Differential Amplifiers, Notes, Electrical and Electrical Engineering Computer Science Engineering (CSE) Notes | EduRev

 Page 1


Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
1 
Chapter No. 3 
Differential Amplifiers 
 
 
Operational Amplifiers:  
The operational amplifier is a direct-coupled high gain amplifier usable from 0 to over 1MH Z to which 
feedback is added to control its overall response characteristic i.e. gain and bandwidth. The op-amp exhibits 
the gain down to zero frequency.  
Such direct coupled (dc) amplifiers do not use blocking (coupling and by pass) capacitors since these would 
reduce the amplification to zero at zero frequency. Large by pass capacitors may be used but it is not possible 
to fabricate large capacitors on a IC chip. The capacitors fabricated are usually less than 20 pf. Transistor, 
diodes and resistors are also fabricated on the same chip.  
Differential Amplifiers:  
Differential amplifier is a basic building block of an op-amp. The function of a differential amplifier is to 
amplify the difference between two input signals.  
How the differential amplifier is developed? Let us consider two emitter-biased circuits as shown in fig. 1.  
 
Fig. 1  
The two transistors Q
1
 and Q
2
 have identical characteristics. The resistances of the circuits are equal, i.e. R
E1
 = 
R 
E2
, R
C1
 = R 
C2
 and the magnitude of +V
CC
 is equal to the magnitude of ?V
EE
. These voltages are measured 
with respect to ground.  
To make a differential amplifier, the two circuits are connected as shown in fig. 1. The two +V
CC
 and ?V
EE
 
supply terminals are made common because they are same. The two emitters are also connected and the 
parallel combination of R
E1
 and R
E2
 is replaced by a resistance R
E
. The two input signals v
1
 & v
2
 are applied 
at the base of Q
1
 and at the base of Q
2
. The output voltage is taken between two collectors. The collector 
Page 2


Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
1 
Chapter No. 3 
Differential Amplifiers 
 
 
Operational Amplifiers:  
The operational amplifier is a direct-coupled high gain amplifier usable from 0 to over 1MH Z to which 
feedback is added to control its overall response characteristic i.e. gain and bandwidth. The op-amp exhibits 
the gain down to zero frequency.  
Such direct coupled (dc) amplifiers do not use blocking (coupling and by pass) capacitors since these would 
reduce the amplification to zero at zero frequency. Large by pass capacitors may be used but it is not possible 
to fabricate large capacitors on a IC chip. The capacitors fabricated are usually less than 20 pf. Transistor, 
diodes and resistors are also fabricated on the same chip.  
Differential Amplifiers:  
Differential amplifier is a basic building block of an op-amp. The function of a differential amplifier is to 
amplify the difference between two input signals.  
How the differential amplifier is developed? Let us consider two emitter-biased circuits as shown in fig. 1.  
 
Fig. 1  
The two transistors Q
1
 and Q
2
 have identical characteristics. The resistances of the circuits are equal, i.e. R
E1
 = 
R 
E2
, R
C1
 = R 
C2
 and the magnitude of +V
CC
 is equal to the magnitude of ?V
EE
. These voltages are measured 
with respect to ground.  
To make a differential amplifier, the two circuits are connected as shown in fig. 1. The two +V
CC
 and ?V
EE
 
supply terminals are made common because they are same. The two emitters are also connected and the 
parallel combination of R
E1
 and R
E2
 is replaced by a resistance R
E
. The two input signals v
1
 & v
2
 are applied 
at the base of Q
1
 and at the base of Q
2
. The output voltage is taken between two collectors. The collector 
Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
2 
resistances are equal and therefore denoted by R
C
 = R
C1
 = R
C2
.  
Ideally, the output voltage is zero when the two inputs are equal. When v
1
 is greater then v
2
 the output voltage 
with the polarity shown appears. When v
1
 is less than v
2
, the output voltage has the opposite polarity.  
The differential amplifiers are of different configurations.  
The four differential amplifier configurations are following:  
1. Dual input, balanced output differential amplifier.  
2. Dual input, unbalanced output differential amplifier.  
3. Single input balanced output differential amplifier.  
4. Single input unbalanced output differential amplifier.  
 
