135k views
4 votes
An ideal differentiator is placed in series with an ideal lowpass filter with a gain of 8 and a cutoff frequency of 26π rad/s. Find the overall frequency response

and plot its magnitude.

User Stryba
by
7.1k points

1 Answer

7 votes

Final answer:

An ideal differentiator and a lowpass filter are placed in series. To find the overall frequency response, multiply the transfer functions of the differentiator and the lowpass filter. Plotting the magnitude of the overall frequency response will give us the frequency response plot.

Step-by-step explanation:

An ideal differentiator is a circuit that performs differentiation on an input signal, while an ideal lowpass filter allows only low-frequency signals to pass through. When the differentiator and lowpass filter are placed in series, the overall frequency response can be determined by multiplying the frequency response of the differentiator with the frequency response of the lowpass filter.

To find the overall frequency response, we need to determine the transfer functions of the differentiator and the lowpass filter. Let's assume the transfer function of the differentiator is H_d(jω) = jω, and the transfer function of the lowpass filter is H_lp(jω) = 8/(1 + (jω/26π)).

Multiplying the transfer functions, we get the overall frequency response H(jω) = H_d(jω) * H_lp(jω) = (jω) * (8/(1 + (jω/26π))).

To plot the magnitude of the overall frequency response, we can substitute jω = s (where s is a complex number with the imaginary part ω), and then calculate the absolute value of H(s). Plotting the magnitude against frequency ω will give us the frequency response plot.

User Rakesh Kalashetti
by
7.5k points