ELECTRONIC CIRCUITS- I
DC Biasing Circuits
•
The ac operation of an
amplifier depends on the initial
dc values of IB, IC, and VCE.
•
By varying IB around an initial
dc value, IC and VCE are made
to vary around their initial dc
values.
•
DC biasing is a static operation
since it deals with setting av in
fixed (steady) level of current
(through the device) with a
desired fixed voltage drop
across the device.
+VCC
RC
RB
v out
ib
vce
ic
Purpose of the DC biasing circuit
• To turn the device “ON”
• To place it in operation in the region of its
characteristic where the device operates
most linearly, i.e. to set up the initial dc
values of IB, IC, and VCE
Voltage-Divider Bias
• The voltage – divider (or
potentiometer) bias circuit is by far
the most commonly used.
• RB1, RB2
 voltage-divider to set the value
of VB , IB , C3
 to short circuit ac signals to
ground, while not effect the DC
operating (or biasing) of a circuit
(RE  stabilizes the ac signals)
 Bypass Capacitor
+VCC
RC
R1
v out
v in
C2
C1
R2
RE
C3
Graphical DC Bias Analysis
+VCC
VCC  ICRC  VCE  IERE  0
for I C  I E
1
VCC
VCE 
RC  RE
RC  RE
Point - slope form of straight line equation :
y  mx  c
IC 
IC
RC
R1
IC(sat) = VCC/(RC+RE)
R2
DC Load Line
IE
RE
IC
(mA)
VCE(off) = VCC
VCE
DC Load Line
The straight line is know as the DC load line
IC(sat) = VCC/(RC+RE)
Its significance is that regardless of the behavior of
the transistor, the collector current IC and the I
collector-emitter voltage VCE must always lie on the(mA)
load line, depends ONLY on the VCC, RC and RE
DC Load Line
C
VCE(off) = VCC
VCE
(i.e. The dc load line is a graph that represents all
the possible combinations of IC and VCE for a
given amplifier. For every possible value of IC, and
amplifier will have a corresponding value of VCE.)
It must be true at the same time as the transistor
characteristic.
Solve two condition using
simultaneous equation
 graphically  Q-point !!
What is IC(sat) and VCE(off) ?
Q-Point (Static Operation Point)
• When a transistor does not have an ac input, it
will have specific dc values of IC and VCE.
• These values correspond to a specific point on the
dc load line. This point is called the Q-point.
• The letter Q corresponds to the word (Latent)
quiescent, meaning at rest.
• A quiescent amplifier is one that has no ac signal
applied and therefore has constant dc values of IC
and VCE.
Q-Point (Static Operation Point)
• The intersection of the dc bias
value of IB with the dc load line
determines the Q-point.
• It is desirable to have the Q-point
centered on the load line. Why?
• When a circuit is designed to have
a centered Q-point, the amplifier is
said to be midpoint biased.
• Midpoint biasing allows optimum
ac operation of the amplifier.
DC Biasing + AC signal
• When an ac signal is applied to the base of
the transistor, IC and VCE will both vary
around their Q-point values.
• When the Q-point is centered, IC and VCE
can both make the maximum possible
transitions above and below their initial dc
values.
• When the Q-point is above the center on
the load line, the input signal may cause
the transistor to saturate.
When this
happens, a part of the output signal will be
clipped off.
• When the Q-point is below midpoint on the
load line, the input signal may cause the
transistor to cutoff. This can also cause a
portion of the output signal to be clipped.
DC Biasing + AC signal
DC and AC Equivalent Circuits
+VCC
+VCC
IC
RC
RC
R1
R1
RL
vce
vin
vin
R2
R2
RE
R1//R2
IE
RE
rC = RC//RL
Bias Circuit
DC equivalent
circuit
AC equivalent
circuit
rC
AC Load Line
IC(sat) = VCC/(RC+RE)
DC Load Line
IC
(mA)
VCE(off) = VCC
VCE
• The ac load line of a given
amplifier will not follow the
plot of the dc load line.
• This is due to the dc load of
an amplifier is different from
the ac load.
IC(sat) = ICQ + (VCEQ/rC)
ac load line
ac load line
IC
IC
Q - point
dc load line
VCE(off) = VCEQ + ICQrC
VCE
VCE
AC Load Line
What does the ac load line tell you?
• The ac load line is used to tell you the maximum possible
output voltage swing for a given common-emitter
amplifier.
• In other words, the ac load line will tell you the
maximum possible peak-to-peak output voltage (Vpp)
from a given amplifier.
• This maximum Vpp is referred to as the compliance of
the amplifier.
(AC Saturation Current Ic(sat) , AC Cutoff Voltage VCE(off) )
AC Saturation Current and
AC Cutoff Voltage
IC(sat) = ICQ + (VCEQ/rC)
ac load line
vce
vin
rC
IC
R1//R2
VCE(off) = VCEQ + ICQrC
rC = RC//RL
VCE
Amplifier Compliance
• The ac load line is used to tell the maximum
possible output voltage swing for a given
common-emitter amplifier. In another words, the
ac load line will tell the maximum possible peakto-peak output voltage (VPP) from a given
amplifier. This maximum VPP is referred to as the
compliance of the amplifier.
• The compliance of an amplifier is found by
determine the maximum possible of IC and VCE
from their respective values of ICQ and VCEQ.
Maximum Possible Compliance
Compliance
The maximum possible transition for VCE is equal to the
difference between VCE(off) and VCEQ. Since this transition
is equal to ICQrC, the maximum peak output voltage from
the amplifier is equal to ICQ rC. Two times this value will
give the maximum peak-to-peak transition of the output
voltage:
VPP = 2ICQrC
(A)
VPP = the output compliance, in peak-to-peak voltage
ICQ = the quiescent value of IC
rC = the ac load resistance in the circuit
Compliance
When IC = IC(sat), VCE is ideally equal to 0V. When IC = ICQ, VCE
is at VCEQ. Note that when IC makes its maximum possible
transition (from ICQ to IC(sat)), the output voltage changes by an
amount equal to VCEQ. Thus the maximum peak-to-peak
transition would be equal to twice this value:
VPP = 2VCEQ
(B)
• Equation (A) sets the limit in terms of VCE(off). If the value
obtained by this equation is exceed, the output voltage will try to
exceed VCE(off), which is not possible. This is called cutoff
clipping, because the output voltage is clipped off at the value of
VCE(off).
• Equation (B) sets of the limit in terms of IC(sat). If the value
obtained by this equation is exceed, the output will experience
saturation clipping.
Cutoff and Saturation Clipping
When determining the output compliance for a given
amplifier, solve both equation (A) and (B). The lower of
the two results is the compliance of the amplifier.
Example
• For the voltage-divider bias amplifier
shown in the figure, what is the ac and dc
load line. Determine the maximum output
+12V
compliance.
R1
33k
RC
4.7k
 = 200
R2
10k
RE
2.2k
RL
10k
Transistor Bias Circuits
Objectives
 Discuss the concept of dc biasing of a transistor
for linear operation
 Analyze voltage-divider bias, base bias, and
collector-feedback bias circuits.
 Basic troubleshooting for transistor bias circuits
Introduction
For the transistor to properly operate it must be
biased. There are several methods to establish the
DC operating point. We will discuss some of the
methods used for biasing transistors as well as
troubleshooting methods used for transistor bias
circuits.
The DC Operating Point
The goal of amplification in most cases is to increase the
amplitude of an ac signal without altering it.
The DC Operating Point
For a transistor circuit to amplify it must be properly biased
with dc voltages. The dc operating point between saturation and
cutoff is called the Q-point. The goal is to set the Q-point such
that that it does not go into saturation or cutoff when an a ac
signal is applied.
The DC Operating Point
Recall that the collector characteristic curves graphically show the
relationship of collector current and VCE for different base currents. With
the dc load line superimposed across the collector curves for this
particular transistor we see that 30 mA of collector current is best for
maximum amplification, giving equal amount above and below the Qpoint. Note that this is three different scenarios of collector current being
viewed simultaneously.
VCC
1
I c  ( )VCE 
•Slope of the dc load line?
Rc
RC
The DC Operating Point
With a good Q-point established, let’s look at the effect a superimposed ac
voltage has on the circuit. Note the collector current swings do not exceed the
limits of operation(saturation and cutoff). However, as you might already
know, applying too much ac voltage to the base would result in driving the
collector current into saturation or cutoff resulting in a distorted or clipped
waveform. (Example 5-1)
Voltage-Divider Bias
Voltage-divider bias is the most widely used
type of bias circuit. Only one power supply
is needed and voltage-divider bias is more
stable( independent) than other bias types.
For this reason it will be the primary focus
for study.
Voltage-Divider Bias
Apply your knowledge of
voltage-dividers to understand
how R1 and R2 are used to
provide the needed voltage to
point A(base). The resistance to
ground from the base is not
significant enough to consider
in most cases. Remember, the
basic operation of the transistor
has not changed.
Voltage-Divider Bias
•In the case where base to ground resistance(input resistance) is
low enough to consider, we can determine it by the simplified
equation RIN(base) = DCRE
•We can view the voltage at point A of the circuit in two ways,
with or without the input resistance(point A to ground)
considered.
Voltage-Divider Bias
•For this circuit we will not take
the input resistance into
consideration. Essentially we
are determining the voltage
across
R2(VB)
by
the
proportional method.
 R 2 ||  DC RE 
VCC
VB  
 R1  ( R2 ||  DC RE ) 
VB = (R2/R1 + R2)VCC
Voltage-Divider Bias
We now take the known base voltage and
subtract VBE to find out what is dropped
across RE. Knowing the voltage across RE we
can apply Ohm’s law to determine the
current in the collector-emitter side of the
circuit. Remember the current in the baseemitter circuit is much smaller, so much in
fact we can for all practical purposes we say
that IE approximately equals IC.
IE≈ IC
Voltage-Divider Bias
Although we have used npn transistors for most of
this discussion, there is basically no difference in its
operation with exception to biasing polarities.
Analysis for each part of the circuit is no different
than npn transistors.
Base Bias
This type of circuit is very unstable since its  changes with
temperature and collector current. Base biasing circuits are
mainly limited to switching applications.
VCC  VBE
IC  (
)  DC
RB
Emitter Bias
•This type of circuit is independent
of  making it as stable as the
voltage-divider
type.
The
drawback is that it requires two
power supplies.
•Two key equations for analysis of
this type of bias circuit are shown
below. With these two currents
known we can apply Ohm’s law
and Kirchhoff's law to solve for
the voltages.
•IB ≈ IE/
•IC ≈ IE ≈( -VEE-VBE)/(RE + RB/DC)
Collector-Feedback Bias
Collector-feedback bias is kept
stable with
negative feedback,
although it is not as stable as
voltage-divider or emitter. With
increases of IC, less voltage is
applied to the base. With less IB ,IC
comes down as well. The two key
formulas are shown below.
•IB = (VC - VBE)/RB
•IC = (VCC - VBE)/(RC + RB/DC)
Summary
 The purpose of biasing is to establish a stable
operating point (Q-point).
 The Q-point is the best point for operation of a
transistor for a given collector current.
 The dc load line helps to establish the Q-point
for a given collector current.
 The linear region of a transistor is the region of
operation within saturation and cutoff.
Stability Factor
Operating Regions
E–B
junction
Reverse
Biased
C–B
junction
Reverse
Biased
Active
Forward
Biased
Reverse
Biased
Saturation
Forward
Biased
Forward
Biased
Region of
operation
Cut off
Ic
Saturation
Region
Active Region
Ib = 60μA
Ic = 10mA
Ib = 50μA
Ic = 8mA
Ib = 40μA
Ic = 6mA
Ib = 30μA
Ic = 4mA
Ib = 20μA
Ic = 2mA
Cut-off Region
0V
24 V
Vce
Typical junction voltages
Transistor
Si
Vce
Vbe
Vbe
Vbe
Vbe
sat
sat active cut-in cut-off
0.2 V 0.8 V 0.7 V 0.5 V 0 V
Ge
0.1 V 0.3 V 0.2 V 0.1 V -0.1 V
•In the saturation region Ic >  Ib
•For active region Vce > Vce(sat)
Problem
Vcc = 10 V
Rb = 300 K
Calculate Ib, Ic & Vce if 
= 100 for the Silicon transistor.
Find the region of operation
Hint
Vbe = 0.7 V
Answer
Ib = 31 A
Vce = 3.8 V
Ic=3.1mA
Active
Rb
Rc
300 K
2K
Ic
Leakage current Io = 2 A at 250 C
Calculate Rb, if the Ge transistor
remains in cut-off at 750 C
Rb
Hints
Leakage current doubles for every
100 C
I’o = Io . 2i/10
i = t2 – t1
Vbe(cut-off) = -0.1V
Answer
Rb = 76.6 K
Vcc
10 V
Vbb
-5 V
Problem
270 K
Io
Rc
5.6 K
If Vbb = 1 V, Rb = 50 K, upto
what temperature, the transistor
will remain in cut-off ? (Room
temp. = 250 C
Hints
Find Io’
I’o = Io . 2i/10
i = t2 – t1
Find t2
Answer
 t2 = 56.70 C
Vcc
10 V
Vbb
-1 V
Problem
Io
Rb
50 K
Rc
5.6 K
+Vcc
10 V
Problem
Show that the transistor is in
saturation region
Hints
In saturation Ic is not equal to  Ib
Ib
100K
2K
Ic
Vbe(sat) = 0.8 V
Ie = Ib + Ic

