Analog Circuits (Unit-2)
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Transistor Amplifier Circuit:-
Transistor equivalent ckt are divided in two
types (i) D.C. equivalent ckt. (ii) A.C. equivalent ckt.
Fig.7.1(a) Transistor Amplifier using Self Bias 2
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Fig.7.1(c) A.C. Equivalent ckt.
Fig.7.1(b) D.C. Equivalent Ckt.
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The capacitors CC1 & CC2 are called the coupling
capacitors. Capacitors CC1 is used to couple the a.c.
input signal to the base of the transistor. A coupling
capacitor is also called a blocking capacitor because
it blocks d.c.
Another capacitor CE is called bypass capacitor
because it bypasses the all a.c. current from the
emitter to ground.
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Hybrid Parameter (h-Parameter):-
h-parameter is widely used because they gives
accurate results & can be measured very easily.
The transistor is a three terminal device but if one
terminal is grounded, then transistor can be used as a
two port network.
The h-parameters are
V1=h11I1+h12V2
I2=h21I1+h22V2
The parameter h11, h12, h21 & h22 are called h-
parameters.
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Fig.7.2 (a) General h-parameter Equivalent Circuit
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Fig.2.2(b) Transistor Two Port Network
the h - parameter is summarized as,
V1
h11 I/P impedance with O/P shorted & unit is ohm
I1
it is also represented as, h11 h i
I2
h 21 forward current gain with O/P shorted & unit is none.
I1
it is also represented as h 21 h f
V1
h12 Reverse voltage gain with I/P open circuited & has no unit.
V2
it is also represented as, h12 h r
I2
h 22 O/P admittance with I/P open ckt. & unit is ohm-1 or mho.
V2
it is also represented as, h 22 h o
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h-Parameter Representation for Transistor:-
Sr. h-Parameter Common Common Common
No. Emitter Base Collector
1. h11 hie hib hic
2. h21 hfe hfb hfc
3. h12 hre hrb hrc
4. h22 hoe hob hoc
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Analysis of Transistor Amplifier by h-Parameter:-
Fig (a) General Amplifier Circuit with Source & Load Resistance
Fig (b) h-Parameter Equivalent Circuit of above General Amplifier
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1. The Current Gain (Ai):- The current gain for the
transistor amplifier is defined as the ratio of O/P
current to the I/P current. Mathematically,
IL I2
A i - ...eq.(1)
I1 I1
from above figure the voltage across the output terminal is V2 ,
V2 I L .R L -I2 .R L ...eq.(2)
Now the h - Parameters equations are,
V1 h i I1 h r V2 ...eq.(3)
I 2 h f I1 h o V2 ...eq.(4)
Now putting the value of V2 in eq.(4) we get,
I 2 h f I1 - I 2 .R L h o
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I 2 (1 R L h o ) h f I1
I2 hf
So
I1 1 R L h o
- I2 IL - hf
Ai
I1 I1 1 R L h o
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2. The Input Resistance (Ri):- The I/P resistance Ri is defined
as the resistance we see looking into the amplifier I/P
terminals (1-1’). Mathematically,
V1
So Ri
I1
Now putting the value of V2 -I2 .R L in eq. of h - parameter
V1 h i I1 h r V2
V1 h i I1 - I 2 .R L h r
Now dividing the above eq. on both side by I1. we have,
V1 I2 V1
h i - .R L h r But R i
I1 I1 I1
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I2 - I2
So therefore R i h i - .R L h r but A i
I1 I1
hf
R i h i A i .R L h r we know that A i
1 h oR L
- hf h f R Lh r
so R i h i .R L h r h i
1 h oR L 1 h oR L
hf hr hf hr
R i h i h i
ho 1 h o YL
RL
1
where YL Load Admittance
RL 14
3. The Voltage gain (Av):- The voltage gain is
defined as the ratio of the O/P voltage V 2 to I/P
V2 I2R L
voltage V1. A v ... eq.(1)
V1 V1
Mathematically, I2
Since we Know that, A i or I 2 A i I1
I1
A i I1R L I1
Therefore Av A i R L
V1 V1
V1 Ai R L
But R i So, A v ..eq.(2)
I1 Ri
hf hrhf
Again we know that, A i & R i h i
1 hoR L 1
