Differential amplifier can be built using both discrete components such as transistor, resistors, diodes or it can be build using operational amplifier(op-amp). The differential amplifier with discrete components are basic building blocks that together with other circuits such as current mirror, voltage level shifter circuit are used within the operational amplifier IC. However when you search for differential amplifier you might be getting op-amp based differential amplifier or discrete transistor based differential amplifier. The discrete transistor for differential amplifier can be BJT, MOSFET or JFET type. For comparison purpose, these two structural form of differential amplifier is shown below.
The transistor based differential amplifier is called a single ended differential amplifier (also known as double input unbalanced output differential amplifier) and the ac output voltage is given by,
\( v_o = A_v(v_1 - v_2) \)
where \(v_1\) and \(v_2\) are the ac input signals and \( A_v \) is the voltage gain of the differential amplifier.
This is the same equation for the output signal for op-amp based differential amplifier.
Differential amplifier are basic building block of many circuits used in communication circuits such as differential amplifier RF modulator, sensor circuits, instrumentation amplifier design etc.
For the transistor based differential amplifier shown above which is a differential input single output the voltage gain of the differential amplifier is given by,
\( A_v = \frac{R_c}{2 r_{e,ac}} \)
where \(R_c\) and \(r_{e,ac}\) are the collector resistance and ac emitter resistance respectively. This voltage gain is close to the voltage gain of a common emitter amplifier.
The ac emitter resistance \(r_{e,ac}\) is given by,
\(r_{e,ac} = \frac{25mV}{I_E} \)
The tail current is by 1st approximation;
\( I_T = \frac{V_{EE}}{R_E} \)
But lets use the 2nd approximation;
\( I_T = \frac{V_{EE}-V_{BE}}{R_E} = \frac{5V-0.7V}{1k\Omega}=5.7mA \)
And the emitter current is half of this tail current,
\(I_E = \frac{I_T}{2}=\frac{5.7mA}{2}=2.85mA\)
The collector voltage is given by,
\(V_c=V_{cc}-I_cR_c\)
If we had used a base resistor on each base,then the current would be given by,
\( I_T = \frac{V_{EE}-V_{BE}}{R_E+ (R_B/2R\beta)}\) but we don't
And so,
\(r_{e,ac} = \frac{25mV}{I_E}=\frac{25mV}{2.85mA}=8.8\Omega\)
Therefore the voltage gain of the differential amplifier is,
\( A_v = \frac{R_c}{2 r_{e,ac}}=\frac{1k\Omega}{2\times8.8\Omega}=57\)
So from the above analysis we can find out the voltage gain, the collector voltage, the tail current, the emitter current, the collector and base current if we know the beta of the transistor.
