to ±16 V).
Rin = 1 M, Rout = 8 k
Aol = 2800
Unity-gain bandwidth = 2.5 MHz (much better
than the LM741)
Not as widely used as voltage op-amps because
circuit designers are less familiar with it.
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65
Norton Amplifiers
Design equations for inverting
and non-inverting amplifiers
are exactly the same:
Zin = RI ;
Inverting
Non-inverting
RF
Av 
RI
Neglecting RS and Ro:
1
Cin 
2f cL RI
Cout
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1

2f cL RL
66
Other Design Equations for Norton Amplifier
The dc output offset voltage:
Voffset
RF (VCC  0.7)

 0.7
RB
For max. swing, Voffset = VCC/2, thus
(VCC  0,7) RF
RB 
VCC / 2  0.7
Note that if dual polarity supply is used,
Voffset can be made to be 0V and Cout
would not be required for both circuits.
H. Chan; Mohawk College
Since max. Iin = 20 mA dc,
VCC  0.7
RB (min) 
0.02
VCC  1.4
RF (min) 
0.04
Also, min. input bias
current is 200 nA, 
VCC  0.7
RB (max) 
200nA
VCC  1.4
RF (max) 
400nA
67
Functional Block Diagram of LM555
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68
Notes on 555 Timer/Oscillator IC







Widely used as a monostable or astable
multivibrator.
Can operate between 4.5 and 16 V.
Output voltage is approximately 2 V < VCC.
Output can typically sink or source 200 mA.
Max. output frequency is about 10 kHz.
fo varies somewhat with VCC.
Threshold input (pin 6) and trigger input (pin 2)
are normally tied together to external timing RC.
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69
555 as a Simple Oscillator
Duty cycle is:
tch
R1  R2
D

T R1  2R2
Given fo and D,
2D  1
1 D
R1 
; R2 
0.693f oC1
0.693f oC1
tch = 0.693(R1 + R2)C1
tdisch = 0.693 R2C1
T = 0.693(R1 + 2R2)C1
H. Chan; Mohawk College
Note that D must always be > 0.5.
To get 50% duty cycle, R1 = 0,
which would short out VCC.
70
555 Square-Wave Oscillator
R1
D
R1  R2
R1 
D
1 D
; R2 
0.693f oC1
0.693f oC1
For 50% duty cycle,
tch = 0.693 R1C1 ; tdisch = 0.693 R2C1
1
fo 
0.693( R1  R2 )C1
H. Chan; Mohawk College
1
R1  R2 
1.386 f oC1
71
555 as a Timer / Monostable Multivibrator
t = 1.1 R1C1
Time pulses from a few
ms to many minutes are
possible. The main
limitation for very long
time delays is the
leakage in the largevalue capacitor required
for C1.
R2 (typically 10 k) is a pull-up resistor.
C2 (typically 0.001 mF) is for bypass.
Timing starts when trigger input is grounded.
H. Chan; Mohawk College
72
ICL8038 Function Generator IC



H. Chan; Mohawk College
Triangle wave at pin10 is
obtained by linear charge
and discharge of C by
two current sources.
Two comparators trigger
the flip-flop which
provides the square wave
and switches the current
sources.
Triangle wave becomes
sine wave via the sine
converter .
73
Notes on ICL8038 IC




To obtain a square wave output, a pull-up
resistor (typically 10 to 15 k) must be
connected between pin 9 and VCC.
Triangle wave has a linearity of 0.1 % or better
and an amplitude of approx. 0.3(VCC-VEE).
Sine wave can be adjusted to a distortion of < 1%
with amplitude of 0.2(VCC-VEE). The distortion
may vary with f (from 0.001 Hz to 200 kHz).
IC can operate from either single supply of 10 to
30 V or dual supply of 5 to 15 V.
H. Chan; Mohawk College
74
ICL8038 Function Generator Circuit
fo 
3(VCC  Vsweep )
2 RC1Vtotal
where R = RA = RB
If pin 7 is tied to pin 8,
fo 
3


RA


5RAC1 1 
 2 RA  RB 
For 50 % duty cycle,
+VCC > Vsweep > Vtotal + VEE + 2
where Vtotal = VCC + |VEE|
H. Chan; Mohawk College
fo 
0.3
RC1
75
Active Filters


Active filters use op-amp(s) and RC components.
Advantages over passive filters:





op-amp(s) provide gain and overcome circuit losses
increase input impedance to minimize circuit loading
higher output power
sharp cutoff characteristics can be produced simply
and efficiently without bulky inductors
Single-chip universal filters (e.g. switchedcapacitor ones) are available that can be
configured for any type of filter or response.
H. Chan; Mohawk College
76
Review of Filter Types & Responses




4 major types of filters: low-pass, high-pass,
band pass, and band-reject or band-stop
0 dB attenuation in the passband (usually)
3 dB attenuation at the critical or cutoff
frequency, fc (for Butterworth filter)
Roll-off at 20 dB/dec (or 6 dB/oct) per pole
outside the passband (# of poles = # of reactive
elements). Attenuation at any frequency, f, is:
 f 
atten. (dB) at f  log  x atten. (dB) at f dec
 fc 
H. Chan; Mohawk College
77
Review of Filters (cont’d)



