differential amplifier
DESCRIPTION
Integrated Circuits DesignTRANSCRIPT
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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)