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DIFFERENTIAL AMPLIFIER
Differential amplifier amplifies the difference between two
input voltage signals. Hence it is
called difference or differential amplifier.
Ideal Differential Amplifier
Fig: Ideal Differential Amplifier
In the above figure,
V1 and V2 are the inputs to the differential amplifier
V0 is the single ended output
Note: Each signal is measured with respect to ground.
According to the definition of differential amplifier, the
output voltage is directly proportional to
the difference between the two input signals.
Hence, we can write
.. (1)
Gain of Amplifier
Differential amplifier has two types of gain
1. Differential Gain, Ad
2. Common Mode Gain, Ac
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Differential Gain, Ad
From equation (1), we can write
Where, Ad is constant of proportionality
Ad is the gain which differential amplifier amplifies the
difference between two input signals.
Hence, it is called differential gain of the differential
amplifier.
The difference between the two inputs (V1 V2) is generally
called difference voltage and is
denoted by Vd.
So, differential gain can be expressed as
And in decibel (dB), it is expressed as
Common Mode Gain, Ac
If we apply two equal input voltages to the differential
amplifier i.e. V1 = V2, then ideally the
output voltage , must be zero. But, practically not is not
zero.
The output voltage of the practical differential amplifier not
only depends on the difference of
the voltages but also depends on the average common level of the
two inputs. Such an average
level of the two input signals is called common mode signal
denoted by Vc.
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Common mode gain is not zero due to mismatch in the internal
circuitry and the value of Ac is
very small while the value of Ad is large.
Practically, the differential amplifier produces the output
voltage proportional to such common
mode signal, Vc.
Or,
Ac is the gain with which the differential amplifier amplifies
the common mode signal. Such gain
is called common mode gain, Ac.
So, total output of any differential amplifier can be expressed
as
Features of Differential Amplifier
High differential voltage gain
Low common mode gain
High CMRR
Two input terminals
High input impedance
Large bandwidth
Low output impedance
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Common Mode rejection Ratio (CMRR)
It is an important property of differential amplifier.
When the same voltage is applied to both the inputs of
differential amplifier, the differential
amplifier is said to be operated in common mode configuration.
In this common configuration,
many problem arises like signal disturbance, noise signals etc.
appear as the common input
signal to both the input terminals of the differential
amplifier, that is why, we need a rejection of
common mode signal.
The ability of differential amplifier to reject a common mode
signal is expressed by a ratio called
common mode rejection ratio. It is denoted by CMRR.
And it is defined as the ratio of differential voltage gain, Ad
to common mode voltage gain, Ac.
Ideally common mode voltage is zero i.e. V0 = 0, which means Ac
is zero, hence the ideal value
of CMRR is infinite.
But practically, Ad is very large and Ac is very small, hence
the value of CMRR is also very
large.
CMRR in dB is expressed as
Total output voltage,V0 of differential amplifier can be
expressed in terms of CMRR as
Or,
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Or,
Or,
Types of Differential amplifier
There are four types of differential amplifier and they are
Dual input, balanced output differential amplifier
Dual input, unbalanced output differential amplifier
Single input, balanced output differential amplifier
Single input, unbalanced output differential amplifier
Differential amplifier uses two transistors in common emitter
configuration.
If output is taken between the two collectors, it is called
balanced output or double ended
output. While if the output is taken between one of the
collector with respect to ground, then it is
called unbalanced output or single ended output.
If signal is given go both the input terminals, it is called
dual input. While if the signal is given
to only one input terminal and the other is grounded, then it is
called single input.
Out of these four configurations, the dual input and balanced
output is the most useful
configuration.
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Transistorized Differential amplifier
Transistorized differential amplifier used two common emitter
amplifiers with emitter resistance
in identical characteristics
Fig: Two Common Emitter Amplifier
Two transistors Q1 and Q2 are identical in characteristics. Two
collector resistances RC1 and RC2
are identical and two emitter resistances RE1 and RE2 are also
identical. Magnitude of Vcc and -
Vee are same.
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Fig: Transistorized Differential Amplifier
The differential amplifier can be obtained by using such two
emitter biased circuits. This is
achieved by connection of emitter of Q1 to emitter of Q2. Due to
this, RE1 appears in parallel with
RE2 and this combination is replaced by a single resistor,
RE.
