Three identical amplifiers each having a voltage gain of 50 are cascaded. The open loop voltage gain of the combined amplifier is

Concept:

Two or more amplifiers circuits can be cascaded to increase the gain of an ac signal.

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

Mathematically, this is defined as:

\({{\rm{A}}_{\rm{v}}} = {{\rm{A}}_{{{\rm{v}}_1}}}.{{\rm{A}}_{{{\rm{v}}_2}}}.{{\rm{A}}_{{{\rm{v}}_3}}} \ldots .\)  

In dB, the overall gain is defined as:

\({A_v}\left( {dB} \right) = 20\;log{A_v}\)

This can be written as:

\({A_v}\left( {dB} \right) = 20\;log{A_v} = 20\;{\rm{log}}({A_{{v_1}}}.{A_{{v_2}}}.{A_{{v_3}}} \ldots .\;\)

\({A_v}\left( {dB} \right) = 20log{A_{v1}} + 20\;log{A_{v2}} + \;20\;log{A_{v3}}\; + \ldots \)

Hence,

\({A_v}\left( {dB} \right) = {A_{v1\left( {dB} \right)}} + {A_{v2\left( {dB} \right)}} + \;{A_{v3\left( {dB} \right)}}\; + \; \ldots \)

∴ 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.

Calculation:

The voltage gain of each amplifier = 50

Voltage gain of the combined amplifier = 50 × 50 × 50 = 125000

= 101.9 dB