 
Page 3


Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
1 
Chapter No. 3 
Differential Amplifiers 
 
 
Operational Amplifiers:  
The operational amplifier is a direct-coupled high gain amplifier usable from 0 to over 1MH Z to which 
feedback is added to control its overall response characteristic i.e. gain and bandwidth. The op-amp exhibits 
the gain down to zero frequency.  
Such direct coupled (dc) amplifiers do not use blocking (coupling and by pass) capacitors since these would 
reduce the amplification to zero at zero frequency. Large by pass capacitors may be used but it is not possible 
to fabricate large capacitors on a IC chip. The capacitors fabricated are usually less than 20 pf. Transistor, 
diodes and resistors are also fabricated on the same chip.  
Differential Amplifiers:  
Differential amplifier is a basic building block of an op-amp. The function of a differential amplifier is to 
amplify the difference between two input signals.  
How the differential amplifier is developed? Let us consider two emitter-biased circuits as shown in fig. 1.  
 
Fig. 1  
The two transistors Q
1
 and Q
2
 have identical characteristics. The resistances of the circuits are equal, i.e. R
E1
 = 
R 
E2
, R
C1
 = R 
C2
 and the magnitude of +V
CC
 is equal to the magnitude of ?V
EE
. These voltages are measured 
with respect to ground.  
To make a differential amplifier, the two circuits are connected as shown in fig. 1. The two +V
CC
 and ?V
EE
 
supply terminals are made common because they are same. The two emitters are also connected and the 
parallel combination of R
E1
 and R
E2
 is replaced by a resistance R
E
. The two input signals v
1
 & v
2
 are applied 
at the base of Q
1
 and at the base of Q
2
. The output voltage is taken between two collectors. The collector 
Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
2 
resistances are equal and therefore denoted by R
C
 = R
C1
 = R
C2
.  
Ideally, the output voltage is zero when the two inputs are equal. When v
1
 is greater then v
2
 the output voltage 
with the polarity shown appears. When v
1
 is less than v
2
, the output voltage has the opposite polarity.  
The differential amplifiers are of different configurations.  
The four differential amplifier configurations are following:  
1. Dual input, balanced output differential amplifier.  
2. Dual input, unbalanced output differential amplifier.  
3. Single input balanced output differential amplifier.  
4. Single input unbalanced output differential amplifier.  
 
 
Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
3 
Fig. 2  
These configurations are shown in fig. 2, and are defined by number of input signals used and the way an 
output voltage is measured. If use two input signals, the configuration is said to be dual input, otherwise it is a 
single input configuration. On the other hand, if the output voltage is measured between two collectors, it is 
referred to as a balanced output because both the collectors are at the same dc potential w.r.t. ground. If the 
output is measured at one of the collectors w.r.t. ground, the configuration is called an unbalanced output.  
A multistage amplifier with a desired gain can be obtained using direct connection between successive stages 
of differential amplifiers. The advantage of direct coupling is that it removes the lower cut off frequency 
imposed by the coupling capacitors, and they are therefore, capable of amplifying dc as well as ac input 
signals.  
 
Dual Input, Balanced Output Differential Amplifier:  
The circuit is shown in fig. 1, v
1
 and v
2
 are the two inputs, applied to the bases of Q
1
 and Q
2
 transistors. The 
output voltage is measured between the two collectors C
1
 and C
2
 , which are at same dc potentials.  
D.C. Analysis:  
To obtain the operating point (I
CC
 and V
CEQ
) for differential amplifier dc equivalent circuit is drawn by 
reducing the input voltages v
1
 and v
2
 to zero as shown in fig. 3. 
 
