EE 214 Electronic Circuits Laboratory
EXPERIMENT V
FREQUENCY RESPONSE
Abstract : The frequency responses of RL, RC and RLC circuits are studied.
Preliminary Work
1) Explain the following terms:
Frequency response, magnitude response, phase response, half-power frequency, halfpower angular frequency, resonant frequency, bandwidth, quality factor, high-pass filter, low-pass
filter, band-pass filter, band-select filter.
2) Consider the circuit of Fig.1.
0.01 µF
vi(t)=Visin(ωt)
33 kΩ
vo(t)
Figure 1
Determine the frequency response function H(jω) = Vo(jω)/Vi(jω) and sketch the magnitude and
phase characteristics (ie. |H(jω)| and arg(H(jω)) vs ω). Indicate the half-power frequency ωc ,
where |H(jωc)| =
1
2
|H(jω)|max.
3) Consider the circuit of Fig. 2.
0.1 H
vi(t)=Visin(ωt)
S
0.01 µF
vo1(t) 33 kΩ
2.7 kΩ
Figure 2
19
vo2(t)
EE 214 Electronic Circuits Laboratory
a. For S open, determine and sketch the frequency response function H1(jω)=Vo1(jω)/Vi(jω).
Indicate the half-power angular frequency.
b. For S closed, determine and sketch the frequency response function H2(jω)=Vo2(jω)/Vi(jω).
Indicate the half-power angular frequencies, ωc1 and ωc2 , the resonant angular frequency ωo,
and the angular bandwidth ∆ω=ωc2-ωc1. Show that H2(jω) ≈ H1(jω)xH(jω) where H(jω) is as
found in Part 1, since loading is negligible.
4) Consider the circuit of Fig. 3.
R
L= 0.1 H
ωo = 10 krad/sec
vi(t) = Visin(ωt)
L
vi(t)
C
vo(t)
Figure 3
a. For R = 2
3.3 kΩ find C, the bandwidth ∆ω and the quality factor Q = ωo/∆ω.
b. For R = 10 kΩ find C, Q and the bandwidth. Determine and sketch the frequency response
function H(jω) = Vo(jω)/Vi(jω). Indicate the half-power angular frequencies and the resonant
angular frequency ωo.
c. A square wave (Figure 4) of frequency fo = ωo/2π is applied to the circuit of Fig.3 with
element values as in Part b.
vi(t)
Vi
-----
-----
t
-To -3To/4
-To/4
To/4
To/2
Figure 4.
20
To
EE 214 Electronic Circuits Laboratory
Since the input is periodic with period To = 1/fo seconds, it can be represented as a linear
combination of sinusoids (Fourier series representation).
2
2
1 2

v (t ) = Vo  + cos(ω o t) −
cos(3ω o t) +
cos(5ω o t)........
i
3π
5π
2 π

Find and sketch vo(t).
5) Comment on the filtering characteristics of the circuits considered in the preliminary work.
6) Propose a method to obtain the frequency response of the circuits experimentally.
Experimental Procedure
1) Set up the circuits of Figure 1. Determine the half-power angular frequency, ωc, of the circuit
experimentally. Find the phase and magnitude response of the circuit at ωc, ωc/5, 5ωc. Using the
data you have obtained, plot the phase and the magnitude response roughly. Vi(t)=10sin(ωt)
2) Setup the circuit in Figure 2. Use Vi(t)=10sin(ωt).
a) Open the switch and determine ωc experimentally. Obtain the frequency response of the
circuit at ωc, ωc/5 and 5ωc.Using the data you have obtained, plot the phase and the
magnitude response roughly.
b)
i) Close the switch and determine ω0, ωc1, ωc2 experimentally. Obtain the frequency
response of the circuit at frequencies ωc1/5, ωc1, ω0, ωc2.5ωc2. Plot the phase and magnitude
response of the circuit roughly. Determine the quality factor of this BP filter.
ii) Apply a square wave at the resonant frequency to the band-pass filter. Observe the
output of the circuit, plot the output roughly.
3) Setup the circuit in Figure 3 using the element values that you have found in Part 4.b of the
preliminary work.
a) Determine ω0, ωc1, ωc2 experimentally. Obtain the frequency response of the circuit at
frequencies ωc1/5, ωc1, ω0, ωc2.5ωc2. Plot the phase and magnitude response of the circuit
roughly. Determine the quality factor of this BP filter.
b) Apply a square wave at the resonant frequency. Observe and plot the output of the
circuit. Comment on the filtering characteristics of this circuit. Comment on the difference
between 2-b-ii.
c) In this part of the experiment, you will obtain the magnitude and the phase response of
the circuit by controlling the Agilent devices by a computer. For this purpose connect the
multimeter appropriately to measure voltage of output waveform. Turn your computer on.
First, run the “Agilent Connection Expert” program which has a shortcut on the desktop.
21
EE 214 Electronic Circuits Laboratory
Then run the “Agilent VEE” program. From the “File” menu of this program, open the file
“freqresp.vee” located on the desktop of your computer. Then press the play (►) button
on the toolbar. Now you should observe that your computer automatically adjusts the
frequency of the function generator and measures the magnitude response of your circuit.
After computer completes its operation, you can observe the magnitude response of your
circuit in the corresponding plot on the program window.
Also connect the CH1 probe of the oscilloscope to the input and CH2 to the output.
Adjust the horizontal scale of the horizontal scale of the oscilloscope to 10 ms/div.
Observe the changes with changing frequency.
Determine and record ω0, ωc1, ωc2 from the observed graphs.
In order to take the devices under your control again press the “LOCAL” button of
each device.
4) Set up the circuit of Fig.5 using the element values in Part 4.b of the preliminary work where
vi(t)=10sin(10000t)
2
S
R
1
vi(t)
vo1(t)
1kΩ
L
C
vo2(t)
Figure 5
a. For S at position 1 observe and plot vo1(t).
b. For S at position 2 observe and plot vo2(t). Why do we obtain a sinusoidal wave at vo2(t)?
Equipment List
Oscilloscope, Function Generator, Computer
Diode (1N 4001),
Capacitors (0.01 µF, 0.1 µF),
Resistors (1 kΩ, 2.7 kΩ, 33 kΩ, 10 kΩ)
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EE 214 Electronic Circuits Laboratory – Experiment 5: Frequency Response
Name - ID:
Section:
Name - ID:
Date:
Assistant Name:
Experimental Results:
Objective:
1)
(
)
( (
))
(
)
( (
))
( (
))
(
)
Magnitude response:
Phase response:
EE 214 Electronic Circuits Laboratory – Experiment 5: Frequency Response
2)
a)
(
)
( (
))
(
)
( (
))
( (
))
(
)
Magnitude response:
Phase response:
EE 214 Electronic Circuits Laboratory – Experiment 5: Frequency Response
2)
b)
(
i)
ii)
)
Magnitude response:
(
)
Phase response:
EE 214 Electronic Circuits Laboratory – Experiment 5: Frequency Response
3) a&b&c)
a)
(
)
(
)
c)
a) Magnitude response:
b)
Comment:
Phase response:
EE 214 Electronic Circuits Laboratory – Experiment 5: Frequency Response
4) a)
b)
Why do we obtain a sinusodial wave at part b?
EE 214 Electronic Circuits Laboratory – Experiment 5: Frequency Response
Comments and Conclusions: