Question

Three amplifiers ${\text{X, Y and Z}}$ are connected in series. If the voltage gains of ${\text{X, Y and Z}}$ are ${\text{10, 20 and 30}}$ respectively and the input signals is $1mV$ peak value, then what is the output signal voltage (Peak value), if dc supply voltage is $10V{\text{ ?}}$

Answer 1

Hint In the question they have provided the value of voltage gain of three amplifiers which are connected in series. Find the total voltage gain of the amplifiers connected in series. We know that the total voltage gain is equal to the ratio of output signal to the input signal, use this relation to find the value of output voltage.

Formula used
${\text{Voltage gain = }}\dfrac{{{\text{output signal voltage}}}}{{{\text{Input signal voltage}}}}$
${{\text{A}}_{\text{V}}}{\text{ = }}\dfrac{{{{\text{V}}_{Out}}}}{{{{\text{V}}_{{\text{In}}}}}}$
${{\text{A}}_{\text{V}}}{\text{ is the voltage gain of the amplifier}}{\text{.}}$
${{\text{V}}_{Out}}{\text{ is the output signal voltage}}{\text{.}}$
${{\text{V}}_{{\text{In}}}}{\text{ is the input signal voltage}}{\text{.}}$

Complete step by step answer
Amplifiers is an electronic device used to amplify (increase) the magnitude of input signal applied to it. The input signal can be in the form of voltage or current or power. Amplifiers can amplify both ac and dc signals based on that amplifiers are divided into two types, dc amplifiers and ac amplifiers.
The amplifier gain is the amount of amplification that an amplifier performs. It is the measure of the ability to amplify a signal.
The amplifier gain is the ratio of output signal to input signal.
Voltage gain: The ratio of output voltage to the input voltage.
Current gain: The ratio of output current to the input current.
Power gain: The ratio of output power to the input power.
Given,
${\text{Voltage gain of X = 10}}$
${\text{Voltage gain of Y = 20}}$
${\text{Voltage gain of Z = 30}}$
${\text{Input voltage signal = 1mV = 1}} \times {\text{1}}{{\text{0}}^{ - 3}}V$
We have to find the output voltage signal.

When amplifiers are connected in series the total gain of the amplifiers is the product of the individual gain of the amplifiers.
The total voltage gain of amplifiers X, Y and Z connected in series is as follows,
${\text{Total voltage gain, }}{{\text{A}}_V}{\text{ = Voltage gain of X }} \times {\text{ Voltage gain of Y }} \times {\text{ Voltage gain of Z}}$
${{\text{A}}_V}{\text{ = 10}} \times {\text{20}} \times {\text{30}}$
${{\text{A}}_V}{\text{ = 6000}}$
We know that,
${\text{Voltage gain = }}\dfrac{{{\text{output signal voltage}}}}{{{\text{Input signal voltage}}}}$
${{\text{A}}_{\text{V}}}{\text{ = }}\dfrac{{{{\text{V}}_{Out}}}}{{{{\text{V}}_{{\text{In}}}}}}$
${\text{6000 = }}\dfrac{{{{\text{V}}_{Out}}}}{{1 \times {{10}^{ - 3}}}}$
${{\text{V}}_{{\text{Out}}}}{\text{ = 6000}} \times {\text{1}} \times {\text{1}}{{\text{0}}^{ - 3}}$
${{\text{V}}_{{\text{Out}}}}{\text{ = 6V}}$
The voltage signal output is $6V$
If the dc supply voltage is $10V$ then the output voltage signal is $6V.$ The output cannot exceed $6V$ because the maximum amplification is done and the output voltage given by the circuit is $6V.$

Note: The output of the amplifier cannot exceed $6V$ even if the supplied dc voltage is more than $6V$ if the supplied dc voltage is less than $6V$ then the output voltage will decrease.