The figure shows a three-stage amplifier, each having voltage gain as indicated. Find the total gain.

Concept:

Two or more amplifier 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:

\({A_v}\left( {dB} \right) = 20\;log{A_v}\) ----(1)

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 1st amplifier = 100

The voltage gain of 2nd amplifier = 200

The voltage gain of 3rd amplifier = 100

Voltage gain of the combined amplifier = 100 x 200 x 100 

= 2000000

Voltage Gain in decibels can be calculated from equation (1):

A_V = 20log(2000000) 

A_V = 20 × 6.3 = 126 dB