ho
RL 15
now putting these value in eq.(2) then we have,
- hf R L
1 hoR L
Av
hrhf
hi
1
ho
RL
hf R L hf R L
Av
h i h i h o - h r h f R L h i Δh.R L
hf R L
Av
h i Δh.R L
where Δh h i h o - h r h f 16
4. Output Resistance (Ro) :- The O/P resistance may be
calculated by reducing the source voltage V s to zero & load
resistance RL to infinity & driving the O/P terminals by a
voltage generator V2. as shown below,
Fig.(c) h-equivalent ckt. to calculate the O/P resistance
O/P resistance Ro is the ratio of the voltage V2 & the
current drawn from the voltage source I2
So Ro=V2/I2 17
from h - parameter eq. I 2 h f I1 h o V2
V2
hence Ro ...eq.(1)
h f I1 h o V2
Applying KVL to the I/P side of the ckt. as shown in fig.7.4(c)
R s I1 h i I1 h r V2 0
or R s h i I1 h r V2
h r V2
I1 ...eq.(2)
R s h i
Now putting the value of I1 in eq.(1) we get,
V2 V2
Ro
h r V2 h f h r V2
h f h o V2 h o V2
R s hi R s hi 18
Re arranging we get,
R s hi R s hi
Ro
h o R s h i h f h r h o R s h o h i h f h r
R s hi
So, Ro where Δh h o h i h f h r
h o R s Δh
if source resistance R s 0 then O/P resistance will be,
hi
Ro
Δh
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5. The Overall Voltage Gain (Avs):- The overall voltage gain of
the transistor amplifier is the ratio of O/P voltage V2 to the
source voltage Vs . It is denoted by Avs.
Fig Equivalent I/P ckt.
V2 V2 V1
Mathematically overall voltage gain, A vs
Vs V1 Vs
V2 V1
but, A v therefore A vs A v . ...eq.(1)
V1 Vs 20
now from equivalent ckt. here Zi represents the amplifier
I/P resistance from figure we have,
Vs .Zi V1 Zi
V1 or
Zi R s Vs Zi R s
putting the value of V1/Vs in eq.(1) we get,
V1 Zi
A vs A v . A v
Vs Zi R s
if R s 0 then A vs A v
therefore A v is the voltage gain with an ideal voltage
source (R s 0)
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6. Overall Current Gain (Ais):- overall current gain of the
transistor amplifier is the ratio of the O/P current (I L) to the
current delivered by the source (Is)
Fig 7.4(e) Modified I/P Equivalent ckt.
IL I2
Mathematic ally overall Current gain, A is
Is Is
modifying the above expression we have,
I 2 I1 I2
but, A is ...eq.(1) but A i 22
I1 I s I1
I1
So A is A i . ...eq.(1)
Is
To determine A is we use modified I/P equivalent ckt.,
here Zi is amplifier I/P resistance, from fig.7.4(e) we have
Rs I1 Rs
I1 I s then ...eq.(2)
R s Zi I s R s Zi
I1
now putting the value of in eq.(1) we get,
Is
I1 Rs
A is A i . A i
Is R s Zi
Now if R s then A is A i therefore A i is the
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current gain with an ideal current source (R s )
7.5 h-Parameter Expression for CE amplifier:-
B
C
E E E
Fig. h-parameter equivalent circuit for CE amplifier
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1. Current gain (Ai):- - hf
Ai (General Expression)
1 R Lh o
Current Gain for Common Emitter Amplifier,
h fe
A i -
1 R L h oe
2. Input Resistance (Ri):-
hf hr
R i h i (General Expression )
ho 1
RL
The I/P resistance for C - E Amplifier,
h fe h re
R i h ie
h oe 1
RL
for the fixed bias ckt. Zi R i R B & for no
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biasing resistance then Z i R i
3. Voltage Gain (Av):- A h f R L (General Expression)
v
h i Δh.R L
h fe R L
Voltage gain for CE amplifier, A v
h ie Δh.R L
where Δh h ie h oe - h re h fe
4. Output Resistance (Ro):-
R s hi
Ro (General Expression)
h o R s Δh
R s h ie
Ro (for CE amplifier)
h oe R s Δh
where Δh h oe h ie h fe h re & R s is the source resistance
The O/P resistance of the amplifier stage will be
Zo R o R L 26
5. Overall Voltage Gain (Avs):-
V1 Zi
A vs A v . A v (general expression)
Vs Zi R s
Zi - h fe R L Zi
A vs A v (for CE amplifier)
Zi R s h ie ΔhR L Zi R s
here Δh h ie h oe h re h fe
6. Overall Current Gain (Ais):-
Rs hf Rs
A is A i (General expression)
R s Zi 1 h o R L R s Zi
h fe R s
A is (For CE amplifier)
1 h oe R L R s Zi
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Properties of Common Emitter Amplifier:-
