ELEC356
Electronics II
Spring 2008
Frequency Response
Homework problems
SOLUTION
Due: Wednesday Feb. 20, 2008
1.- For the circuit given below, obtain the transfer function Vout(ω) / Vin(ω). Identify the type of filter the
circuit represents and determine the corner frequency. Take R1 = R2 = 100 Ω, and L = 2 mH. Using
MATLAB plot the magnitude and phase of the function. Use log scale for the frequency axis. Plot both, the
linear magnitude and the magnitude in dB.
Vout = [ Z2 / (Z2 + R1) ] Vin
Z2 = R2 ║ sL = (sR2 L) / ( R2 + sL)
H(s) = Vout (s) / Vin (s) = (sLR2) / [sL(R1 + R2) + R1 R2 ]
H(s) = [s R2 / (R1 + R2)] /{ s + R1 R2 / [ L (R1 + R2) ] }
s = jω , H(ω) = [ jω R2 / (R1 + R2)] /{ jω + R1 R2 / [ L (R1 + R2 ) ] }
the cutoff frequency is: ωc = R1 R2 / [ L (R1 + R2 ) ]
At ω = 0 , H(0) = 0
As ω Æ ∞ , H( ∞ ) Æ R2/ (R1 + R2)
therefore this is a highpass filter
If R1 = R2 = 100 Ω and L = 2 mH, then
H( ∞ ) = 0.5, the – 3dB gain is 0.7071 * 0.5 = 0.3535
ωc = R1 R2 / [ L (R1 + R2 ) ] = 10000/(0.002 * 200) = 25000 rad/sec
1
ELEC356
Electronics II
Spring 2008
2.- Given the following transfer function:
a) Find the poles and zeros of the function.
b) Using MATLAB plot the magnitude and phase of the function. Use log scale for the frequency axis. Plot
both, the linear magnitude and the magnitude in dB.
c) What type of filter is this function (lowpass of highpass) ? Explain.
G(s) = s3 / [ s3 +14.8 s2 + 38.1 s + 2554]
num = [1
0
0
0];
den = [1
14.8
38.1
2554];
poles =roots(den);
zeors = roots(num);
w = logspace (0, 2);
Hs = freqresp(num,den,w);
magHdb = 20*log10(abs(Hs));
plot(w,magHdb)
title('Magnitude plot of a highpass filter ')
>> poles =
-19.5396
2.3698 +11.1845i
2.3698 -11.1845i
>> zeros
ans =
0
2