Question

What is meant by feedback? Derive an expression for voltage gain of an amplifier with negative feedback.

Answer 1

Feedback in Amplifiers: Feedback is when a fraction of the output signal is returned or fed back to the input and combined with the input signal.
Principle of Feedback Amplifier: For an ordinary amplifier i.e., without feedback, let $V_0$ and $V_1$ be the output voltage and input voltage respectively. If A be the voltage gain of the amplifier, then $A=\frac{V_o}{V_i}$. The gain A is often called as open-loop gain. The general theory of feedback can be explained with the help of block diagram shown in Figure. The feedback amplifier has two parts [i.e.] amplifier and feedback circuit. The feedback circuit usually consists of passive components(resistor, capacitor, inductor). A fraction(say $\beta$) of the output voltage is fed back to the input through the feedback circuit. Let $V_o^{\prime }$ be the output voltage with feedback.
Therefore, after feedback the input voltage ${}^{\prime }{v}_1^{\prime }$ becomes,
$V_1^{\prime }=V_1+\beta V_0$ ............$\left(1\right)$
For positive feedback, $b$ is taken as positive. For negative feedback, b is taken as negative.
For positive feedback, the input voltage will be $V_1+\beta V_0^{\prime }$. When this is amplified A time by the amplifier, the output voltage after feedback $\left(V_0^{\prime }\right)$ will be $A(V_1+\beta V_0^{\prime })$.
$V_0^{\prime }=A(V_1+\beta V_0^{\prime })$ ...............$\left(2\right)$
$V_0^{\prime }(1-\beta A)=A{V}_1$ ................$\left(3\right)$
Then the voltage gain of the amplifier with feedback is.
$A_f=\frac{V_o}{V_i}=\frac{A}{1-A\beta }$ .............$\left(4\right)$
Since $|1-A\beta |<1,A_f>A$. The positive feedback increases the amplifier gain.
For negative feedback, the feedback fraction is $-b$.
$A_f=\frac{A}{1-(-A\beta )}=\frac{A}{1+A\beta }$
The transmitter is essentially a high power magnetron oscillator which generates high power pulses. This transmitter is turned on and off with a periodic pulse from the pulser. Thus the transmitter generates periodic pulses of very short duration. These short pulses are fed to the antenna which radiates them into the space. The antenna is highly directional.
If the transmitted pulse hits any target, a weak echo signal returns to the same antenna. But, now the TR switch puts the antenna in contact with the receiver. This echo signal is amplified and demodulated by the superheterodyne amplifier.
Since $|1+\beta A|>1,A_f<A$. Therefore negative feedback reduces the amplifier gain.
The tern $A\beta$ is called loop gain and $\beta$ is called feedback ratio.