Iowa Hills Software Digital and Analog Filters

OpAmp Filter Design. Do's and Don'ts
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This page shows the schematics and design equations for VCVS and MFB low pass, high pass, band pass filters. It also gives a number of implementation guidelines for each filter.

There are many excellent texts on the subject of active filter design. One in
particular is: "A Handbook of Active Filters" by Johnson, Johnson, and Moore,
1980 Prentice Hall.

As you know, there is an infinite number of ways to design even the simplest of
filters. On a simple RC filter, we normally choose one of the component values,
somewhat arbitrarily, and calculate the other value. The design of op amp
filters takes the same approach.

All of the filter designs start by setting at least one capacitor value, and
then calculating the resistor values from that. Some of the filters allow two of
the capacitors to be set by the user, while other designs require the second
capacitor value to be calculated from the first.

Some of the designs have a maximum allowable capacitor value. These limits come
from the design equations and are usually set to prevent a negative value under
a square root.

If the filter response isn't what you expect, remember that the element values
are setting the impedance that the op amp must drive. Large capacitor values
require an op amp with low output impedance. Remember that many op amps have a
relatively high output impedance since they are designed for low power
consumption. This is another good reason to simulate these circuits with a Spice
simulator and use the correct op amp model.

The filters are designed in sections where each section implements at most 2
poles of the filter. Therefore, a 3 pole design has the same number of sections
as a 4 pole. Of course, the 1 pole section requires fewer RC components than a 2
pole.

The filter’s gain requirements also play a big role in the design. Since
implementing gain in a filter section can add complexity, it is probably the
case that an engineer will want to put gain in as few sections as possible. For
this reason, the gain setting is in dB per section rather than overall gain. If
you are designing a 3 pole filter with 6 dB gain, and want to put all of the
gain in one of the sections, set the gain to 6 dB to get the values for the
section with gain, then set the gain to 0 dB to get the values for the section
without gain.

Since the VCVS designs are non-inverting, they must have a gain >= 0 dB. The MFB
designs may have gain < 0 dB.

The need for appropriate op amp selection is obvious. It may not be obvious
however that its characteristics are just as important in the stop band as they
are in the pass band. For example, if you are designing a low pass filter, the
op amps bandwidth requirements may be determined by stop band performance, not
pass band performance. In other words, don't assume a 100 kHz op amp will
suffice for a 3 kHz low pass filter. If the input signal has a significant
amount of high frequency power that needs to be attenuated, a low bandwidth op
amp probably won’t get the job done.

VCVS Low Pass Filter (Voltage Controlled Voltage Source or Sallen Key)

The design is started by setting the value for C2, somewhat arbitrarily, and
then setting C1 per the requirements given above.

The filter gain is non inverting and is given by 1 + R4/R3. For filters with
unity gain, the program sets R4 = 0 and shows R3 as Not Used.

The input to this circuit must have a return path to ground (not AC coupled). As
such, the DC bias level on the input signal is quite important.

The implementation shows a useful way to offset the DC bias on the input signal.
Set the parallel combination of Ra and Rb to R3. The program's tools menu can
help calculate the required bias voltage at the inverting input and the values
for Ra and Rb.

As with all op amp circuits, high frequency feedback is very important in order
to keep the circuit stable. A small capacitor across R4, typically 10 pF, will
accomplish this. The need for this cap becomes more important when high
bandwidth op amp's are used.

MFB Low Pass Filters (Multiple Feed Back)

The design is started by setting the value for C2, somewhat arbitrarily, and
then setting C1 per the requirements given above.

The filter gain is inverting and equal to R2/R1.

Don't overlook the DC bias level on your input signal. The inverting terminal
has a path to ground via R2, so you may capacitively couple to the input. Of
course, this will generate a high pass response that you may not desire.

This circuit is usually shown with the non-inverting terminal tied to ground,
which is fine if the input signal doesn't have a DC bias.
Depending on the supply voltages and the DC level at the input, you will
probably need to apply a voltage to the non-inverting terminal. The program's
tools menu can help calculate Ra and Rb.

This circuit ensures good high frequency stability via C1.

The one pole MFB is implemented by setting R3 and C2 equal to zero. Its corner
frequency is set by C1 and R2. If unity gain is needed, the VCVS 1 pole is much
simpler to implement.

VCVS High Pass

The design is started by setting the values for C1 and C2, somewhat
arbitrarily. C1 = C2.

The filter gain is non inverting and is given by 1 + R4/R3. For filters with
unity gain, the program sets R4 = 0 and shows R3 as Not Used. One pole sections
are shown with R1 and C1 as Not Used.

If the op amp is biased from a single supply the non inverting terminal must be
biased to a value appropriate for the gain. The program's tools menu can help
calculate the required values.

Since this filter doesn’t have any capacitive feedback, it is particularly
susceptible to high frequency instability. Approximate the capacitance of the
traces on your PWB with approximately 3 pF of shunt capacitance at the op amps
input terminals. Then do a frequency sweep in a Spice simulator to frequencies
greater than the Op Amp’s Gain BW product. Unexpected gain at the high
frequencies is a sure sign of trouble.

Adding a small capacitor across R4, typically 10 pF is good way to keep the
circuit stable. The need for this cap becomes more important with high bandwidth
op amps. This additional cap will, of course, cause high frequency roll off.

MFB High Pass

The design is started by setting the values for C1 and C2, somewhat
arbitrarily. The filter's AC gain is inverting and equal to C2 / C1.

Note: Since the gain is determined by the cap values, it isn't possible to fine
tune the gain. Lower the percent tolerance on the caps to get more precision on
the gain setting.

Depending on the supply voltages, you will probably need to apply a voltage at
the non-inverting terminal. The program's tools menu can help calculate Ra and
Rb.

Although the feedback cap C2 should ensure good high frequency stability, be
careful with this circuit’s input impedance. It is relatively low and
capacitive. If you are implementing multiple stages, the op amp needs to be able
to drive large capacitive loads.

Be sure to do a frequency sweep in a Spice simulator to frequencies greater than
the Op Amp’s Gain BW product. Unexpected gain at the high frequencies is a sure
sign of trouble.

The one pole MFB is implemented without R1 and the second C1. Its corner
frequency is set by C2 and R2. If unity gain is needed, the VCVS 1 pole is much
simpler to implement.

Band Pass Filters

We showed the design equations for the circuits above, but theey are too
involved to show here. This is due in part because these filters have a section
for each pole (rather than 2 poles per section) and the 2nd order polynomials
first need to be factored, and used individually.

It is important to note that the two R4's are required on the VCVS design.
They are an integral part of the filter design and cannot be removed.

Unless the the op amp is biased from a +/- supplies, the non inverting input
must be biased to approximately Vcc / 2 on both the VCVS and MFB.

Pay particular attention to the op amp's bandwidth. You may need as much as 50 x
Fo for these implementations.

To ensure stability, it would be wise to place a small cap, approx 10 pF, across
R4 on the VCVS. On the MFB, C1 and C2 should provide sufficient high frequency
feedbck.

Notch Filter

This filter doesn't implement a Butterworth, Chebyshev, or any other
polynomial, so all the sections use the same part values. As a consequence, it
makes for a poor filter.

If AC coupling is used at the input, then the inverting terminal will need to be
biased.

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