EE-2302
Passive Filters and Frequency Response
Objective
The student should become acquainted with simple passive filters for performing
highpass, lowpass, and bandpass operations. The experimental tasks also provide an introduction
to Complex Frequency Response and Phasor Algebra.
Discussion
Filters are used to remove unwanted frequency components from a signal. Filters can be
implemented using a combination of active elements (independently powered elements like
operational amplifiers) and passive elements (non-powered circuit elements like resistors,
capacitors, and inductors). Filters can also be constructed solely using passive elements. In this
experiment, you will construct several simple passive filters and evaluate their performance.
The frequency response is a complex gain as a function of frequency. The frequency
response magnitude is the amplitude gain for a sinusoidal input at the given frequency. The
frequency response's argument is the phase shift obtained for a sinusoidal input at the given
frequency. The frequency response can be obtained by replacing the capacitor with the
impedance 1/jωC and the inductor with the impedance jωL. The circuit is then analyzed treating
these impedances as normal resistors. The output voltage divided by the input voltage
Vo(jω)/Vi(jω) (typically a complex number for given circuit element values) is the frequency
response.
Pre-lab
Determine the frequency response, Vo(jω)/Vi(jω), for each of the following filters. Let R,
C, and L be variables in these frequency responses.
R
+
+
Vi
C
Vo
-
-
Filter 1
R
+
+
Vi
L
Vo
-
-
Filter 2
L
C
+
+
Vi
Vo
R
-
-
Filter 3
Procedure
1.
Select the following components: a 470 Ω resistor, a 1 µF capacitor, and a 20 mH
inductor. These values are only approximate. Measure the actual resistance,
capacitance, and inductance of these components, and record your answers on the
data sheet.
2.
Construct each of the filters (one at a time) using the selected components.
3.
Connect the NI 5411 Function Generator output to the input terminals of each
filter and Channel 1 of the NI 5102 Oscilloscope. Connect the filter output to
channel 2 of the oscilloscope. Select a sinusoid output for the NI 5411 Function
Generator with an amplitude of 200 mV Vp.
4.
Set the Vertical Volts/Div control and Horizontal seconds/division controls for
ease of measurement.
5.
Measure the voltage gain (magnitude) and the phase shift of the output of each
filter for the frequencies indicated on the data sheet.
The voltage gain is the amplitude of the output signal (Vo) divided by the
amplitude of the input signal (Vi).
To find the phase shift, measure the time difference between the zero crossing
(going positive) of the two waves. This time difference is denoted ∆t. The
sinusoid’s period, denoted T, is the time between successive zero crossings (going
positive) of a single wave. This can be measured of computed from the frequency.
The phase shift is to 360° in the same ratio as ∆t is to the period:
phase shift = 360° ∆t/T.
If the input signal’s zero crossing occurs before the output signal’s zero crossing,
the output signal is said to lag the input, and the phase shift will be negative. If
the output waveform's zero crossing occurs before the input waveform’s, it is said
to lead and the phase shift is positive. Its important to note which signal’s zero
crossing occurred first when measuring ∆T.
Filter 1: R_____________
C____________
50 Hz 100 Hz
200 Hz
300 Hz
400 Hz
500 Hz
800 Hz
1500 Hz.
50 Hz 100 Hz
200 Hz
300 Hz
400 Hz
500 Hz
800 Hz
1500 Hz.
Vo
Vi
Gain
∆t
T
∆Φ
Filter 2 : R__________ L____________
200 Hz 500 Hz
Vi
Vo
Gain
1000 Hz
2000 Hz
5000 Hz
10 kHz
20 kHz
200 Hz 500 Hz
1000 Hz
2000 Hz
5000 Hz
10 kHz
20 kHz
∆t
T
∆Φ
Filter 3: R_________
200 Hz 500 Hz
L_________ C_________
1000 Hz
2000 Hz
5000 Hz
10 kHz
20 kHz
1000 Hz
2000 Hz
5000 Hz
10 kHz
20 kHz
Vi
Vo
Gain
200 Hz 500 Hz
∆t
T
∆Φ
4.
5.
6.
7.
Using your measured values, plot the amplitude gain verses the frequency and the
phase shift (in degrees) verses the frequency. Semi-Log graph paper can be very
effective for this graph. Use the linear axis for the gain and phase data and the log
axis for frequency.
Substitute the measured values for R, C, and L into the theoretical frequency
responses obtained in the prelab, plot the resulting theoretical amplitude gain
verses the frequency and the theoretical phase shift (in degrees) verses the
frequency.
Compare the results of the theoretical values with the experimental values. Note
that phase shift is ambiguous with respect to phase shifts of 360°, so you can add
±360° phase shifts into your experimental results to obtain better agreement.
The passband of the filter is defined as the range of frequencies where the
amplitude gain exceeds 0.707. Use the equation you derived for the theoretical
gain to compute the passband of each filter. Can you think of applications for
these different types of filters?