1. Large current gain (Ai=100).
2. Large voltage gain (Av=500).
3. Large power gain (Ap=Av.Ai)
4. Moderate I/P impedance (50KΩ).
5. Moderate O/P impedance (10KΩ).
6. Phase shift is 180º bet I/P & O/P voltage.
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7.6 h-Parameter Expression for CB amplifier:-
1. Current gain (Ai):-
Current Gain for Common Base Amplifier,
h fb
A i -
1 R L h ob
2. Input Resistance (Ri):-
The I/P resistance for C - B Amplifier,
h fb h rb
R i h ib
h ob 1
RL
The i/p resistance of the amplifier stage depends upon the
biasing arrangement.if there is no biasing then,
Zi R i 29
3. Voltage Gain (Av):-
h fb R L
Voltage gain for CB amplifier, A v
h ib Δh.R L
where Δh h ib h ob - h rb h fb
4. Output Resistance (Ro):-
R s h ib
Ro
h ob R s Δh
where Δh h ob h ib h fb h rb & R s is the source resistance
The O/P resistance of the amplifier stage will be
Zo R o R L
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5. Overall Voltage Gain (Avs):-
Zi - h fb R L Zi
A vs A v
Zi R s h ib ΔhR L Zi R s
here Δh h ob h ib h fb h rb
6. Overall Current Gain (Ais):-
The overall current gain for the CB amplifier is,
h fb R s
A is
1 h ob R L R s Zi
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Properties of Common base Amplifier:-
1. current gain is less than 1(Ai<1).
2. Large voltage gain (Av=150).
3. Power gain is less than CE configuration (Ap=Av.Ai)
4. Small I/P impedance (40Ω).
5. Large O/P impedance (1MΩ).
6. No voltage & current Phase shift.
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h-Parameter Expression for CC amplifier:-
1. Current gain (Ai):-
Current Gain for Common collector Amplifier,
h fc
A i -
1 R L h oc
2. Input Resistance (Ri):-
The I/P resistance for C - C Amplifier,
h fc h rc
R i h ic
h oc 1
RL
The i/p resistance of the amplifier stage depends upon the
biasing arrangement.if there is no biasing then,
Zi R i 33
3. Voltage Gain (Av):-
h fc R L
Voltage gain for CC amplifier, A v
h ic Δh.R L
where Δh h ic h oc - h rc h fc
4. Output Resistance (Ro):-
The O/P resistance of the CC amplifier is,
R s h ic
Ro
h oc R s Δh
where Δh h oc h ic h fc h rc
R s is the source resistance
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5. Overall Voltage Gain (Avs):-
Zi - h fc R L Zi
A vs A v
Zi R s h ic ΔhR L Zi R s
here Δh h oc h ic h fc h rc
6. Overall Current Gain (Ais):-
The overall current gain for the CC amplifier is,
h fc R s
A is
1 h oc R L R s Zi
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Properties of Common Collector Amplifier:-
1. current gain is Very high (Ai=100).
2. Voltage gain is less than unity (Av<1).
3. Power gain is less than CE configuration (Ap=Av.Ai)
4. Large I/P impedance (750KΩ).
5. Small O/P impedance (50Ω).
6. No voltage & current Phase shift.
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