Answer to Question #166789 in Electric Circuits for Vivek

Question #166789

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


1
Expert's answer
2021-02-25T10:53:18-0500

First, we will use the

T(jω)=K1+(ωωo)2|T(j\omega)| = \large\frac{|K|}{\sqrt{1+(\large\frac{\omega}{\omega_o})^2}}

low pass Magnitude response equation.

AVdB=20log10(AV)A_{VdB} = 20*log_{10}(A_V)

60=20log10(AV)60 = 20*log_{10}(A_{V})

3=log10(AV)AV=103=10003 = log_{10}(A_V) \to A_V = 10^3 = 1000

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

AV(f)=10001+(f1000)2=A_V(f) = \frac{1000}{\sqrt{1+(\frac{f}{1000})^2}} = 995.95995.95


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