Lecture 27. Active Sallen & Key Butterworth Filter Design
1. Sallen and Key LP Circuit
2. Sallen and Key Circuit Transfer Function
K
V (s)
R1R2C1C2
H SK ( s ) = out
=
Vin ( s )
1
1
1 K
1
s2 +
+
+
s+ R R CC
R1C1 R2C1 R2C2
1 2 1 2
where K = Vout Va = 1
EE202
HOMEWORK PROBLEMS
POEMS FOR THE LIBERAL PART OF YOUR EDUCATION
Part 1Nerd Poetry
A dozen, a gross, and a score
Plus three times the square root of four
Divided by seven
Plus five times eleven
Is nine squared, not a bit more.
Integral t-squared dt
Fr
(c) Consider the circuit below. Suppose L = 1 H, R1 = 15 , C = 0.01 F, and R2 = 5 .
Suppose vin (t) , the voltage + to across the current source is the desired output. The transfer function
V (s)
?
H (s) = in = Zin (s) =
. Find the phase and magnitude of
202 HW Probs
page 5
Fall 14
t
(iii) Compute L [ g2 (t)] = L f ( )d using the integral property.
(b) Repeat part (a) for fnew (t) = f (t + T ) .
DUE WEDNESDAY WEEK 3 (SEPT 10) HW3
V (s)
9. (a) Compute the relationship H (s) = out
associated with the int
(b) (i) Now suppose vin (t) = 4eat u(t 4) + 2teat u(t 1) V. Find Vin (s) . (Be Careful, the time shift
property applies directly to functions of the form f (t T )u(t T ) but not directly to f (t)u(t T ) .
Use properties wherever possible, akin to e1e 1 =
EE202
HOMEWORK PROBLEMS (SET 2)
FALL 14
TO THE STUDENT: ALWAYS CHECK THE ERRATA on the web.
Quotes for your Parent's Parties: 1. It requires a very unusual mind to undertake the analysis of the
obvious. Alfred North Whitehead.
2. No race can prosper until
ECE-202
HOMEWORK PROBLEMS (SET 1)
FALL 14
TO THE STUDENT: ALWAYS CHECK THE ERRATA on the web.
ANCIENT ASIAN PROVERB: If you give someone a fish, you give them food for a day; teach a person to fish
and you give them food for a lifetime. The Moral of the P
EE202
HOMEWORK PROBLEMS
FALL 14
TO THE STUDENT: ALWAYS CHECK THE ERRATA on the web.
Quotes for your Parent's Parties: 1. Only with nodal analysis is the rest of the semester a possibility.
Ray DeCarlo
2. (The need for uniqueness.) Anybody, who is any good
HW 11, DUE FRIDAY OCTOBER 24
41.
Consider the circuit shown in the figure below.
V (s)
(a) Compute the transfer function H (s) = C
in terms of the circuit parameters, R1, Rs , etc.
Vin (s)
First do a source transformation but make sure you obtain the corr
HW 12, DUE THURSDAY OCTOBER 30, 5:00 PM AS USUAL
45.
Consider the RLC circuits in the figure below in which R p = 12 k, L = 0.6 mH, Rs = 80
C = 0.9375 nF.
1
(a) Find the coil Q, Qcoil at 0 =
of the practical inductor.
LC
(b) Find an approximate parallel
MATLAB CODE
% Problem 41
clc
clear
close all
L = 1;
C = 10^-6;
Rs = 6250;
R1 = 25000;
wm = 1000;
B = [1/Rs/C,0];
A = [1, (R1+Rs)/R1/Rs/C, 1/L/C];
w = 0:1:2.5*wm;
freqs(B,A,w)
H = freqs(B,A,w);
% find the maximum height of the magnitude plot and use this v