Question

The amplifiers $X,Y$ and $Z$ are connected in series. If the voltage gains of $X,Y$ and $Z$ are $10,20$ and $30$, respectively and the input signal is $1mV$ peak value, then what is the output signal voltage (peak value)

(i) if $dc$ supply voltage is $10V$?

(ii) if $dc$ supply voltage is $5V$?

Answer 1

$\text{Find the net gain of amplifiers}.$

Given,

voltage gain of $X,V_X=10$

voltage gain of $Y,V_Y=20$

voltage gain of $Z,V_Z=30$

As given the three amplifiers are connected in series,

So net gain,

$\frac{V_o}{V_i}=V_X\times V_Y\times V_Z$

$\frac{V_o}{V_i}=10\times 20\times 30=6\times {10}^3$

$\text{Find the output signal voltage}.$

Given,

input signal, $V_i=1mV$

So, output signal voltage, $V_o=6\times {10}^3\times 1mV$

$V_o=6V$

Now, if the supply voltage is $10V$, the output voltage will be $6V$, so the output can never be greater than $6V$.

$\text{Final answer}:6V$


$\text{Find the net gain of amplifiers}.$

Given,

voltage gain of $X,V_X=10$

voltage gain of $Y,V_Y=20$

voltage gain of $Z,V_Z=30$

As given the three amplifiers are connected in series,

So net gain,

$\frac{V_o}{V_i}=V_X\times V_Y\times V_Z$

$\frac{V_o}{V_i}=10\times 20\times 30=6\times {10}^3$

$\text{Find the output signal voltage}.$

Given, input signal, $V_i=1mV$

So, output signal voltage, $V_o=6\times {10}^3\times 1mV$

$V_o=6V$

As the supply voltage is $5V$, saturation occurs, and output voltage will not exceed $5V$, therefore peak output voltage $=5V$.

$\text{Final answer}:5V$