Differential Amplifier

1

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

2 OLatus Systems Pvt Ltd

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.

www.olatus.com


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

www.olatus.com


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,

www.olatus.com


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.

www.olatus.com


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.

www.olatus.com


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.

www.olatus.com


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

www.olatus.com


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

www.olatus.com


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.

www.olatus.com


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.

www.olatus.com


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

www.olatus.com


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),

www.olatus.com


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

www.olatus.com


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)

Documents

Differential Amplifier