A multistage amplifier employs four stages, each of which has a voltage gain of 40. The overall gain of the amplifier is approximately

Multistage amplifier:

• In practical applications, the output of a single-stage amplifier is usually insufficient, though it is a voltage or power amplifier .hence they are replaced by multi-stage amplifiers.
• In multi-stage amplifiers, the output of the first stage is coupled to the input of the next stage using a coupling device.
• These coupling devices usually be a capacitor or a transformer, this process of joining two amplifier stages using a coupling device is called cascading
• Now the overall gain is equal to the product of individual gains.

The overall gain Av can be calculated by simply multiplying each gain together. This is as shown:

Mathematically, this is defined as:

In dB, the overall gain is defined as:

This can be written as:

Hence,

∴ If the gain of each amplifier stage is expressed in decibels (dB), the total gain will be the sum of the gains of individual stages.

Application:

Overall gain for 4 stages (A_v) = 40 × 40 × 40 × 40 = 256 × 10⁴

Now, overall gain in dB = 20 log A_v = 20 log (256 × 104) = 20 log 256 + 20 log 104 ≈ 128 dB