Fig. 3  
The internal resistances of the input signals are denoted by R
S
 because R
S1
= R
S2
. Since both emitter biased 
sections of the different amplifier are symmetrical in all respects, therefore, the operating point for only one 
section need to be determined. The same values of I
CQ
 and V
CEQ
 can be used for second transistor Q
2
.  
Applying KVL to the base emitter loop of the transistor Q
1
.  
Page 4


Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
1 
Chapter No. 3 
Differential Amplifiers 
 
 
Operational Amplifiers:  
The operational amplifier is a direct-coupled high gain amplifier usable from 0 to over 1MH Z to which 
feedback is added to control its overall response characteristic i.e. gain and bandwidth. The op-amp exhibits 
the gain down to zero frequency.  
Such direct coupled (dc) amplifiers do not use blocking (coupling and by pass) capacitors since these would 
reduce the amplification to zero at zero frequency. Large by pass capacitors may be used but it is not possible 
to fabricate large capacitors on a IC chip. The capacitors fabricated are usually less than 20 pf. Transistor, 
diodes and resistors are also fabricated on the same chip.  
Differential Amplifiers:  
Differential amplifier is a basic building block of an op-amp. The function of a differential amplifier is to 
amplify the difference between two input signals.  
How the differential amplifier is developed? Let us consider two emitter-biased circuits as shown in fig. 1.  
 
Fig. 1  
The two transistors Q
1
 and Q
2
 have identical characteristics. The resistances of the circuits are equal, i.e. R
E1
 = 
R 
E2
, R
C1
 = R 
C2
 and the magnitude of +V
CC
 is equal to the magnitude of ?V
EE
. These voltages are measured 
with respect to ground.  
To make a differential amplifier, the two circuits are connected as shown in fig. 1. The two +V
CC
 and ?V
EE
 
supply terminals are made common because they are same. The two emitters are also connected and the 
parallel combination of R
E1
 and R
E2
 is replaced by a resistance R
E
. The two input signals v
1
 & v
2
 are applied 
at the base of Q
1
 and at the base of Q
2
. The output voltage is taken between two collectors. The collector 
Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
2 
resistances are equal and therefore denoted by R
C
 = R
C1
 = R
C2
.  
Ideally, the output voltage is zero when the two inputs are equal. When v
1
 is greater then v
2
 the output voltage 
with the polarity shown appears. When v
1
 is less than v
2
, the output voltage has the opposite polarity.  
The differential amplifiers are of different configurations.  
The four differential amplifier configurations are following:  
1. Dual input, balanced output differential amplifier.  
2. Dual input, unbalanced output differential amplifier.  
3. Single input balanced output differential amplifier.  
4. Single input unbalanced output differential amplifier.  
 
 
Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
3 
Fig. 2  
These configurations are shown in fig. 2, and are defined by number of input signals used and the way an 
output voltage is measured. If use two input signals, the configuration is said to be dual input, otherwise it is a 
single input configuration. On the other hand, if the output voltage is measured between two collectors, it is 
referred to as a balanced output because both the collectors are at the same dc potential w.r.t. ground. If the 
output is measured at one of the collectors w.r.t. ground, the configuration is called an unbalanced output.  
A multistage amplifier with a desired gain can be obtained using direct connection between successive stages 
of differential amplifiers. The advantage of direct coupling is that it removes the lower cut off frequency 
imposed by the coupling capacitors, and they are therefore, capable of amplifying dc as well as ac input 
signals.  
 
Dual Input, Balanced Output Differential Amplifier:  
The circuit is shown in fig. 1, v
1
 and v
2
 are the two inputs, applied to the bases of Q
1
 and Q
2
 transistors. The 
output voltage is measured between the two collectors C
1
 and C
2
 , which are at same dc potentials.  
D.C. Analysis:  
To obtain the operating point (I
CC
 and V
CEQ
) for differential amplifier dc equivalent circuit is drawn by 
reducing the input voltages v
1
 and v
2
 to zero as shown in fig. 3. 
 
