EE 214 Electronic Circuits Laboratory
Spring 2015
EXPERIMENT VI
FREQUENCY RESPONSE
Objectives
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, half-power angular
frequency, resonant frequency, bandwidth, quality factor, high-pass filter, low-pass filter, band-pass filter,
band-select filter.
2. Consider the circuit given in Figure 1.
C
vi(t)=Visin(t)
R
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(𝑗𝜔)| =
1
√2
|𝐻(𝑗𝜔)|𝑚𝑎𝑥. Calculate 𝜔𝑐 for C=0.01μF and
R=33 kΩ.
3. Consider the circuit given in Figure 2.
L=0.1 H
vi(t)=Visin(t)
R=2.7 kΩ
0.01 μF
S
vo1 (t) 33 kΩ
Figure 2
1
vo2(t)
EE 214 Electronic Circuits Laboratory
a.
Spring 2015
For S open, determine and the frequency response function 𝐻1 (𝑗𝜔) = 𝑉𝑜1 (𝑗𝜔)/𝑉𝑖 (𝑗𝜔) in terms of L
and R. Indicate the half-power angular frequency. Calculate 𝜔𝑐 for the given values.
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)𝐻(𝑗𝜔), where 𝐻(𝑗𝜔) is as
found in Part 1, since loading is negligible.
4. Consider the circuit given in Figure 3.
R
L= 0.1 H
o = 10 krad/sec
vi(t) = Visin(t)
C
L
vi(t)
vo (t)
Figure 3
a. For R = 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 represented in Figure 4 of frequency 𝑓𝑜 = 𝜔𝑜 /2𝜋 is applied to the circuit given in Figure
3 with element values as in Part b.
vi(t)
Vi
-----
-----
t
-T o -3T o /4
-To /4
T o /4
Figure 4.
2
T o /2
To
EE 214 Electronic Circuits Laboratory
Spring 2015
Since the input is periodic with period 𝑇𝑜 = 1/𝑓𝑜 seconds, it can be represented as a linear
combination of sinusoids (Fourier series representation) as given in Equation 1.
1
2
2
2
𝜋
3𝜋
𝑣𝑖 (𝑡) = 𝑉𝑜 ( + cos(𝜔𝑜 𝑡) −
cos(3𝜔𝑜 𝑡) +
2
5𝜋
cos(5𝜔𝑜 𝑡) − ⋯ )
(1)
Find and sketch 𝑣𝑜 (𝑡).
5.
Propose a method to obtain the frequency response of the circuits experimentally.
6.
Simulation & MATLAB Work (MUST)
You may obtain the magnitude response of a circuit using any simulation software. In LTSpice4, you need
to do “AC Analysis”, which is the second tab in “Edit Simulation Command” window. For this purpose, do
not forget to adjust AC Amplitude of the independent voltage source, whose function is set to none option,
to 1.
a. Simulate the circuit in Figure 1 with the specified component values in order to obtain the magnitude
response.
b. Simulate the circuit in Figure 2 in order to obtain the magnitude response when the switch is open.
c. Simulate the circuit in Figure 3 for the values calculated in 4.a and 4.b.
i.
Obtain the magnitude response.
ii.
Set the input of the circuit a square wave with frequency 𝑓𝑜 = 𝜔𝑜 /2𝜋 calculated in Part 4.c and
peak 1 V. Obtain and plot input and output waveforms.
Indicate the half power frequency/frequencies (and the re sonant frequency,if applicable) for parts ac.
d. Using MATLAB, plot the frequency response (magnitude and phase) of Figure 3 for the values
calculated in parts 4.a and 4.b. Note that MATLAB is available for the METU students under this link.
Experimental Procedure
1.
Set up the circuit given in Figure 1 adjust the input to a sine wave of 10V peak. Determine the half-power
angular frequency, 𝜔𝑐 , of the circuit experimentally. Find the phase and magnitude response of the circuit
at 𝜔𝑐, 𝜔𝑐/5 and 5𝜔𝑐 . Using the data you have obtained, plot the phase and the magnitude response
roughly. Comment on the results.
2. Set up the circuit given in Figure 1 adjust the input to a sine wave of 10V peak.
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.
Comment on the results.
b. Close the switch.
i. Determine 𝜔𝑐1, 𝜔𝑜, 𝜔𝑐2 experimentally. Obtain the frequency response of the circuit at
frequencies 𝜔𝑐1 /5, 𝜔𝑐1, 𝜔𝑜, 𝜔𝑐2 and 5𝜔𝑐2. Plot the phase and magnitude response of the circuit
roughly. Determine the quality factor of this BP filter. Comment on the results.
ii. Apply a square wave at the resonant frequency to the band-pass filter. Observe the output of the
circuit and comment on the results.
