ECE 3235 Electronics II
Experiment # 10
Active Filter Circuits
1. Single Amplifier Band Pass Filter
Figure 8.1 Single Amplifier Bandpass Filter.
Figure 8.1 shows a single amplifier active filter circuit of the bandpass variety. It is also
called a Sallen-Key filter, after the discoverers of this topology, or a KRC filter because it
uses R and C components, as well as a noninverting amplifier (whose gain is usually
denoted by K, where K = 1 + Rb/Ra in the circuit shown). The components shown are for
a center frequency of approximately 1 kHz.
Wire up this circuit, after having measured all component values (with the exception of
the potentiometer’s) accurately. Use a decade capacitance box for either C1 or C2 and a
decade resistance box for R. Adjust so that C1 and C2 are equal, and so that R = R1 R2.
Then compute the value of required amplifier gain K for Q = 2 from equation (2) below
(equation 1 is given for future reference):
Then, noting that
Compute the required value of Ra. Take your 50K potentiometer from the circuit (you
do not have to physically remove it, just remove the ground wire) and use your DMM in
its ohmmeter function to adjust the potentiometer to the required value. (Be precise
here!) Now, taking care not to alter the setting of the potentiometer, wire it back into the
circuit.
Connect the sinusoidal source to the input at a frequency of approximately 1 KHz and a
level of about 1V peak-to-peak. Observe the output with your oscilloscope as you
slowly change the frequency up and down (around 1 KHz). Can you find a frequency fo
where the gain peaks? Attach your frequency counter and DMM (on an ac voltage scale)
to the output, and measure the peaking frequency precisely. Now, adjust the input level
of your circuit so that the output reads 100mV rms (Root Mean Square) precisely on your
DMM at the peaking frequency. Then find the two frequencies (fu above and fL below
the peaking frequency, respectively) where the output level drops to 70.7mV rms.
Compute your experimental Q from the following expression
Now change the input waveform to a square wave at an initial frequency of 100 Hz (at
the same amplitude as before), but vary the frequency so that you see a complete period
of the output waveform accurately. It should be a damped sinusoid. (It might be of
benefit here to learn to use the “delayed sweep” mode of your scope). Measure the
amplitudes of the first and second peaks adjacent (+ and – excursions) of the output
waveform. You may adjust the input level by a small amount to make these
measurements easier. Use these values in equation (5) below to compute an experimental
value of Q from this step response test:
where
Measure the period of the damped oscillation (or “ringing”). Again, it might prove
advantageous to use the delayed sweep mode of your oscilloscope, and then compute the
peaking frequency from equation (7) below:
Where T is the period you have just measured, and Q is the value of Q’ exp in equation (5)
above.
Repeat the entire procedure above for a desired Q of 10. Note that you must be very
precise in your measurements, particularly in the adjustment of the 50 K potentiometer.
2. Multiple Amplifier Active Filter
Figure 8.2 depicts a multiple amplifier active network known as a “state variable” filter.
Figure 8.2 A State Variable Active Filter Circuit.
Wire this circuit, after having measured all component values accurately.
In this circuit
Compute the value of Ra required to achieve a Q of 2. Then select the nearest standard
value and measure this value using your DMM in its ohmmeter function. Carefully wire
it into the circuit. Now repeat the frequency and time response measurements of Part 1
[1]
. Then select a new value of Ra to achieve a Q of 5 and repeat these measurements.
3. Cadence Simulation
Simulate the two circuit in Cadence and compare your simulation results with those that
you have measured.
[1]
This circuit is somewhat prone to oscillation. If it does oscillate, carefully bypass the positive and
negative supplies using a high quality (non-electrolytic) capacitor of 0.01 microfarad, or larger. If
attaching an oscilloscope or ac meter to the output causes oscillation to occur, place a 1 KΩ resistor
between the circuit and the instrument.
Compound Problems
(A)
Derive equations (1) and (2).
(B) Express Q in terms of Ra and Rb. Then plot Q versus Ra using MS Excel,
carefully labeling your axes. Plot Q on the vertical axis and Ra on the horizontal axis,
assuming Rb = 100 K.
(C) Compute the value of Ra required for a Q of 20 (assuming that Rb = 100 K.)
Then assume that Ra decreases by 1%, and compute the resulting value of Q. On the
basis of your result, do you consider the single amplifier KRC circuit a good one for high
Q applications? Why?
(D) Using the fact that the general second order bandpass transfer function (for any
realization) is
Show that the steady state sinusoidal frequency response peaks (has a maximum) at  =
0. Hint: Consider H(j)2 and “manipulate” the result. From your result, obtain the
peak gain Hp = H(jo).
(E) By computing the upper and lower corner frequencies (u and 1, respectively),
show that equation (4) is valid.
(F) Derive the transfer function H(s) = Vout(s)/Vin(s) for the state variable filter, and
verify equations (8) and (9).
(G) Compute the value of Ra required for a Q of 20, assuming R = 100 KΩ. Then let
Ra increase by 1%, and compute the resulting Q. Is this filter circuit better or worse
than the KRC circuit for their peak-to-peak values? Also, carefully measure the value of
Rb without disturbing its setting. (Simply disconnect one terminal from the circuit to
measure).