Question

Question 2 The open loop gain of an amplifier is given by 105 Av = 10 105 If the closed loop gain is 100: 1. Show that this amplifier will be stable 2. Calculate the phase margin

Solve

Answer 1

1.

First of all we determine $\beta$ for the closed-loop gain of 100.

$A_{vf}=\frac{A_{v}}{1+\beta A _{v}}$

  
10010* 1+B(105)

= 9.99 × 10

Now we find the frequency where the magnitude of the loop gain function is 1:

  

9.99 × 10-3(105)

So,

$f\cong 3.08\times 10^{5}Hz$

The phase of the loop gain function $T(f)=\beta A_{v}$ at this frequency is-

  $\Phi =-tan^{-1}\frac{f}{10^{3}}-tan^{-1}\frac{f}{10^{5}}$

  
Φー-tan-ı 308 × 105 103 tan-13.08 × 105 105 - tan

  
,-161.8

As $\Phi$ is greater than $-180^{\circ}$. So the system will be stable.

2. The Phase margin is -

  $PM=180-161.8 = 18.2^{\circ}$