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1. Differential amplifier with one op-amp
2. Differential amplifier with two op-amps.

**Differential amplifier:**

We will
evaluate 2 different arrangements of the differential amplifier with -ve
feedback. Classify these arrangements according to the number of op-amps used.
i.e

1.
Differential amplifier with one op-amp

2.
Differential amplifier with two op-amps.

Differential
amplifier are used in instrumentation and industrial applications to amplify
differences between 2 input signals such as output of the wheat stone bridge
circuit.

Differential
amplifier preferred to these application because they are better able to reject
common mode (noise) voltages than single input circuit such as inverting and
non-inverting amplifier.

**1. Differential Amplifier with
one op-amp:**

To
analyse this circuit by deriving voltage gain and input resistance. This
circuit is a combination of inverting and non-inverting amplifier. (i.e) WhenVx
is reduced to zero the circuit is non-inverting amplifier and when Vy is
reduced to zero the circuit is inverting amplifier.

**Voltage Gain:**

The
circuit has 2 inputs Vx and Vy . Use superposition theorem, when Vy = 0V,
becomes inverting amplifier. Hence the o/p due to Vx only is

Similarly,
when Vx = 0V, becomes Non-inverting amplifier having a voltage divider network
composed of R2 and R3 at the Non – inverting input.

Note :
the gain of the differential amplifier is same as that of inverting amplifier.

**Input Resistance:**

The input
resistance Rif of the differential amplifier is resistance determined looking
into either one of the 2 input terminals with the other grounded,

With V_{y}
= 0V,

Inverting
amplifier, the input resistance which is,

R_{i}F_{x}
≈ R_{1} -----------------

(26.a)
Similarly, ,V_{x} = 0V,

Non-inverting
amplifier, the input resistance which is,

R_{i}F_{y}
≈ (R_{2} + R_{3} ) ------(26.b)

V_{x}
and V_{y} are not the same. Both the input resistance can be made
equal, if we modify the basic differential amplifier. Both R_{1} and (R_{2}
+ R_{3}) can be made much larger than the source resistances. So that
the loading of the signal sources does not occur.

Note: If
we need a variable gain, we can use the differential amplifier. In this circuit
R_{1} = R_{2} , R_{F} = R_{3} and the
potentiometer R_{p} = R_{4}.

Depending
on the position of the wiper in R voltage can be varied from the closed loop
gain of - 2R_{F} /R_{1} to the open loop gain of A.

**2. Differential Amplifier with 2
op-amps:**

We can
increase the gain of the differential amplifier and also increase the input
resistance Rif if we use 2 op-amps.

**Voltage gain:**

It is compares of 2 stages

1. Non-inverting

2. Differential amplifier with gain.

By
finding the gain of these 2 stages, we can obtain the overall gain of the
circuit,

**Input Resistance:**

The input
resistance Rif of the differential amplifier is the resistance determined from
either one of the two non-inverting terminals with the other grounded. The
first stage A_{1} is the non-inverting amplifier, its input resistance
is

R_{i}F_{y}
= R_{i} (1+AB) -----(29. a)

Where R_{i}
= open loop input resistance of the op-amp.

B = R_{2}
/R_{2} + R_{3}

Similarly,
with V_{y} shorted to ground (V_{y} = 0 V), the 2^{nd}
stage (A_{2} ) also becomes non-inverting amplifier, whose input
resistance is

RiFx = Ri (1+AB) -----(29. b)

Where R_{i}
= open loop input resistance of the op-amp

B = R_{1} /(R_{1} + R_{F})

Since R_{1}
= R_{3} and RF = R_{2} , the Rify ≠ RiFx because the loading of
the input sources V_{x} and V_{y} may occur. (Or)

The
output signal may be smaller in amplitude than expected. This possible
reduction in the amplitude of the output signal is drawback of differential
amplifier.

To overcome
this:

With
proper selection of components, both RiFy and RiFx can be made much larger than
the sources resistance so that the loading of the input sources does not occur.

**Output resistance and Bandwidth
of differential amplifier with feedback:**

The
output resistance of the differential amplifier should be the same as that of
the non-inverting amplifier expect that B = 1/AD (i.e)

A_{D}
= closed loop gain of the differential amplifier

R0 =
output resistance of the op-amp

A = open
– loop volt gain of the op-amp

Remember
that AD is different for differential amplifier.In the case of Inverting and
Non-inverting amplifier, the bandwidth of the differential amplifier also
depends on the closed loop gain of the amplifier and is given by,

f_{F}
= Unity gain Bandwidth closed loop gain AD (or) fF = (A) (f0 )

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