100
Find Ib & Ic
1K
Answer
Ib = 58.9 A
Ic = 3.24mA
Ie
Common Base Configuration
Ie
E
Ic
-- ----- -- ----
-- -- --------------- - -- --
C
B
Input
_
+
Vbe
_
Ib
+
Output
Vcb
•Here the input is applied at the Emitter & the output taken
from the Collector
•In this arrangement Base is common to the input & output
•This is called Common Base configuration
Vcc
Common Base Configuration
Ie
Ic
Output
Input
Re
Rb1
Rc
Rc
_
output
+
Vee
_
+
Vcc
•The circuit can be re-drawn as shown,
with input at Emitter & output at
Collector
input
Rb2
Ib
Re
•Vb is obtained using Rb1 & Rb2
•This is called potential divider
arrangement
Common Emitter Configuration
Ie
Vcc
Ic
Output
E
C
Rb1
B
Rc
_
+
Ib
_
+
Output
Vee
Input
Rb2
Input Vcc
•The circuit has been re-configured with
input at Base & output at Collector
Re
• The Emitter is common to input & output
•This is called Common Emitter
configuration
Reverse Saturation current Ico
Ico
Vee
_
+
_
Vcc
+
•When Emitter is open, the base & collector act as a reverse
biased diode
•Since CB junction is reverse biased there will not be any Ic
•However, there will be a current due to the minority charge
carriers
•This is called Reverse Saturation Current Ico
Reverse Collector Saturation current Icbo
Ie
_
Icbo
+
Vee
_
+
Vcc
•Icbo is the leakage current that flows at the collector due to the
minority charge carriers, in the common base mode
• Is the current gain in the CB mode
Reverse Collector Saturation current Iceo
Ie
_
Iceo
+
Vee
_
+
Vcc
•Iceo is the leakage current that flows at the collector due to the
minority charge carriers, in the common emitter mode
• Is the current gain in the CE mode
Ic = .Ie + Icbo
= (Ib + Ic) + Icbo
Ic (1- ) = Ib + Icbo
Ic =
Since  =
1
1-
Ib
1-
+
Icbo
1-

