EE 322

Lab 8: Voltage-Controlled Voltage Source Filters

In this lab we will experiment with a simple 2-pole low pass filter, as implemented by the `voltage-controlled 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 s-domain 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.

1. The basic configuration of the low-pass VCVS filter is as shown below. Design and construct a single-stage filter having its poles at a radius f₀ = 10 kHz and 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.




• First test the amplifier without the filter by first measuring its low-frequency gain and comparing with what the gain should be. NOTE: the resistors for the amplifier are not equal to each other or to the filter resistors.
• Confirm that the filter has a low-pass frequency response and measure its cutoff or 3-dB frequency f_c. For a Butterworth filter, the 3-dB cutoff frequency should be the same as the pole radius, i.e., w₀ = w_c. Is it?
• What is the low frequency gain, and how does this compare to what it should be?
• Measure and document 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.
2. Replace the feedback resistor R₂ in your amplifier with a 10K pot and change R₁ so that the gain K of the amplifier can be varied from 1 to 3. Sketch the new amplifier schematic. This will enable the pole locations to be varied at constant radius f₀ from the negative real axis onto the j omega axis.
• What are the effects of varying the pole locations on the step response of the amplifier? Document for the particular cases of a Bessel filter (K = 1.268) and a 2.0 dB Chebyshev filter (K = 2.114). Don't change the R's and C's that determine f_c.
• Observe the frequency response (measure and plot the gain at each kHz from about 1 to 15 kHz) 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 = f₀ / f_c f₀ is determined by RC, and f_c is the 3-dB 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.
• Measure and plot the frequency response and f_n for the Bessel filter and compare with theory. Does the Bessel filter have ripple? Sketch its pole locations, as before.
• Measure and plot the frequency response and f_n for the Butterworth filter and compare with theory and the other filters. Does the Butterworth filter have the flatest responce?
3. Homework: Use the normalized polynomial (normalized to w₀=1) for a two-pole Butterworth filter, H(s) = 1/(s²+1.414s+1), show that K = 1.586 and f_n = 1 for the filter. Repeat for for a 2-pole Bessel, H(s) = 1/(s²+1.732s+1), and 2.0 dB Chebyshev filter, H(s) = 0.794/(s²+0.886s+1), to confirm the values of K and f_n given in Table 5.2 of Horowitz and Hill.