Fig. 3  
The internal resistances of the input signals are denoted by R
S
 because R
S1
= R
S2
. Since both emitter biased 
sections of the different amplifier are symmetrical in all respects, therefore, the operating point for only one 
section need to be determined. The same values of I
CQ
 and V
CEQ
 can be used for second transistor Q
2
.  
Applying KVL to the base emitter loop of the transistor Q
1
.  
Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
4 
 
The value of R
E
 sets up the emitter current in transistors Q
1
 and Q
2
 for a given value of V
EE
. The emitter 
current in Q
1
 and Q
2
 are independent of collector resistance R
C
.  
The voltage at the emitter of Q
1
 is approximately equal to -V
BE
 if the voltage drop across R is negligible. 
Knowing the value of I
C
 the voltage at the collector V
C
is given by  
          V
C
 =V
CC
 ? I
C
 R
C
 
and V
CE
 = V
C
 ? V
E
  
               = V
CC
 ? I
C
 R
C
 + V
BE
 
       V
CE
 = V
CC
 + V
BE
 ? I
C
R
C
       (E-2) 
From the two equations V
CEQ
 and I
CQ
 can be determined. This dc analysis applicable for all types of 
differential amplifier.  
Example - 1  
The following specifications are given for the dual input, balanced-output differential amplifier of fig.1:  
R
C
 = 2.2 k?, R
B
 = 4.7 k?, R
in 1
 = R
in 2
 = 50 ? , +V
CC
 = 10V, -V
EE
 = -10 V, ß
dc
 =100 and V
BE
 = 0.715V. 
Determine the operating points (I
CQ
 and V
CEQ
) of the two transistors.  
Solution:  
The value of I
CQ
 can be obtained from equation (E-1).  
 
       
Page 5


Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
1 
Chapter No. 3 
Differential Amplifiers 
 
 
Operational Amplifiers:  
The operational amplifier is a direct-coupled high gain amplifier usable from 0 to over 1MH Z to which 
feedback is added to control its overall response characteristic i.e. gain and bandwidth. The op-amp exhibits 
the gain down to zero frequency.  
Such direct coupled (dc) amplifiers do not use blocking (coupling and by pass) capacitors since these would 
reduce the amplification to zero at zero frequency. Large by pass capacitors may be used but it is not possible 
to fabricate large capacitors on a IC chip. The capacitors fabricated are usually less than 20 pf. Transistor, 
diodes and resistors are also fabricated on the same chip.  
Differential Amplifiers:  
Differential amplifier is a basic building block of an op-amp. The function of a differential amplifier is to 
amplify the difference between two input signals.  
How the differential amplifier is developed? Let us consider two emitter-biased circuits as shown in fig. 1.  
 
Fig. 1  
The two transistors Q
1
 and Q
2
 have identical characteristics. The resistances of the circuits are equal, i.e. R
E1
 = 
R 
E2
, R
C1
 = R 
C2
 and the magnitude of +V
CC
 is equal to the magnitude of ?V
EE
. These voltages are measured 
with respect to ground.  
To make a differential amplifier, the two circuits are connected as shown in fig. 1. The two +V
CC
 and ?V
EE
 
supply terminals are made common because they are same. The two emitters are also connected and the 
parallel combination of R
E1
 and R
E2
 is replaced by a resistance R
E
. The two input signals v
1
 & v
2
 are applied 
at the base of Q
1
 and at the base of Q
2
. The output voltage is taken between two collectors. The collector 
Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
2 
resistances are equal and therefore denoted by R
C
 = R
C1
 = R
C2
.  
Ideally, the output voltage is zero when the two inputs are equal. When v
1
 is greater then v
2
 the output voltage 
with the polarity shown appears. When v
1
 is less than v
2
, the output voltage has the opposite polarity.  
The differential amplifiers are of different configurations.  
The four differential amplifier configurations are following:  
1. Dual input, balanced output differential amplifier.  
2. Dual input, unbalanced output differential amplifier.  
3. Single input balanced output differential amplifier.  
4. Single input unbalanced output differential amplifier.  
 
