Download presentation
Presentation is loading. Please wait.
Published byAllan Brown Modified over 9 years ago
1
1 Lecture #20 EGR 272 – Circuit Theory II General 2 nd Order Transfer Function For 2 nd order circuits, the denominator of any transfer function will take on the following form: s 2 + 2 s + w o 2 Various types of 2 nd order filters can be formed using a second order circuit, including: Read: Chapter 14 in Electric Circuits, 6 th Edition by Nilsson
2
2 Lecture #20 EGR 272 – Circuit Theory II Series RLC Circuit (2 nd Order Circuit) Draw a series RLC circuit and find transfer functions for LPF, BPF, and HPF. Note that the denominator is the same in each case (s 2 + 2 s + w o 2 ). Also show that:
3
3 Lecture #20 EGR 272 – Circuit Theory II Parallel RLC Circuit (2 nd Order Circuit) Draw a parallel RLC circuit and find transfer functions for LPF, BPF, and HPF. Note that the denominator is the same in each case (s 2 + 2 s + w o 2 ). Also show that:
4
4 Lecture #20 EGR 272 – Circuit Theory II 2 nd Order Bandpass Filter A 2nd order BPF will now be examined in more detail. The transfer function, H(s), will have the following form: Magnitude response Show a general sketch of the magnitude response for H(s) above Define w o, w c1, w c2, H max, BW, and Q Sketch the magnitude response for various values of Q (in general)
5
5 Lecture #20 EGR 272 – Circuit Theory II Determining H max Find H(jw) and then H(jw) . Show that
6
6 Lecture #20 EGR 272 – Circuit Theory II Determining w c1 and w c2 : leads to Show that
7
7 Lecture #20 EGR 272 – Circuit Theory II Determining w o, BW, and Q: Show that w o is the geometric mean of the cutoff frequencies, not the arithmetic mean. Also find BW and Q. Specifically, show that: Damping ratio is simply defined here. Its significance will be seen later in this course and in other courses (such as Control Theory). Circuits with similar values of have similar types of responses.
8
8 Lecture #20 EGR 272 – Circuit Theory II Example: A parallel RLC circuit has components R, L = 100 mH, and C = 0.1 uF 1) Find w o, , H max, w c1, w c2, H max, BW, Q, and 2) Show that w o is the geometric mean of the w c1 and w c2, not the arithmetic mean. A) Use R = 1 k
9
9 Lecture #20 EGR 272 – Circuit Theory II Example: A parallel RLC circuit has components R, L = 100 mH, and C = 0.1 uF 1) Find w o, , H max, w c1, w c2, H max, BW, Q, and 2) Show that w o is the geometric mean of the w c1 and w c2, not the arithmetic mean. B) Use R 20 k
10
10 Lecture #20 EGR 272 – Circuit Theory II Example: Plot the magnitude response, |H(jw)|, for parts A and B in the last example. (Note that a curve with a geometric mean will appear symmetrical on a log scale and a curve with an arithmetic mean will appear symmetrical on a linear scale.) 5k6k7k8k9k10k20k w (log scale) |H(jw)|
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.