3
EE 214 Electronic Circuits Laboratory
Spring 2015
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 𝜔𝑐1, 𝜔𝑜, 𝜔𝑐2 experimentally. Obtain the frequency response of the circuit at frequencies
𝜔𝑐1 /5, 𝜔𝑐1, 𝜔𝑜, 𝜔𝑐2 and 5𝜔𝑐2 Plot the phase and magnitude response of the circuit roughly.
Determine the quality factor of this BP filter. Comment on the results.
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 “Agil ent Connection
Expert” program which has a shortcut on the desktop. 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 given in Figure 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 v o1(t).
b. For S at position 2 observe and plot v o2(t). Why do we obtain a sinusoidal wave at v o2(t)?
Equipment List
Oscilloscope, Function Generator, Multimeter, Computer
Diode (1N 4001),
Capacitors (0.01 μF, 0.1 μF),
Resistors (1 kΩ, 2.7 kΩ, 33 kΩ, 10 kΩ)
4
EE 214 Electronic Circuits Laboratory
Spring 2015
Student 1 :
Student 2 :
Assistant :
Group:
Date:
EXPERIMENT VI
FREQUENCY RESPONSE
Experimental Results
1. 𝜔𝑐 =
|𝐻(𝑗𝜔𝑐 )| =
𝑗𝜔𝑐
|𝐻 (
5
)| =
|𝐻(𝑗5𝜔𝑐 )| =
arg(𝐻(𝑗𝜔𝑐 )) =
𝑗𝜔𝑐
arg(𝐻 (
5
)) =
arg(𝐻(𝑗5𝜔𝑐 )) =
5
EE 214 Electronic Circuits Laboratory
Spring 2015
Comments:
2. a. 𝜔𝑐 =
|𝐻(𝑗𝜔𝑐 )| =
𝑗𝜔𝑐
|𝐻 (
5
arg(𝐻(𝑗𝜔𝑐 )) =
𝑗𝜔𝑐
)| =
arg(𝐻 (
|𝐻(𝑗5𝜔𝑐 )| =
5
)) =
arg(𝐻(𝑗5𝜔𝑐 )) =
6
EE 214 Electronic Circuits Laboratory
Spring 2015
Comments:
b. i. 𝜔𝑜 =
𝑗𝜔𝑐1
|𝐻 (
)| =
5
|𝐻(𝑗𝜔𝑐2 )| =
𝑗𝜔𝑐1
arg(𝐻 (
5
)) =
arg(𝐻(𝑗𝜔𝑐2 )) =
𝜔𝑐1 =
𝜔𝑐2 =
|𝐻(𝑗𝜔𝑐1 )| =
|𝐻(𝑗𝜔𝑜 )| =
|𝐻(𝑗5𝜔𝑐2 )| =
arg(𝐻(𝑗𝜔𝑐1 )) =
arg(𝐻(𝑗5𝜔𝑐2 )) =
𝑄=
7
arg(𝐻(𝑗𝜔𝑜 )) =
EE 214 Electronic Circuits Laboratory
Spring 2015
Comments:
ii.
Comments:
3. a. 𝜔𝑜 =
𝑗𝜔𝑐1
|𝐻 (
)| =
5
|𝐻(𝑗𝜔𝑐2 )| =
𝑗𝜔𝑐1
arg(𝐻 (
5
)) =
arg(𝐻(𝑗𝜔𝑐2 )) =
𝜔𝑐1 =
𝜔𝑐2 =
|𝐻(𝑗𝜔𝑐1 )| =
|𝐻(𝑗𝜔𝑜 )| =
|𝐻(𝑗5𝜔𝑐2 )| =
arg(𝐻(𝑗𝜔𝑐1 )) =
arg(𝐻(𝑗5𝜔𝑐2 )) =
𝑄=
8
arg(𝐻(𝑗𝜔𝑜 )) =
EE 214 Electronic Circuits Laboratory
Spring 2015
Comments:
b.
Comments:
9
EE 214 Electronic Circuits Laboratory
c. 𝜔𝑜 =
Spring 2015
𝜔𝑐1 =
𝜔𝑐2 =
4.
Comments:
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EE 214 Electronic Circuits Laboratory
Spring 2015
Conclusion
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