Differential amplifier and CMRR

Differential amplifiers :

The amplifiers which amplify the difference of input signal as output signal is called as differential amplifiers. This amplifiers is also is also called as difference amplifier as it produce the difference of output signal as its output. The differential amplifier consist of two C- E amplifier with input signal. It’s gain is very high and never contains coupling as well as bypass capacitor. It is widely applicable amplifier.

The output of differential amplifier is given by,

$$ V_\circ=V_{\circ 2}-V_{\circ 1}$$

Inverting and non-inverting

If the input signal is only given at \(V_{i1}\) the output signal \(V_\circ=­V_{\circ 2}-V_{\circ 1}\) is in same phase with that of input signal then it is called as non-inverting input.

If the input signal is only given at \(V_{i2}\), then the output signal is in output if phase with input signal. Thus the \(V_{i2}\) is called as inverting inputs.

Depending upon the configuration of differential amplifier, there are of following types:

1.Differential input(doubled ended) and balanced (or differential) output:

In this case, the two input signals are given through \(V_{i1}\) and \(V_{i2}\) which are of opposite phase and output signal is taken as difference of output of them.

Also from DC equivalent circuit,

$$ V_{EE}=V_{BE}+2I_E R_+R_E$$

$$I_E=\frac {V_{EE}-V_{BE}}{2R_E}$$

Also from AC equivalent circuit,

The overall gain at this mode of differential amplifier,

$$A_v=\frac{R_c}{r_e’}$$

2.Differential input signal ended output:

In this case the output signal taken across either of output terminal but input signal is given from both of input terminals

Also from DC-equivalent circuit,

$$I_E=\frac{V_{EE}-V_{BE}}{2R_E}$$

The overall gain of this mode of differential amplifier,

$$A_v=\frac{R_c}{2r_e’}$$

3.Single ended input differential output :

In this case, the input signal is given through emitter of the input terminal (say \(V_{i1}\)) and output signal is taken as differential of output signal of two amplifier.

The average gain of this mode of differential amplifier ,

$$A_V=\frac{R_c}{r_e’}$$

4.Single indeed input single ended output

In this case, the input signal is given through emitter of the input terminal (say \(v_1\)) and output signal is taken as emitter of the output terminal (say\(V_{02}\)).

The overall gain of this mode differential amplifier is given by,

$$A_v=\frac{R_c}{2r_e’}$$

Common mode rejection ratio(CMRR):

It is the input signal having same magnitude with same phase are given to the two input terminal of the differential amplifier is called as common mode differential amplifier.

For ideal differential amplifier, the value of /(R_c/) is same for both transistor so that output of them are same.

Hence, overall gain of ideal differential amplifier in common mode case is zero.i.e.

$$V_\circ=V_{\circ 2}-V_{\circ 1}=0$$

Thus for better performance of differential amplifier the common mode signal should be avoided. And hence its common mode rejection ratio(CMRR) should be very high.

The common mode rejection ratio is defined as the ratio of gain of differential amplifier in differential mode(\(A_{dm}\)) to the gain in common mode(\(A_{cm}\)).i.e.

$$\therefore CMRR=\frac{|A_{dm}|}{|A_{cm}|}$$

i.e. magnitude of ratio of gain in difference mode to that of common mode.

Thus for higher value of CMRR \(A_{cm}\) should be very low. Hence, common signal are restricted as far as possible.

For ideal differential amplifier ,

\(A_{cm}=0\) and CMRR=\(\infty\)

References:

(1)Theraja, B.L. Basic Electronics. N.p.: S.Chand, n.d. Print.

(2)C.L.Arora. Refresher Course in Physics. Vol. II and III. N.p.: S.Chand, 2006. Print.

(3)Malvino. Electronic Principles. N.p.: Tata McGraw-Hill, n.d. Print.

(4)N.Nelkon and P.Parker. Advanced Level Physics. 5th ed. N.p.: Arnold Heinemann, n.d. Print.

(5)Priti Bhakta Adhikari,Diya Nidhi Chaatkuli, Ishowr Prasad Koirala. A Textbook of Physics (2nd Year). N.p.: Sukunda Pustak Bhawan, 2070. Print

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