Transistor Based Differential Amplifier

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Purpose of differential amplifier is to generate output signal that is proportional to input signals difference. Block scheme of an general differential amplifier is given in figure bellow.

differential-amplifier-block

Desired output voltage is proportional (or equal) to voltage difference:

diff_bjt_eq01

However, in practice, there is always some side effects and imperfectness, so

diff_bjt_eq02

Output voltage of an differential amplifier suppose to be free from averaged voltage

diff_bjt_eq03

Assuming that differential amplifier is linear circuit, we can do further analyses by using superposition theorem. Output voltage can be marked as:

diff_bjt_eq04

In here, AA is voltage gain of input signal VA

diff_bjt_eq05

and AB is voltage gain of input signal VB

diff_bjt_eq06

Output voltage of differential amplifier can be expressed with averaged voltage VM and differential voltage VD.

diff_bjt_geometry

With the output voltage expressed over averaged and differential voltage, and separating gains, we obtain

diff_bjt_eq07

i.e.

diff_bjt_eq08

In here, AM is averaged signal gain defined as

diff_bjt_eq09

and AD is differential signal gain defined as

diff_bjt_eq10

For ideal differential amplifier, it must be obtained that VA=-VB. Measure for imperfection of an differential amplifier is Common Mode Rejection parameter CMRR defined as

diff_bjt_eq11

Differential amplifier is an input stage of every operational amplifier. In a case of ideal differential amplifier, CMRR would be infinite, since AM would be zero. In real operational amplifiers, CMRR is larger then 1000000. Depending on technology how op-amp is integrated, input differential amplifier can be realized with BJT transistors, JFET transistors or MOSFET transistors. BJT transistor differential amplifier is given in figure bellow.

differential-amplifier-bjt

In the upper scheme, Q0 is the current source. Differential gain AD for BJT transistor differential amplifier is

diff_bjt_eq12

In here, RC1=RC2=RC, VT is threshold voltage, I0 is current of the current source Q0 (collector current of Q0). Parameters hFE and h11 are Q1 i.e Q2 transistors current gain, and base resistance, respectively. BJT transistor differential amplifier can be improved if collectors resistors are replaced with active load (current mirror). Scheme of BJT transistor differential amplifier with current mirror is given bellow.

differential-amplifier-current-source

Differential gain of BJT transistor differential amplifier with current mirror is

diff_bjt_eq13

BJT transistor differential amplifier has it’s limitations. Voltage difference VA-VB must not be lower then -3VT or higher then +3VT, otherwise, differential amplifier will be saturated. Take a look at transfer characteristic.

differential-amplifier-bjt-transfer

JFET transistor based differential amplifier is very similar, and it’s given in figure bellow.

differential-amplifier-jfet

Generally, if input stage of an operational amplifier is realized as BJT transistor differential amplifier, op-amp has smaller slew rate, smaller voltage offset and better CMRR. If it’s realized as JFET transistor based differential amplifier, voltage offset is higher, CMRR is smaller but slew rate is better.

External links:

Differential Amplifier on Ecircuitcenter
Differential Amplifier on Wikipedia
Differential Amplifier on Circuitstoday

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