Describe the operation of differential amplifier with circuit diagram. Give in details the terms: (i) Common mode rejection ratio (CMRR) (ii) Differential gain (b) Explain the bootstrapping method. Also discuss the bootstrapping technique.

Differential Amplifier Operation with Circuit Diagram

A differential amplifier is a type of electronic amplifier that amplifies the difference between two input voltages but suppresses any voltage common to the two inputs. It is an important building block in analog circuits, especially in operational amplifiers.

Circuit Diagram

Here is a basic circuit diagram of a differential amplifier using two bipolar junction transistors (BJTs):

      Vcc
       |
       R_C
       |
Q1   -----   Q2
| \         / |
|  \       /  |
|   \     /   |
|    \   /    |
|     \ /     |
|      X      |
|     / \     |
|    /   \    |
|   /     \   |
|  /       \  |
| /         \ |
V1           V2
|            |
|            |
|            |
----------------
       |
      GND

In this diagram:

• Q1 and Q2 are the transistors.
• R_C is the collector resistor.
• V1 and V2 are the input voltages.
• Vcc is the supply voltage.
• The output is taken across the collectors of Q1 and Q2.

Operation

1. The input signals V1 and V2 are applied to the bases of Q1 and Q2, respectively.
2. The differential input voltage (V1 - V2) causes a difference in the currents flowing through the collectors of Q1 and Q2.
3. This current difference creates a voltage difference across the collector resistor R_C, which is the amplified output.

Terms

(i) Common Mode Rejection Ratio (CMRR)

CMRR is a measure of the ability of a differential amplifier to reject common-mode signals, which are the signals that appear simultaneously and in-phase on both inputs.

Formula:

[ CMRR = \frac{A_d}{A_{cm}} ]

Where:

• A_d is the differential gain (the gain when the input is purely differential).
• A_{cm} is the common-mode gain (the gain when the input is purely common-mode).

High CMRR Value: A high CMRR value means that the amplifier is very effective at rejecting common-mode signals and is primarily amplifying the differential signal.

(ii) Differential Gain

Differential gain is the gain of the amplifier when a differential input signal is applied. It is the ratio of the output voltage change to the difference in the input voltages.

Formula:

[ A_d = \frac{\Delta V_{out}}{\Delta V_{in(differential)}} ]

Where:

• ΔV_out is the change in output voltage.
• ΔV_in(differential) is the change in the differential input voltage.

Bootstrapping Method

Bootstrapping is a technique used in electronic circuits to improve the performance of the circuit by reducing the loading effect and increasing the input impedance.

Explanation

In bootstrapping, a part of the output is fed back to the input through a capacitor. This feedback effectively isolates the input from variations in the output, leading to a higher input impedance and less loading of the previous stage.

Bootstrapping Technique

Here's an example of a bootstrapping technique applied to a common-emitter amplifier:

      Vcc
       |
       R_C
       |
       |
      / \
     |   |
     |   |
     |   | Q1
     |   |
     \_ /
       |
       |----||---- (Bootstrapped node)
       |    C1
       |
      R1
       |
      R2
       |
      GND

In this circuit:

• Q1 is the transistor in a common-emitter configuration.
• R1 is the base resistor.
• R2 is the emitter resistor.
• C1 is the bootstrapping capacitor.

The node between R1 and C1 is the bootstrapped node. The capacitor C1 feeds a part of the AC output signal back to this node. Since the AC voltage across C1 is nearly constant (due to the feedback), the voltage at the base of Q1 does not change much with the output signal. This makes the base appear as a high impedance to the signal source, thus reducing the loading effect.

In summary, bootstrapping is a useful technique for improving the input impedance of an amplifier without significantly altering other properties of the circuit.