Bandwidth of a filter: BW = fcu - fcl
Phase shift: 45o/pole at fc; 90o/pole at >> fc
4 types of filter responses are commonly used:
 Butterworth - maximally flat in passband; highly nonlinear phase response with frequecny
 Bessel - gentle roll-off; linear phase shift with freq.
 Chebyshev - steep initial roll-off with ripples in
passband
 Cauer (or elliptic) - steepest roll-off of the four types
but has ripples in the passband and in the stopband
H. Chan; Mohawk College
78
Frequency Response of Filters
A(dB)
A(dB)
LPF
A(dB)
HPF
BPF
Passband
fc
f
f
fc
A(dB)
fcl
f
fcu
A(dB)
Butterworth
BRF
Chebyshev
Bessel
fcl
fcu
f
H. Chan; Mohawk College
f
79
Unity-Gain Low-Pass Filter Circuits
2-pole
3-pole
4-pole
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80
Design Procedure for Unity-Gain LPF
 Determine/select number of poles required.
 Calculate the frequency scaling constant, Kf = 2f
 Divide normalized C values (from table) by Kf to obtain
frequency-scaled C values.
 Select a desired value for one of the frequency-scaled C
values and calculate the impedance scaling factor:
frequency scaled C value
Kx 
desired C value
 Divide all frequency-scaled C values by Kx
 Set R = Kx 
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81
An Example
Design a unity-gain LP Butterworth filter with a critical
frequency of 5 kHz and an attenuation of at least 38 dB at
15 kHz.
The attenuation at 15 kHz is 38 dB
 the attenuation at 1 decade (50 kHz) = 79.64 dB.
We require a filter with a roll-off of at least 4 poles.
Kf = 31,416 rad/s. Let’s pick C1 = 0.01 mF (or 10 nF). Then
C2 = 8.54 nF, C3 = 24.15 nF, and C4 = 3.53 nF.
Pick standard values of 8.2 nF, 22 nF, and 3.3 nF.
Kx = 3,444
Make all R = 3.6 k (standard value)
H. Chan; Mohawk College
82
Unity-Gain High-Pass Filter Circuits
2-pole
3-pole
4-pole
H. Chan; Mohawk College
83
Design Procedure for Unity-Gain HPF


The same procedure as for LP filters is used
except for step #3, the normalized C value of 1 F
is divided by Kf. Then pick a desired value for
C, such as 0.001 mF to 0.1 mF, to calculate Kx.
(Note that all capacitors have the same value).
For step #6, multiply all normalized R values
(from table) by Kx.
E.g. Design a unity-gain Butterworth HPF with a critical
frequency of 1 kHz, and a roll-off of 55 dB/dec. (Ans.: C
= 0.01 mF, R1 = 4.49 k, R2 = 11.43 k, R3 = 78.64 k.;
pick standard values of 4.3 k, 11 k, and 75 k).
H. Chan; Mohawk College
84
Equal-Component Filter Design
2-pole LPF
Same value R & same value C
are used in filter.
Select C (e.g. 0.01 mF), then:
1
R
2f oC
2-pole HPF
Av for # of poles is given in
a table and is the same for
LP and HP filter design.
RF
Av 
1
RI
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85
Example
Design an equal-component LPF with a critical
frequency of 3 kHz and a roll-off of 20 dB/oct.
Minimum # of poles = 4
Choose C = 0.01 mF;  R = 5.3 k
From table, Av1 = 1.1523, and Av2 = 2.2346.
Choose RI1 = RI2 = 10 k; then RF1 = 1.5 k, and
RF2 = 12.3 k .
Select standard values: 5.1 k, 1.5 k, and 12 k.
H. Chan; Mohawk College
86
BPF
fcl fctr fcu
f
Attenuation (dB)
Attenuation (dB)
Bandpass and Band-Rejection Filter
BRF
fcl
The quality factor, Q, of a filter is given by:
where BW = fcu - fcl and
f ctr 
fctr
f
fcu
f ctr
Q
BW
f cu f cl
H. Chan; Mohawk College
87
More On Bandpass Filter
If BW and fcentre are given, then:
2
BW 2
BW
BW
BW
2
2
f cl 
 f ctr 
; f cu 
 f ctr 
4
2
4
2
A broadband BPF can be obtained by combining a LPF and a HPF:
The Q of
this filter
is usually
> 1.
H. Chan; Mohawk College
88
Broadband Band-Reject Filter
A LPF and a HPF can also be combined to give a broadband
BRF:
2-pole band-reject filter
H. Chan; Mohawk College
89
Narrow-band Bandpass Filter
f ctr
1
BW 

Q 2R1C
C1 = C2 = C
R2 = 2 R1
R1
R3 
2Q 2  1
f ctr
1
R1

1
R3
2 2R1C
R3 can be adjusted or trimmed
to change fctr without affecting
the BW. Note that Q < 1.
H. Chan; Mohawk College
90
Narrow-band Band-Reject Filter
Easily obtained by combining the inverting output of a
narrow-band BRF and the original signal:
The equations for R1, R2, R3, C1, and C2 are the same as before.
RI = RF for unity gain and is often chosen to be >> R1.
H. Chan; Mohawk College
91