1-
= +1
Ic =  Ib+ (+1)Icbo
i.e. Ic =  Ib + Iceo
where Iceo = (+1) Icbo
Stability
• Temperature & Current gain variation may change
the Q point
• Stability refers to the design that prevents any
change in the Q point
• Temperature effect
• When the temperature increases it results in the
production of more charge carriers
• This increases the forward bias of the transistor
and Ib increases
Temperature effect
• When the temperature increases it results in the production
of more charge carriers
• This increases the minority charge carrier and hence the
leakage current as
Iceo = (+1) Icbo
• Icbo doubles for every 100 C
As Ic =  Ib + Icbo
• The increase in the temperature increases Ic
• This in turn increases the power dissipation and again
more heat is produced
Thermal Runaway
•
•
•
•
•
This increases the power dissipation
This results in more heat
Again the charge carrier increases
The whole process repeats
Ultimately Ic may become too large and burn the
transistor
• This is called Thermal Runaway
Change in Vbe
• Vbe changes @ 25 mV per degree Celcius
• Ib depends on Vbe
• Ic depends on Ib
• Hence Ic changes with temperature
• This shifts the operating point
Change in 
• The current gain  also depends on temperature
• As Ic =  Ib, Ic varies with temperature
• This shifts the Q point
• Thermal stability should ensure that in spite of
temperature change, the selected Vce, Ic & Power
max do not change
Techniques
• Stabilization technique
• Resistive biasing circuits change Ib suitably and
keep Ic constant
• Compensation technique
• Temperature sensitive devices such as diodes,
thermistors & transistors are used to provide
suitable compensation and retain the operating
point without shifting
Stability Factor
• It indicates the degree of change in the operating
point due to variation in temperature
• There are 3 stability factors corresponding to the 3
variables – Ico, Vbe & 
S =
S’ =
S’’ =
Ic
Ico
Vbe,  constant
Ic
Vbe
Ico,  constant
Ic

