Lab 13
Passive Filters
OBJECTIVES
1. Become familiar with the characteristics of passive low-pass and high-pass filters.
2. Analyze the frequency response of tuned band-pass and band-stop filters.
EQUIPMENT
Lab Kit, oscilloscope, and Function Generator
THEORY
To be discussed in lab.
PROCEDURE
Part 1: First Order Passive Filter Circuits
Part 1A: High-Pass RC Filter
Construct the following circuit.
a. Using VDR in phasor form, the ratio of input to output voltages across the resistor:
=
VR
R∠0°
V
V
R − jXC
VS
Vin
magnitude
R
=
VS →
≡ out
R
R + XC
2
2
The condition R = XC establishes the low cutoff frequency, which is the frequency at
which the output voltage drops to 1/√2 of its maximum value. This cutoff frequency is
1
1

→ ( fcut )=
=
R X=
C
thy
2πfC
2πRC
b. Energize the circuit and set the function generator to each of the frequencies
appearing in the table (label it Table 1) at the end of this lab write-up. For each
setting of the function generator make sure that VS = 8 V(p-p).
c. Plot Vout/Vin vs f (log scale) using Excel. Draw a horizontal line at the 1/√2 level and
determine the experimental cutoff frequency (fcut)expt at which intersects the curve.
Compare the theoretical and experimental cutoff frequencies using a percent
difference. How do they compare?
d. Simulate the circuit using an AC sweep over the indicated frequency range.
Part 1B: Low-Pass RC Filter
f.
In the High-pass RC circuit, reverse the VS leads so that now the capacitor and
resistor have switch positions. Repeat parts (1b-1e).
Part 2: Band Filters
Part 2A: Tuned Band-Pass Filters
Construct the following circuit.
a. The bandwidth and Q-factor of a series resonant circuit is
fR
1
=
BWSeries
XL
=
=
where
fR
and
QSeries
QS
Req
2π LC




Series Resonant Frequency
Series Quality Factor
b. Determine the resonant frequency and the Quantity Factor of this series circuit.
c. Using VDR in phasor form, the ratio of input to output voltages across the resistor is
VR
R∠0°
V
V
R
magnitude
R
VS
→
≡ out
=
R + RL + jXL - jXC
V
Vin
R + RL
S
X =X
L
C
d. Repeat parts (1b-1d), plotting extra points near the resonant frequency.
e. Be sure to record the upper and lower cutoff frequencies as defined by the horizontal
line at the 1/√2 level. What range of frequencies will, therefore, pass through the
filter with a measurable amount of power? That is, what is BW = f2 – f1?
Part 2B: Tuned Band-Pass Filters
Construct the following circuit.
a. The bandwidth and Q-factor of a parallel resonant circuit is
fR
BWParallel =
where
QParallel
R 2C
1
fR =
1− L
L
2π 
LC


and
Parallel Resonant Frequency
XL
QParallel =
RL



Parallel Quality Factor
b. Determine the resonant frequency and the Quantity Factor of this parallel circuit.
c. Using VDR in phasor form, the ratio of input to output voltages across the resistor is
=
VR
R∠θ
V
V
R + ZP
VS
Vin
magnitude
R
=
VS →
≡ out
R
R + L/RL C
d. Repeat parts (1b-1d), plotting extra points near the resonant frequency.
e. Be sure to record the upper and lower cutoff frequencies as defined by the horizontal
line at the 1/√2 level. What range of frequencies will, therefore, be blocked through
the filter with a measurable amount of power? That is, what is BW = f2 – f1.
Frequency (kHz)
0.1 kHz
0.2 kHz
0.4 kHz
0.6 kHz
0.8 kHz
1 kHz
1.2 kHz
1.4 kHz
1.6 kHz
1.8 kHz
2.0 kHz
3.0 kHz
4.0 kHz
5.0 kHz
6.0 kHz
8.0 kHz
10.0 kHz
12.0 kHz
14.0 kHz
16.0 kHz
18.0 kHz
20.0 kHz
40.0 kHz
60.0 kHz
80.0 kHz
100.0 kHz
VS(p-p)
Vout /Vin