 
Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
3 
Fig. 2  
These configurations are shown in fig. 2, and are defined by number of input signals used and the way an 
output voltage is measured. If use two input signals, the configuration is said to be dual input, otherwise it is a 
single input configuration. On the other hand, if the output voltage is measured between two collectors, it is 
referred to as a balanced output because both the collectors are at the same dc potential w.r.t. ground. If the 
output is measured at one of the collectors w.r.t. ground, the configuration is called an unbalanced output.  
A multistage amplifier with a desired gain can be obtained using direct connection between successive stages 
of differential amplifiers. The advantage of direct coupling is that it removes the lower cut off frequency 
imposed by the coupling capacitors, and they are therefore, capable of amplifying dc as well as ac input 
signals.  
 
Dual Input, Balanced Output Differential Amplifier:  
The circuit is shown in fig. 1, v
1
 and v
2
 are the two inputs, applied to the bases of Q
1
 and Q
2
 transistors. The 
output voltage is measured between the two collectors C
1
 and C
2
 , which are at same dc potentials.  
D.C. Analysis:  
To obtain the operating point (I
CC
 and V
CEQ
) for differential amplifier dc equivalent circuit is drawn by 
reducing the input voltages v
1
 and v
2
 to zero as shown in fig. 3. 
 
Fig. 3  
The internal resistances of the input signals are denoted by R
S
 because R
S1
= R
S2
. Since both emitter biased 
sections of the different amplifier are symmetrical in all respects, therefore, the operating point for only one 
section need to be determined. The same values of I
CQ
 and V
CEQ
 can be used for second transistor Q
2
.  
Applying KVL to the base emitter loop of the transistor Q
1
.  
Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
4 
 
The value of R
E
 sets up the emitter current in transistors Q
1
 and Q
2
 for a given value of V
EE
. The emitter 
current in Q
1
 and Q
2
 are independent of collector resistance R
C
.  
The voltage at the emitter of Q
1
 is approximately equal to -V
BE
 if the voltage drop across R is negligible. 
Knowing the value of I
C
 the voltage at the collector V
C
is given by  
          V
C
 =V
CC
 ? I
C
 R
C
 
and V
CE
 = V
C
 ? V
E
  
               = V
CC
 ? I
C
 R
C
 + V
BE
 
       V
CE
 = V
CC
 + V
BE
 ? I
C
R
C
       (E-2) 
From the two equations V
CEQ
 and I
CQ
 can be determined. This dc analysis applicable for all types of 
differential amplifier.  
Example - 1  
The following specifications are given for the dual input, balanced-output differential amplifier of fig.1:  
R
C
 = 2.2 k?, R
B
 = 4.7 k?, R
in 1
 = R
in 2
 = 50 ? , +V
CC
 = 10V, -V
EE
 = -10 V, ß
dc
 =100 and V
BE
 = 0.715V. 
Determine the operating points (I
CQ
 and V
CEQ
) of the two transistors.  
Solution:  
The value of I
CQ
 can be obtained from equation (E-1).  
 
       
Operational Amplifier 
 
Notes prepared by Mrs. Sejal Shah 
 
5 
The voltage V
CEQ
 can be obtained from equation (E-2).  
 
The values of I
CQ
 and V
CEQ
 are same for both the transistors. 
 
 
Dual Input, Balanced Output Difference Amplifier:  
The circuit is shown in fig. 1 v
1
 and v
2
 are the two inputs, applied to the bases of Q
1
 and Q
2
 transistors. The 
output voltage is measured between the two collectors C
1
 and C
2
, which are at same dc potentials.  
 
Fig. 1  
A.C. Analysis :  
In previous lecture dc analysis has been done to obtain the operatiing point of the two transistors. 
To find the voltage gain A
d
 and the input resistance R
i
 of the differential amplifier, the ac equivalent circuit is 
drawn using r-parameters as shown in fig. 2. The dc voltages are reduced to zero and the ac equivalent of CE 
configuration is used.