Ico, Vbe constant
The stability factor should
be as minimum as possible
Ic =  Ib + Iceo
Stability Factor S
=  Ib + (I +  ) Icbo
i.e. Ic = Ib + (I +  ) Icbo
Ib
Icbo
+ (I +  )
Ic
Ic
Icbo
= (I +  )
Ic
i.e. 1 = 
i.e. 1 - 
Ib
Ic
Icbo
Ic
i.e.
S=
Ic
Icbo
1- 
=
Ib
Ic
(I+)
(I+)
=
1- 
Ib
Ic
Design of biasing system
Vcc
Fixed Bias Circuit
• When Ib flows through
Rb, there will be a
voltage drop across Rb
Vb = Vcc – (Ib x Rb)
Ib = (Vcc – Vb) / Rb
= Vcc / Rb (approx)
• Supply voltage Vcc is
fixed
• Hence once Rb is chosen
Ib is also fixed
• Hence the name Fixed
bias circuit
Ib
Rb
Vbe
• When collector current Ic
flows through Collector
load resistor Rc, there will
be a voltage drop across
Rc
Vcc
Rc
Ib
Ic
Rb
Vc = Vcc – (Ic x Rc)
Or, Vc < Vcc
Vce
Or, Ic < Vcc / Rc
Vbe
• In case Ic > Vcc / Rc,
then the operating point
lies in the saturation
region
Problem
• Design a fixed biased circuit using a silicon
transistor having
•  = 100
• Vcc = 10 V
• Vce = 5 V
• Ic = 5 mA
Answer: Rc = 1 K Rb = 186 K
Problem
•
•
•
•
•
•
A fixed bias circuit has
 = 100 @ 250 C &  = 125 @ 750 C
Vcc = 12 V
Rb = 100 K
Rc = 600 
Determine % change in Q point values over the
temperature range
Answer: %change in Ic = + 25%
%change in Vc = - 32.5%
Stability Factor S
For Fixed Bias Circuit
Ic
S = Ico
Vbe,  constant
(I+)
=
Ib
1- 
Ic
For the fixed Bias Circuit Ib = Vcc / Rb
.
. .
Ib
=0
Ic
(I+)
.
. .
S=
1 - (0)
.
. .
S=1+
Stability Factor S’
For Fixed Bias Circuit
Ic =  Ib + Iceo
S’ =
=  Ib + ( + 1) Icbo
Vcc - Vbe
= 
+ ( + 1) Icbo
Rb
 Vcc
 Vbe
+ ( + 1) Icbo
=
Rb
Rb
.
. .
.
. .
Ib
Vbe
= 0 _

+ 0
Rb
S = -  / Rb
Ic
Vbe Ico,  constant
Stability Factor S’’
For Fixed Bias Circuit
Ic = Ib + Iceo
S’’ =
= Ib + (+1)Icbo
Ic

Vcc - Vbe
= 
+ ( + 1) Icbo
Rb
 Vcc
 Vbe
+ ( + 1) Icbo
=
Rb
Rb
.
. .
Ic

Vcc
=
Rb
Vbe
Rb
= Ib + Icbo
= Ib (approx)
= Ic / 
.
. .
S’’ = Ic / 
+ Icbo
Ico, Vbe constant
Vcc = 10 V
Problem
Rb = 100 K
Rc = 2 K
Vcc = 10 V
Vce = 4 V
For this emitter grounded
Fixed Bias circuit with Si
transistor, find the stability
factor S
Answer
S = 33.3
Rb
•270 K
100 K
Rc
•5.6 K
•
Ic
2K
4V
Advantages of fixed bias circuit
• Simple circuit with minimum components
• Operating point can be fixed conveniently in the
active region, by selecting appropriate value for
Rb
• Hence fixed bias circuit provides flexibility in the
design
Disadvantages of fixed bias circuit
• Ic increases with temperature & there is no control
over it
• Hence there is poor thermal stability Ic =  Ib
• Hence Ic depends on 
•  may change from transistor to transistor
• This will shift the operating point
• Hence stabilization is very poor in fixed bias
circuit
Vcc
Collector to Base Bias
• Here Rb is connected
between Base &
Collector
Rc
Ib
Rb
Ic+Ib
Ic
Vce
• So, Ic & Ib flow through
Rc
Vcc
Vc = Vcc – (Ic + Ib) x Rc
Also, Vc = (Ib x Rb) + Vbe
Equating the two equations
Vcc – (Ic + Ib)Rc
Rc
= (Ib Rb) + Vbe
Or, Ib(Rc + Rb) = Vcc – IcRc - Vbe
As Ic = Ib
Ib
Vcc – IcRc - Vbe
.
. .
Ic+Ib
Ib =
Rc + Rb
( Vcc – IcRc – Vbe)
Ic =
Rc + Rb
Rb
Ic
Vce
Vcc
•Rb provides a feedback
between Collector & Base
•If Ib or Ic tries to increase
either due to temperature
effect or due to variation in 
•Voltage drop across Rc
increases
Rc
Ib
Ic+Ib
Rb
•This decreases Vce
•This in turn reduces Ib,
stabilizing the circuit
Vce
+12 V
• Problem
Calculate the values of Ic & Vce
for the given circuit
Hint
Vcc = Rc(Ic + Ib) + Vce
Ic =  Ib
Vce = Rb Ib + Vbe
Vbe = 0.6
Answer
Ic = 1.018 mA
Vce = 1.72 V
10 K
100 K

