EXP. 6
LOWPASS AND HIGHPASS RC FILTERS 1
PURPOSE:
To experimentally demonstrate the frequency responses of a lowpass and a highpass RC circuit
To plot the frequency and phase response of the RC filters
LAB EQUIPMENT:
1
1
1
1
1
3
1
Agilent 33120A Function Generator (FG)
Agilent 34410A Digital Multimeter
Agilent 54621A Oscilloscope
Capacitance Decade Box, 0.01 µF/step
Resistance Decade Box, 100 Ω/step
BNC-Banana
Bag of short leads
Scope
Channel 2
DISCUSSION
A typical RC lowpass filter is formed when the output Vo is taken
R
off the capacitor (Figure 1).
The transfer function is:
Scope
Channel 1
+
+
+
-
VS
C
-
Vo
-
H(ω) = Vo / Vs = [1 / jωC] / [ R + 1 / jωC ]
Figure 1
Lowpass RC filter
= 1 / [ 1 + jωRC ]
Note that H(0) = 1 and H(∞) =0 which indicates that the circuit acts
as a lowpass filter.
A typical RC highpass filter is formed when the output Vo is
Scope
Channel 2
taken off the resistor (Figure 2).
Scope
Channel 1
The transfer function is:
+
H(ω) = Vo / Vs = R / [ R + 1 / jωC ]
= jωRC / [ 1 + jωRC ]
Note that H(0) = 0 and H(∞) =1 which indicates that the circuit acts
as a hiphpass filter.
1
+
-
VS
+
C
R
-
Vo
Figure 2
Highpass RC filter
Original experiment, amended and revised 02/15/05, John Saghri, modified 03/02/06, Taufik
1
PRELAB
1. For the lowpass RC filter, calculate the phase and magnitude of the transfer function at frequencies of 20,
50, 100, 200, 500, 1000, and 1500 Hz. Tabulate the result and then sketch the magnitude and the phase of
the response as function of the frequency (use log scale for frequency). Use R=50 kΩ, C=0.02 µF
2. Determine the half power frequency fc defined as the frequency at which the magnitude of the transfer
function is at 1/√2 of its maximum value. Assuming C is fixed at 0.02 µF, calculate the half power
frequencies corresponding to R=20 kΩ, 50 kΩ, and 100 kΩ.
3. Repeat steps above for the highpass filter.
PROCEDURE
Section 1. Measurement of the magnitude and phase response of RC lowpass and highpass filters
1. Set up the circuit shown in Figure 1 with C= 0.02 µF. For the value of resistor R use 20 KΩ, 50 KΩ, and
100 KΩ. Set the function generator at high-Z output termination and adjust it to provide a 2 Vpp
sinusoidal waveform
2. For each value of R, construct a table as shown below. Enter the measured rms values of Vs and Vo , and
the phase difference between Vo and Vs, while setting the frequency of the function generator to the
values shown in the table below.
f (Hz)
Log10 (f)
Vs (Vrms)
Vo (Vrms)
Vo/ Vs
∠ Vo/ Vs (degrees)
5
25
50
250
500
2500
5000
25000
2
3. Plot the magnitude and phase of the transfer function as a function of the frequency for each value of R
using the tables you generated in step 2. Use log scale for frequency and plot the three magnitude
responses on one graph and the three phase responses on another.
4. Obtain the half power frequencies directly from your magnitude plots for each value of the resistor used.
Enter your results in the table below
Table 1. Calculated and measured half power frequencies for the RC lowpass filter
fc (calculated)
fc (measured)
Percent difference
R= 20 kΩ
C= 0.02 µF
R= 50 kΩ
C= 0.02 µF
R= 100 kΩ
C= 0.02 µF
5. Repeat steps 1 through 4 except use the highpass filter of Figure 2.
Table 2. Calculated and measured half power frequencies for the RC Highpass filter
fc (calculated)
fc (measured)
Percent difference
R= 20 kΩ
C= 0.02 µF
R= 50 kΩ
C= 0.02 µF
R=100 kΩ
C= 0.02 µF
QUESTIONS
1. How well do the calculated magnitude and the phase plots in your prelab compare with the corresponding
plots obtained via experimental measurements? Explain the reasons for the difference.
2. Explain the reasons or percent differences between the calculated and measured values of the half power
frequencies.
3. Why is fccalled ‘half power’ frequency?
Section 2. PSPICE simulation of the magnitude response of RC lowpass and highpass filters
3
Use PSPICE to obtain the plot of the
magnitude response of the transfer function
for the lowpass and highpass filters. For
simplicity, use R=50 kΩ and C = 0.02 µF.
For your source, choose ‘VAC’ for the
source from the PSPICE ‘SOURCE’ library.
Use the default voltage setting of 1 VP. Edit
50
0.02 µF
the ‘Simulation Settings’ menu as shown
below.
Include the hardcopy of the
magnitude response for both the lowpass and
the highpass RC filters in your report. The
plots should be well annotated.
5hz
25000hz
4