Question

Two amplifiers are connected one after the other in series (cascade). The first amplifier has a voltage gain of 10 and the second has a voltage gain of 20. If the input signal is 0.01 volt, calculate the output ac signal.

Answer 1

- Hint: In this question use the given gain that is ${K_1}$ and ${K_2}$ of the two amplifiers, then use the direct relationship between the output voltage, input voltage and the gain of amplifiers in cascade that is ${V_{out}} = \left( {{K_1}{K_2}} \right){V_{in}}$. This will help get the right answer.

Complete step-by-step solution -

Two amplifiers are connected one after the other in series (cascaded) as shown in the figure.
The first amplifier has a voltage gain of 10 as shown in the figure.
Therefore, ${K_1}$ = 10, where ${K_1}$ is the gain of the first amplifier.
Second amplifier has a voltage gain of 20 as shown in the figure.
Therefore, ${K_2}$ = 20, where ${K_2}$ is the gain of the second amplifier.
It is given that the input signal has the voltage of 0.01 volts.
Therefore, ${V_{in}}$ = 0.01 Volts, where ${V_{in}}$ is the input voltage
Now the output voltage of the given cascaded system is given as
${V_{out}} = \left( {{K_1}{K_2}} \right){V_{in}}$
Where, ${V_{out}}$ = output voltage
Now substitute the values in the above equation we have,
$ \Rightarrow {V_{out}} = \left( {10 \times 20} \right)0.01$
Now simplify this we have,
$ \Rightarrow {V_{out}} = \left( {200} \right)0.01 = 2$ Volts.
So this is the required output voltage of the cascaded series system.
 So this is the required answer.

Note – Cascade is somewhat similar to the series combination. In cascade amplifier configuration the gains of the amplifier that are the part of the system gets multiplied. This was the trick point here in this question. Some students may confuse that gains should be added but however this what eventually differentiate between the series resistor combination and the cascade amplifier configuration.