ESE 271 / Spring 2013 / Lecture 21 Frequency response.

After partial fraction expansion

Natural response For stable circuit:

In steady-state:

1 ESE 271 / Spring 2013 / Lecture 21 Magnitude and Phase frequency responses.

2 ESE 271 / Spring 2013 / Lecture 21 Example.

Find Transfer function in s‐domain

3 ESE 271 / Spring 2013 / Lecture 21 Example ‐ cont.

Find frequency response function in frequency domain

Freqqyuency response function

4 ESE 271 / Spring 2013 / Lecture 21 Example ‐ cont.

Let’s plug in some numbers

5 ESE 271 / Spring 2013 / Lecture 21 Example ‐ cont.

Plot of magnitude frequency response for:

1. Circuit is low pass filter (LPF). 2. Linear scale is not good for plotting magnitude frequency response function 6 ESE 271 / Spring 2013 / Lecture 21 Logarithmic scale. These two frequencies can not be shown on the same plot if linear scale is used. But they can be shown together easily on log scale.

Same is true for voltages. Log scale would allow to see both 5 and 0.05 V on one plot.

7 ESE 271 / Spring 2013 / Lecture 21 Decibel scale

Can change by several orders of magnitude, hence, should plot in dB scale

When

If frequency is changed by decade

8 ESE 271 / Spring 2013 / Lecture 21 Plot of Magnitude Frequency response from example in dB scale

9 ESE 271 / Spring 2013 / Lecture 21 Plot of Magnitude Frequency response from example in dB scale

10 ESE 271 / Spring 2013 / Lecture 21 Frequency response function of linear circuits Transfer function Zeros (roots of nominator) Poles (roots of denominator)

Frequency response function

For complex zeros or poles there are always complex conjugate present.

‐ Natural frequency (positive real number)

‐ Damping factor (positive real number for stable circuits)

11 ESE 271 / Spring 2013 / Lecture 21 Gain Bode Plots plots of magnitude frequency response in dB scale

Magnitude frequency response function in dB scale

‐ Simple constant (does not depend on frequency)

‐ For real zeros or poles

‐ For complex zeros or poles

12 ESE 271 / Spring 2013 / Lecture 21 Example 1.

13 ESE 271 / Spring 2013 / Lecture 21 Example 1 –cont.

14 ESE 271 / Spring 2013 / Lecture 21 Example 1 –cont.

15 ESE 271 / Spring 2013 / Lecture 21 Example 2.

16 ESE 271 / Spring 2013 / Lecture 21 Example 2.

17