100
Problem
Design a collector to base circuit for the
specified conditions:
•Vcc = 15 V
•Vce = 5 V
•Ic = 5 mA
• = 100
Hint
•Vcc = Rc(Ic + Ib) + Vce
• Ic =  Ib
• Vce = Rb Ib + Vbe
Answer
Rc = 1.98 mA
Rb = 86 K
Stability Factor S
For Collector-Base Bias
Vcc = (Ib + Ic)Rc + IbRb + Vbe
S
=
Ic
Ico Vbe,  constant
=IcRc + Ib(Rc + Rb) + Vbe
0 = IcRc + Ib(Rc + Rb) + 0
after differentiation
or - IcRc = Ib(Rc + Rb)
.
. .
Ib
Ic
=
-Rc
Rc + Rb
(I + )
S=
1-
Ib
Ic
(I + )
=
1+
Rc
Rc + Rb
Stabilization with changes in 
• If we design our circuit such that Rc >>Rb
• Then S becomes independent of 
• Hence  variation from transistor to transistor has no
effect on the stability
(1 + )
S=
1+
Rc
Rc + Rb
1+
S=
1+
=1
Stability Factor S’
For Collector-Base Bias
Vcc – IcRc - Vbe
Ic
Vbe Ico,  constant
S’ =
Ib =
Rc + Rb
Vcc – IcRc - Vbe
Ic

Ic
Rb + ( + 1) Rc
Rc + Rb
Ic

Ic =
=
IcRc
+
Vcc - Vbe
=
Rc + Rb
Rc + Rb + Rc
 (Rc + Rb)
(Vcc – Vbe)
Rc + Rb
Vcc - Vbe
=
Rc + Rb
S’ =
=
Ic
Vbe
-
Rb + ( + 1) Rc
Stability Factor S’’
For Collector-Base Bias
S’’ =
Ic

Ico, Vbe constant
Vcc = (Ib + Ic)Rc + IbRb + Vbe
Vcc –Vbe = (Ib + Ic)Rc + IbRb
= Ib [(1 + )Rc +Rb]
Vcc – Vbe
.
. .
Ib =
( Vcc – Vbe)
.
. .
(1 + ) Rc + Rb
Ic =
(1 + ) Rc + Rb
[(1 + )Rc +Rb](Vcc –Vbe) - (Vcc –Vbe) Rc
Ic
.
. .

=
[(1 + ) Rc + Rb]2
(Vcc –Vbe)[(1 + )Rc +Rb] - Rc
=
[(1 + ) Rc + Rb]2
(Vcc –Vbe)(Rc +Rb)
=
[(1 + ) Rc + Rb]2
Vcc – Vbe
=
(1 + ) Rc + Rb
Rc + Rb
x
(1 + ) Rc + Rb
Ib(Rc + Rb)
=
.
. .
S’’ =
(1 + ) Rc + Rb
Ic(Rc + Rb)
[(1 + ) Rc + Rb]
S’’ =
Ic(Rc + Rb)
[(1 + ) Rc + Rb]
Ic 1+ 
=
=
=
(Rc + Rb)

1+ 
(1 + ) Rc + Rb
Ic
1
(1+ ) (Rc + Rb)

1+ 
(1 + ) Rc + Rb
Ic
S

1+ 
If S is small, S’’ will also be small
Hence if we provide stability against Ico variations, it will take care
of  variation as well
Vcc
Voltage Divider Bias

Ib1
Rb1
270 K
Rc
Ic
Ib2
Ie
Rb2
Vb = Vc – Ib Rb
5.6 K
Ib
Re
Usually Vb is obtained
using Rb & Ib

Thus Ib depends on Vb &
Vb depends on Ib

To avoid this anomaly, two
resistors Rb1 & Rb2 have
been used

Rb1 & Rb2 act as Voltage
Divider circuit giving Vb,
irrespective of Ib
Vcc
• Rb1 is called Base Bias
Resistor
Ib1
Rb1
270 K
Rc
Ic
5.6 K
• Rb2 is called Base Bleeder
Resistor
• Vb is obtained based on
the ratio of Rb1 and Rb2
Ib
Ib2
Rb2
Ie
Rb2
Re
Vb = Vcc
Rb1 + Rb2
Vcc
Ib1
Rb1
270 K
Rc
Ic
5.6 K
Rest of the equations remain
the same
Vc = Vcc – Ic Rc
Vb = Ve + Vbe
Ib
Ve = Ie Re
Ib2
Ie
Rb2
Re
+10 V
Problem
Rb1
10 K
Rc
1K
For the Si transistor, if  is
100, find
Vce & Ic
Hints
Find Vb, Ve, Ie, Ib
Rb 2
5K
Answer
Re 500
Ic = 5.2 mA
Vce = 2.16 V
Vcc
Vcc
We can draw the Thevenin
Equivalent Circuit for the
base circuit
Ib1
Rb1
Rc
270 K
5.6 K
Ic VT = Vb
&
Rc
Ic
5.6 K
R = Rb1 II Rb2
R
Ib
Ib
Ib2
VT
Rb2
Re
Ie
Rb2
Re
Stability Factor S
For Voltage Divider Bias
S =
Vb = IbRb +Vbe + IeRe
= IbRb +Vbe + (Ib + Ic)Re
Ic
Ico Vbe,  constant
where Rb = Rb1 ll Rb2
Differentiating,
0 = IbRb + 0 + IbRe + IcRe
i.e. Ib(Rb + Re) = - IcRe
.
. .
Ib
Ic
=
-Re
Rb + Re
(I + )
(I + )
S=
Ib
1-
Ic
=
1+
Re
Re + Rb
(I + )
S=
1+
Re
Re + Rb
• In the above equation, if Rb << Re, then S
becomes 1
Rb = Rb1 ll Rb2
• Hence either Rb1 or Rb2 must be << Re
• Since Vb << Vcc, Rb2 is kept small wrt Rb1
(I + )
S=
1+
Re
Re + Rb
(I + )
S=
1+
1
S = (I + )
1 + Rb/Re
• Re cannot be increased beyond a limit, as it will
affect Ic and hence the Q point
• If Rb-Re ratio is fixed, and if Rb >> Re, S increases
with 
• Thus stability decreases with increasing 
(I + )
S=
1+
Re
Re + Rb
(I + )
S=
1+
1
S= I
1 + Rb/Re
• If Rb << Re, then S becomes independent of 
• Stability factor S for Voltage Divider circuit is less
compared to other circuits
• Hence it is preferred over other circuits
+20 V
Rb1
100 K
Problem
 For the Ge transistor, if 
is 50, find
 Vce & Ic
 Find Ib,Vce, Ic & S
Rc
2K
Hint Vbe = 0.2 V
Rb2
5K
Re
100
Answer
 Ib = 76.3 uA
 Vce = 11.98 V
 Ic = 3.81 mA
 S = 25.14
+20 V
Problem

