Answer to Question #166789 in Electric Circuits for Vivek

Question

Consider a voltage amplifier having a frequency response of the low-

pass STC type with a dc gain of 60 dB and a 3-dB frequency of 1000 

Hz. Find the gain in dB at f = 10 Hz

Answer 1

First, we will use the

$$|T(j\omega)| = \large\frac{|K|}{\sqrt{1+(\large\frac{\omega}{\omega_o})^2}}$$

low pass Magnitude response equation.

$A_{VdB} = 20*log_{10}(A_V)$

$60 = 20*log_{10}(A_{V})$

$3 = log_{10}(A_V) \to A_V = 10^3 = 1000$

Next, knowing that $\large\frac{f}{f_o} = \frac{\omega}{\omega_o}$, and that $f_o$ is given we can plug that in formula:

$A_V(f) = \frac{1000}{\sqrt{1+(\frac{f}{1000})^2}} =$ $995.95$