EE 322
Lab 8: VoltageControlled Voltage Source Filters
In this lab we will experiment with a simple 2pole low pass filter,
as implemented by the `voltagecontrolled voltage source' (VCVS) configuration.
The VCVS filter is discussed in Sections 5.06 and 5.07 of Horowitz and
Hill; you have also seen it in the circuit theory lab. It has the nice
feature that the pole locations of the transfer function in the sdomain
can be varied by changing the amplifier gain (see below), without changing
the radius of the poles from the origin. We will use this feature to determine
the effect of varying the pole locations upon the frequency and transient
response of the filter.
PreLab
 Table 5.2 of Horowitz and Hill gives values of the amplifier gain K and
frequency multiplier f_{n} (f_{0}=f_{n}f_{c}
where f_{0} is the pole radius, and f_{c} 3dB cutoff frequency).
These values can be found from transfer functions for each filter.
The gain K can be found from our in class analysis. The cutoff frequency is found by
solving Abs(H(jw_{c}))=0.707 for w_{c}.
Use the normalized polynomial (normalized to
w_{0}=1) for a
twopole Butterworth filter, H(s) = 1/(s^{2}+1.414s+1), show
that K = 1.586 and f_{n} = 1 for the filter. Repeat for for a
2pole Bessel, H(s) = 1/(s^{2}+1.732s+1), and 2.0 dB Chebyshev
filter, H(s) = 0.794/(s^{2}+0.886s+1), to confirm the values of
K and f_{n} given in Table 5.2 of Horowitz and Hill.

Use Matlab to plot the frequency response (the plot should be linear for
easy comparison to the lab measurements) and step response for each of these 2pole
filters
The Lab
 The basic configuration of the lowpass VCVS filter is as shown below.
 First build and test the amplifier.
Use a 10k pot for the feedback resistor R_{2}
and choose R_{1} so that the gain K of the amplifier
can be varied from 1 to 3. Sketch the amplifier schematic. This amplifier
enable the pole locations to be varied at constant radius f_{0}
from the negative real axis onto the j omega axis.

Design and construct a singlestage filter having its poles at a radius
f_{0} = 10 kHz. Set the gain for a Butterworth frequency response. This circuit
will be tested with your function generator, which has a 50 ohms source
impedance. The source impedance will be in series with the input resistor
R of the filter, so you will need either to make R large in comparison,
and/or to take the source impedance into account when constructing the
circuit. NOTE: the resistors for the amplifier are
not equal to each other or to the filter resistors.
 First test the amplifier by first measuring its lowfrequency gain and comparing
with what the gain should be.
 Confirm that the filter has a lowpass frequency response and measure
its cutoff or 3dB frequency f_{c}. For a Butterworth filter, the
3dB cutoff frequency should be the same as the pole radius, i.e.,
w_{0} = w_{c}. Is it?
 Measure and plot the frequency response (measure and plot the gain
at each kHz from
about 1 to 15 kHz). Compare this with theory and Matlab plot form the prelab.
 Measure and document (carefully draw) the step response of the filter for comparison
with later results. Does the step response overshoot? What is the gain
after the transient response dies out, and what should the gain be?
 Sketch the pole locations of this filter, approximately to scale. Use the transfer
function for this.

Chebyshev and Bessel Filters
Don't change the R's and C's that determine f_{c}.
 What are the effects of varying the amplifier gain and thus the
pole locations on the step response
of the filter?
 Document for the step response of a Bessel filter
(K = 1.268). Compare this with the Matlab plot form the prelab.
 Document for the step response of a 2.0 dB Chebyshev filter (K = 2.114).
Compare this with the Matlab plot form the prelab.
 Measure and plot the frequency response of the 2.0 dB Chebyshev filter
(measure and plot the gain at each kHz from
about 1 to 15 kHz). Compare this with theory and Matlab plot form the prelab.
 Observe the plot of the frequency response of the 2.0 dB Chebyshev filter.
Why is it peaked? The peaking constitutes the `ripple' of the (frequency
response of the) filter. Is the ripple equal to 2.0 dB? Measure the 3
dB cutoff frequency and compare with the theoretical value obtained from
f_{n} = 0.907. (f_{n} = f_{0} / f_{c},
f_{0} is determined by RC, and f_{c} is the 3dB frequency)
Why is the cutoff frequency larger than the pole
radius? Illustrate using a sketch of the pole locations similar to that
of part 1. Compare this with the Matlab plot form the prelab.
 Measure and plot the frequency response and f_{n} for the
Bessel filter and compare with theory (measure and plot the gain
at each kHz from
about 1 to 15 kHz). Does the Bessel filter have
ripple? Sketch its pole locations, as before. Compare this with the
Matlab plot form the prelab.
 Compare the filters. Does the Butterworth filter have
the flattest response? Which has the fastest falloff at high frequencies?
Which has the best step response?
© Copyright 2001 New Mexico Institute of Mining and Technology