Rb1
50 K
Rc
2K
For the Si transistor, if  is
100 & Ic = 2 mA find
Re,Vce, & S
Answer
Rb2
5K
Re

Re = 149 

Vce = 7.7 V

S = 24.25
Problem
• Design a voltage divider bias circuit for the given
specifications:
• Vcc = 12 V, Vce = 6 V, Ic = 1 mA, S = 20,  = 100
& Ve = 1 V
Answer:
Rb1= 150 K , Rb2 = 27 K, Rc = 4.7 K , Re = 1 K
Stability Factor S’
For Voltage Divider Bias
Vb = IbRb +Vbe + IeRe
= IbRb + Vbe + (Ib + Ic)Re
S’ =
Ic
Vbe Ico,  constant
= Ib(Rb + Re) + Vbe + IcRe
= Ic /  (Rb +Re) + Vbe + IcRe
Or, Vb = Ic(Rb +Re) +  Vbe +  IcRe
= Ic[Rb +( + 1)Re] +  Vbe
0 = Ic[Rb +( + 1)Re] + Vbe
Or, Vbe = - Ic [Rb +( + 1)Re]
Ic
S’ =
=
Vbe
-
Rb + ( + 1) Re
Differentiating,
Stability Factor S’’
For Voltage Divider Bias
Vb = IbRb +Vbe + IeRe
S’’ =
= Ib(Rb + Re) + Vbe + IcRe
Ic

Ico, Vbe constant
= Ic /  (Rb +Re) + Vbe + IcRe
Or, Vb = Ic(Rb +Re) +  Vbe +  IcRe
Or, (Vb – Vbe) = Ic(Rb +Re) +  IcRe
Differentiating,
(Vb – Vbe) = Ic(Rb +Re) + IcRe + Ic Re
(Vb – Vbe – IcRe) = Ic[Rb + Re+ Re]
.
. . S’’ =
Ic

=
Vb – Vbe - IcRe
Rb + Re(1+ )
S’’ =
Ic

=
=
=
=
Vb – Vbe - IcRe
Rb + Re(1+ )
Vb – Vbe - IeRe
Rb + Re(1+ )
As Ie = Ic
Ib Rb
Rb + Re(1+ )
Ib
1 +(Re/Rb)(1+ )
Hence Rb / Re must be small to make S’’ smaller
Vcc
Self Bias
•In this circuit Re provides Self
bias
Ib1
Rb1
Rc
270 K
5.6 K
Ic
•When Ib or Ic tries to increase,
Ie increases
•This produces more drop across
Re & increases Ve
•This reduces Vbe which is
Vb – Ve
Ib
•This in turn reduces Ib and
hence Ic
Ib2
Rb2
Re
•Thus Re provides a negative
feed back and improves the
stability
Bias Compensation
• The biasing circuits seen so far provide stability of
operating point for any change in Ico, Vbe or 
• The collector- base bias & emitter bias circuits
provide negative feedback & make the circuit
stable, but the gain falls down
• In such cases it is necessary to use compensation
techniques
• Diode Compensation
Technique
Vcc
Here diode D has been connected
as shown
It is given forward bias through
Vdd
Rb
Rc
270 K
5.6 K
The diode D is identical to the BE
junction of the transistor
The charge carriers will increase
in the BE jn. due to temperature or
other variations
Rd
-
Vdd
+
Re
D
Vcc
Since diode D has similar
properties, its charge carrier also
increases, for any change in the
parameters
Rb
Rc
270 K
5.6 K
Thus the increase in current in
the BE junction is compensated
by the current flow through the
diode in the reverse direction.
Rd
-
Vdd
+
Re
D
Vcc
Another technique
Here the diode D has been
connected in the bleeder path
When there is increase in
current in the BE junction due to
parameter changes, current
through D also increases by the
same amount
Ib1
Rb1
270 K
Ib2
Rc
5.6 K
D
Rb2
Re
Vcc
This increases Ib1, produces more
drop across Rb1& reduces Vb
As Vb decreases, Ib falls down
Rb1
Rc
270 K
5.6 K
Thus the transistor currents are
arrested and not allowed to increase
Thus diode D provides suitable
compensation
D
Rb2
Re
Thermistor Compensation
Here a Negative Temperature
Coefficient Resistor has been used
Vcc
Ib1
Rb1
Rc
270 K
5.6 K
As temperature increases, its
resistance decreases
This increases Ib1 & voltage drop
across Rb1
This decreases Vb and hence Ib &
Ic, thus keeping the circuit stable.
Ib
Ib2
NTC
Re
Sensitor Compensation
Here a Positive Temperature
Coefficient Resistor has been used
As temperature increases, its
resistance increases
This increases the voltage drop
across Rb1(PTC)
This reduces Vb and Ib, thus
keeping the circuit stable.
Vcc
Rb1
270 K
5.6 K
Rc
PTC
Ib
Rb2
Re
Vcc
Constant Current circuit
Rb1
Rc