The output can be taken between the two collectors or between
one collector and ground. When
the input is taken between the two collectors and none of them
is grounded then it is called
balanced output or double ended output or floating output.
When the output is taken between one of the collectors and the
ground, then it is called
unbalanced output or single ended output.
Such an amplifier is called emitter coupled differential
amplifier.
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Operation of Differential Amplifier (Dual input, Balanced
output)
In the differential mode, the two input signals are different
from each other.
Considering two input signals which are same in magnitude but
180 out of phase. Assuming
that the sine wave on base of Q1 is positive going, while on the
base of Q2 is negative going.
With a positive going signal on the base of Q1, an amplified
negative going signal develops on
the collector of Q1. Due to this, the current through emitter
resistance, RE also increases and
hence a positive going wave is developed across RE.
Due to negative going signal on the base of Q2, an amplified
positive going signal develops on
the collector of Q2 and a negative going signal develops across
RE.
So signal voltage across RE due to the effect of Q1 and Q2 are
equal in magnitude and 180 out
of phase due to matched pair of transistors. Hence, two signals
cancel out each other and there is
no signal across RE.
Hence there is no ac signal across RE and thus no ac signal
current flowing through RE.
Fig: Common Mode Operation
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DC Analysis of Differential Amplifier
DC analysis means to obtain the operating point values VCEQ and
ICQ.
Supply voltages are dc while the input signals are ac. So for dc
analysis, ac signal must be zero.
Fig: DC Analysis of Differential Amplifier
Assuming RS1 = RS2 = RS, Q1 and Q2 are matched transistors.
For the matched transistors, we can assume
Both the transistors have same characteristics
RS1 = RS2 and hence, RE = RE1 || RE2
RC1 = RC2 = RC
|VCC| = |VEE|, both are measured with respect to ground
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As the two transistors are matched and circuit is symmetrical,
it is enough to find out operating
points VCEQ and ICQ for any one of the two transistors. The same
is applicable for the other
transistor.
Applying KCL to the base-emitter loop of transistor Q1,
Since,
and ,
or,
where,
VBE = 0.6 to 0.7V for Si
= 0.2V for Ge
But,
Therefore,
.. (1)
So from this equation, we can observe that
RE determines the emitter current of Q1 and Q2 for the known
value of VEE.
The emitter current through Q1 and Q2 is independent of
collector resistor, RC.
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Now, let us determine VCE
The collector voltage of Q1,
Voltage for collector to emitter is
But,
So,
Or, (2)
So, equations (1) and (2) are the operating point values of Q1
and Q2.
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AC Analysis of Differential Amplifier using h-parameters
In the ac analysis, we will calculate the differential gain
(Ad), input resistance (Ri) and the output
resistance (Ro) of the differential amplifier using
h-parameters.
Differential Gain (Ad)
For the differential gain calculation, the two input signals
must be different from each other.
Let the two ac input signals be equal in magnitude but having
180 phase difference between
them. Since both the transistors are matched and identical in
characteristics,
The two ac emitter current IC1 and IC2 are equal in magnitude
and 180 out of phase. Hence, they
cancel each other to give resultant ac current through the
emitter as zero. Hence for the ac
purpose, emitter terminal can be grounded.
Here by applying half circuit concept, gain can be calculated
using only one of the transistors.
Fig: Half Circuit Concept
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The approximate hybrid model for the above circuit is shown in
the figure below
Fig: Hybrid Model of the Circuit
Applying KVL to the input loop,
Or,
Or,
. (i)
Applying KVL to the output loop,
Or,
Or,
.. (ii)
Equating equations (i) and (ii),
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But,
So,
Or,
The negative sign indicates the phase difference between the
input and the output.
Therefore,
Here, we have measured output with respect to ground. But in
case of dual output, Ad is
multiplied by 2.
Differential Input Impedance (Zi)
Fig: Differential Input Impedance
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Input impedance means total resistance that appears at the input
terminals of the circuit.
Applying KVL at the input loop,
Or,
Or,
Therefore, input impedance,
Output Impedance (Zo)