# Differential Amplifier | Common-mode Rejection Ratio | Common and Differential-mode Signals

## Differential Amplifier

A * differential amplifier* is a circuit that can accept two input signals and amplify the difference between these two input signals. Differential amplifier (DA) is key to the operation of OP-Amp, we shall discuss this in detail.

Block Diagram of Differential Amplifier |

The block diagram of a differential amplifier is shown in above fig. There are two input voltages v_{1} and v_{2}.
This amplifier amplifies the difference between the two input voltages. Therefore, the output voltage is V_{o }= A(v_{1}-v_{2}) where A is the voltage gain of the amplifier.

### Basic Circuit of Differential Amplifier

The basics circuit of
a differential amplifier is shown below in Fig. It consists of two transistors Q1 and Q2 that have identical characteristics. They share a common positive supply V_{CC, }common emitter resistor R_{C }and
common negative supply V_{EE}.

Symbol of Differential Amplifier |

The differential amplifier (DA) is a two input terminal device using at
least two transistors and there are two output terminals marked ( V_{out
1}) and ( V_{out 2}). In * Differential Amplifier*, transistor T1 and T2 are matched so that their
characteristics are the same. Both the collector resistors R

_{C1 }and R

_{C2 }are also equal. The equality of the matched circuit components makes the DA circuit arrangement completely symmetrical. The signal is applied either to one input of DA and the other input is grounded, it is called

*single-ended input**arrangement or the signals are applied to both inputs of DA, it is called*

**arrangement. Similarly, the output of DA can be taken from either one of the output terminals and ground (**

*double-ended input***arrangement) or two output terminals (**

*single-ended output*

*double-ended output**arrangement). Generally, the differential amplifier (DA) is operated for single-ended output.*

### Operation of Differential Amplifier

The operation of differential amplifier can be easily understood by giving one input (say at 1 as shown in the below figure) and which produces output at both the output terminals.

Operation of Differential Amplifier |

If the input signal (1) is supplied to the base of
transistor Q_{1}, then a high voltage drop appears across the resistor
connected to the transistor Q_{1} collector terminal which will get less
positive. If no input signal (1) is supplied to the base of transistor Q_{1}, then a low voltage drop appears across the resistor connected to the
transistor Q_{1} collector terminal which will get more positive. Thus,
we can say that the inverting output appearing across collector terminal of
transistor Q_{1} is based on the input signal 1 supplied at the base
terminal of Q_{1}.

If Q_{1} is turned ON by applying the positive value
of 1, then the current passing through emitter resistance increases as the
emitter current & collector current are almost equal. Thus, if the voltage
drop across emitter resistance increases, then the emitter of both the
transistors goes in a positive direction. If the transistor Q_{2} emitter
is positive, then the base of Q_{2} will be negative and in this
condition, current conduction is less.

Thus, there will be less voltage drop across resistor
connected at the collector terminal of transistor Q_{2}. Hence, for the given
positive input signal collector of Q_{2} will go in a positive
direction. Thus, we can say that the non-inverting output appearing across
collector terminal of transistor Q_{2} is based on the input signal
applied at the base of Q_{1}.

The amplification can be driven differentially by taking
output between the collector terminals of transistors Q_{1} and Q_{2}.
From the above circuit diagram, assuming all the characteristics of
transistors Q_{1} & Q_{2} are identical and if base voltages
V_{b1} is equal to V_{b2} (base voltage of transistor Q_{1} is equal to base
voltage of transistor Q_{2}), then emitter currents of both transistors will
be equal (Iem1=Iem2). Thus, total emitter current will be equal to the sum of
emitter currents of Q_{1} (em1) and Q_{2} (em2).

## Common-mode and Differential-mode Signals

### (i) Common-mode signals

When the input signals to a DA are in phase and exactly
equal in amplitude, they are called * common-mode signals*. The
common-mode signals are rejected By the differential amplifier. It is because a
differential amplifier amplifies the difference between the two signals
between (v

_{1}-v

_{2}) and for common-mode signals, this differences zero. Note that for common mode operations, v

_{1}= v

_{2}.

### (ii) Differential-mode signals

When the input signals to a DA are 180áµ’ out of
phase and exactly equal in amplitude, They are called * differential-mode
signals*. The differential-mode signals are amplified by the differential
amplifier. It is because the difference in the signals is twice the value of
each signal. For differential-mode signals v

_{1}= -v

_{2}.

## Voltage Gains of Differential Amplifier

The voltage gain of a Differential Amplifier operating in
differential mode is called differential mode * voltage gain* and is denoted
by A

_{DM}. The voltage gain of Differential Amplifier in common-mode is called common-mode voltage gain it is denoted by A

_{CM}.

## Common-mode Rejection Ratio (CMRR)

_{DM}) and very low common-mode voltage gain (A

_{CM}). The ratio of A

_{DM}to A

_{CM}by is called

*(CMRR). i.e.,*

**common-mode rejection ratio**CMRR = A_{DM}/A_{CM}

Very often, the CMRR is expressed in decibels (dB). The decibel measure for CMRR is given by;

CMRR_{dB} = `20\log_{10}(A_{DM}/A_{CM})`

CMRR_{dB} = `20 \log_{10}`(CMRR)

## Applications of Differential Amplifier

There are numerous application of differential amplifier in practical circuits, signal amplification, controlling of motors & servo motors, input stage emitter coupled logic, switch, and so on are common applications of the differential amplifier circuit.