Re provides self bias

Vb is fixed depending on
the ratio of Rb1 & Rb2 &
the value of Vcc

Ve = Vb - Vbe

Vbe is fixed for a transistor

Hence Ve is fixed &

Ie = Ve / Re is also fixed

Hence it acts as a constant
current circuit
5.6 K
Rb2
Re
Problem
 For the given Si transistor
find the constant current I
Rb1
I
270 K
5.6 K
Answer
 I = 4.22 mA
Rb2
4K7
Re
2K2
-20 V
FET Biasing
Introduction
• For the JFET, the relationship between input and
output quantities is nonlinear due to the squared term
in Shockley’s equation.
• Nonlinear functions results in curves as obtained for
transfer characteristic of a JFET.
• Graphical approach will be used to examine the dc
analysis for FET because it is most popularly used
rather than mathematical approach
• The input of BJT and FET controlling variables are
the current and the voltage levels respectively
Introduction
JFETs differ from BJTs:
• Nonlinear relationship between input (VGS) and
output (ID)
• JFETs are voltage controlled devices, whereas
BJTs are current controlled
Introduction
Common FET Biasing Circuits
• JFET
– Fixed – Bias
– Self-Bias
– Voltage-Divider Bias
• Depletion-Type MOSFET
– Self-Bias
– Voltage-Divider Bias
• Enhancement-Type MOSFET
– Feedback Configuration
– Voltage-Divider Bias
General Relationships
• For all FETs:
IG  0A
ID  IS
• For JFETs and Depletion-Type MOSFETs:
ID  IDSS(1
VGS 2
)
VP
• For Enhancement-Type MOSFETs:
I D  k (VGS VT ) 2
Fixed-Bias Configuration
• The configuration includes the ac levels Vi and Vo and the
coupling capacitors.
• The resistor is present to ensure that Vi appears at the input to
the FET amplifier for the AC analysis.
Fixed-Bias Configuration
• For the DC analysis,
• Capacitors are open circuits and
• The zero-volt drop across RG permits replacing RG by a short-circuit
IG  0A
VRG  I G RG  (0 A) RG  0V
Fixed-Bias Configuration
Investigating the input loop
• IG=0A, therefore
VRG=IGRG=0V
• Applying KVL for the input loop,
-VGG-VGS=0
VGG= -VGS
• It is called fixed-bias configuration due to VGG is a
fixed power supply so VGS is fixed
• The resulting current, ID  IDSS(1 VGS )2
VP
• Investigating the graphical approach.
• Using below tables, we can draw the graph
VGS
ID
0
IDSS
0.3VP
IDSS/2
0.5
IDSS/4
VP
0mA
• The fixed level of VGS has been superimposed as a
vertical line at VGS  VGG
• At any point on the vertical line, the level of VG is VGG--- the level of ID must simply be determined on
this vertical line.
• The point where the two curves intersect is the common
solution to the configuration – commonly referrers to as
the quiescent or operating point.
• The quiescent level of ID is determine by drawing a
horizontal line from the Q-point to the vertical ID axis.
• Output loop
VDS  VDD  I D RD
VS  0V
VDS  VD  VS
VD  VDS  VS
VS  0
VD  VDS
VGS  VG  VS
VG  VGS  VS
VG  VGS
VS  0
Example
• Determine VGSQ, IDQ, VDS, VD, VG, VS
Exercise
• Determine IDQ, VGSQ, VDS, VD, VG and VS
Self Bias Configuration
• The self-bias configuration eliminates the need for two dc
supplies.
• The controlling VGS is now determined by the voltage across
the resistor RS
• For the indicated input loop:
VGS   I D RS
• Mathematical approach:
ID
ID

VGS

 I DSS 1 
VP





I D RS
 I DSS 1 
VP

rearrange and solve.
2



2
• Graphical approach
– Draw the device transfer characteristic
– Draw the network load line
• Use VGS   I D RS to draw straight line.
• First point, I D  0, VGS  0
• Second point, any point from ID = 0 to ID = IDSS. Choose
I DSS
then
2
I R
  DSS S
2
ID 
VGS
– the quiescent point obtained at the intersection of the
straight line plot and the device characteristic curve.
– The quiescent value for ID and VGS can then be
determined and used to find the other quantities of
interest.
• For output loop
– Apply KVL of output loop
– Use ID = IS
VDS  VDD  I D ( RS  RD )
VS  I D RS
VD  VDS VS  VDD VRD
Example
• Determine VGSQ, IDQ,VDS,VS,VG and VD.
Example
• Determine VGSQ, IDQ, VD,VG,VS and VDS.
Voltage-Divider Bias
• The arrangement is the same as BJT but the DC
analysis is different
• In BJT, IB provide link to input and output circuit, in
FET VGS does the same
Voltage-Divider Bias
• The source VDD was separated into two equivalent sources to
permit a further separation of the input and output regions of the
network.
• IG = 0A ,Kirchoff’s current law requires that IR1= IR2 and the
series equivalent circuit appearing to the left of the figure can be
used to find the level of VG.
Voltage-Divider Bias
• VG can be found using the voltage divider rule :
R2VDD
VG 
R1  R2
• Using Kirchoff’s Law on the input loop:
• Rearranging and using ID =IS:
VG VGS VRS  0
VGS  VG  I D RS
• Again the Q point needs to be established by plotting a
line that intersects the transfer curve.
Procedures for plotting
1. Plot the line: By plotting two points: VGS = VG, ID =0 and VGS = 0,
ID = VG/RS
2. Plot the transfer curve by plotting IDSS, VP and calculated values of ID.
3. Where the line intersects the transfer curve is the Q point for the
circuit.
• Once the quiescent values of IDQ and VGSQ are
determined, the remaining network analysis can be
found.
I R1  I R 2
• Output loop:
VDD

R1  R2
VDS  VDD  I D ( RD  I D RS )
VD  VDD  I D RD
VS  I D RS
Effect of increasing values of RS
Example
• Determine IDQ, VGSQ, VD, VS, VDS and VDG.
Example
• Determine IDQ, VGSQ, VDS, VD and VS
Depletion-Type MOSFETs
•Depletion-type MOSFET bias circuits are similar to JFETs. The
only difference is that the depletion-Type MOSFETs can operate
with positive values of VGS and with ID values that exceed IDSS.
Depletion-Type MOSFETs
The DC Analysis


Same as the FET calculations
 Plotting the transfer characteristics of the device
 Plotting the at a point that VGS exceeds the 0V or more
positive values
 Plotting point when VGS=0V and ID=0A
 The intersection between Shockley characteristics and linear
characteristics defined the Q-point of the MOSFET
The problem is that how long does the transfer
characteristics have to be draw?
 We have to analyze the input loop parameter relationship.
 As RS become smaller, the linear characteristics will be in
narrow slope therefore needs to consider the extend of
V V V  0
transfer characteristics for example of voltage divider G GS RS
VGS  VG  I D RS
MOSFET,
 The bigger values of VP the more positive values we should
draw for the transfer characteristics
•Analyzing the MOSFET circuit for DC
analysis
How to analyze dc analysis
for the shown network?





It is a …. Type network
Find VG or VGS
Draw the linear
characteristics
Draw the transfer
characteristics
Obtain VGSQ and IDQ from
the graph intersection
1. Plot line for VGS = VG, ID = 0 and ID = VG/RS, VGS = 0
2. Plot the transfer curve by plotting IDSS, VP and calculated values
of ID.
3. Where the line intersects the transfer curve is the Q-point.
Use the ID at the Q-point to solve for the other variables in the
voltage-divider bias circuit. These are the same calculations as used
by a JFET circuit.
•When RS change…the linear characteristics will change..
1. Plot line for VGS = VG, ID = 0 and ID = VG/RS, VGS = 0
2. Plot the transfer curve by plotting IDSS, VP and calculated values
of ID.
3. Where the line intersects the transfer curve is the Q-point.
Use the ID at the Q-point to solve for the other variables in the
voltage-divider bias circuit. These are the same calculations as used
by a JFET circuit.
Enhancement-Type MOSFET
•The transfer characteristic for the enhancement-type MOSFET is
very different from that of a simple JFET or the depletion-type
MOSFET.
• Transfer characteristic for E-MOSFET
I D  k (VGS  VGS (Th ) )
and
k
I D ( on)
(VGS ( on)  VGS (Th ) ) 2
2
Feedback Biasing Arrangement
• IG =0A, therefore VRG = 0V
•Therefore:
•Which makes
VDS = VGS
VGS  VDD  I D RD
Feedback Biasing Q-Point
1. Plot the line using VGS = VDD, ID = 0 and ID = VDD / RD and VGS
=0
2. Plot the transfer curve using VGSTh , ID = 0 and VGS(on), ID(on); all
given in the specification sheet.
3. Where the line and the transfer curve intersect is the Q-Point.
4. Using the value of ID at the Q-point, solve for the other variables
in the bias circuit.
DC analysis step for Feedback Biasing
Enhancement type MOSFET





Find k using the datasheet or specification given;
ex: VGS(ON),VGS(TH)
Plot transfer characteristics using the formula
ID=k(VGS – VT)2. Three point already defined that is
ID(ON), VGS(ON) and VGS(TH)
Plot a point that is slightly greater than VGS
Plot the linear characteristics (network bias line)
The intersection defines the Q-point
Example
• Determine IDQ and VDSQ for network below
Voltage-Divider Biasing
Again plot the line and the transfer curve to find the Q-point.
Using the following equations: VG  R2VDD
R1  R2
Input loop : VGS  VG  I D RS
Output loop: VDS  VDD  I D ( RS  RD )
Voltage-Divider Bias Q-Point
1. Plot the line using VGS = VG = (R2VDD)/(R1 + R2), ID = 0 and ID
= VG/RS and VGS = 0
2. Find k
3. Plot the transfer curve using VGSTh, ID = 0 and VGS(on), ID(on); all
given in the specification sheet.
4. Where the line and the transfer curve intersect is the Q-Point.
5. Using the value of ID at the Q-point, solve for the other variables
in the bias circuit.
Example
• Determine IDQ and VGSQ and VDS for network
below
•= ••= •-
•= ••- •( •+ •)
•=
•=
•+
•= ••= •- •( •+ •)
•=
•=
•+
••- •( •+ •)
•=
•=
•=••=
•=
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Troubleshooting
N-channel VGSQ will be 0V or negative if
properly checked
 Level of VDS is ranging from 25%~75% of VDD.
If 0V indicated, there’s problem
 Check with the calculation between each terminal
and ground. There must be a reading, RG will be
excluded

P-Channel FETs
For p-channel FETs the same calculations and graphs are used,
except that the voltage polarities and current directions are the
opposite. The graphs will be mirrors of the n-channel graphs.
Practical Applications
• Voltage-Controlled Resistor
• JFET Voltmeter
• Timer Network
• Fiber Optic Circuitry
• MOSFET Relay Driver