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Bonnie Baker - WEBENCH Design
Center

Jun 12, 2015

WEBENCH
Filter Designer

filter

OPA124

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Is your op amp filter ringing? Look at Q!

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How do you anticipate ringing in the active analog filter of your operational
amplifier (op amp)? The purpose of analog filters is to remove signal in an
intentional frequency band, not to inadvertently add additional ringing into the
signal path. Consider looking at the value of Q, or quality factor, of each
filter stage. Figure 1 shows an example of the characteristics of a second-order
low-pass Butterworth filter.

Figure 1: Sallen-key, 6kHz
low-pass filter using the WEBENCH®
Filter Designer tool

The header in Figure 1 provides filter topology, gain, cut-off
frequency, Q and the minimum op amp bandwidth, in this case for the OPA124
precision op amp.

These are all valuable entities when designing your filter, but let’s
consider the Q in Figure 1, which is equal to 0.864. The value of Q is primarily
dependent on the resistor and capacitor values in the circuit and relatively
independent of the amplifier. This value of Q indicates that this system is
underdamped. This unit-less variable actually quantifies the quality and amount
of decay in the system. Q is related to ζ, the damping factor, by Q = 1/(2ζ).
Each stage in multi-order filters generates its own Q factor.

If the maximum Q is less than 0.5, the system is overdamped. This type of
system output does not ring at all. When the output voltage is displaced from
its steady state, the filter’s output returns to its steady state with an
exponential decay.

A Q value equal to 0.5 indicates that the system is critically damped. If you
are designing a low- or high-pass filter, the first-order filters are the only
filters that have a Q this low.

An underdamped circumstance occurs if Q is higher than 0.5. A Q greater than
0.5 indicates a lower rate of energy loss relative to the stored energy in the
filter. At the output of these filter systems there will be a degree of ringing
with input excitation. As the value of Q increases, it takes longer for the
ringing to die out.

Figure 2 compares the low-pass filter responses of different Q values with
respect to the frequency-domain and time-domain characteristics.

Figure
2: Impact of Q on the frequency response of low-pass filters (top) as well as
the unit-step response (bottom) with a corner frequency of 1Hz

The top plot in Figure 2 shows the level of filter gain overshoot
versus frequency for various Q values. The combination of this gain/frequency
response, combined with the impact on the phase margins, results in the ringing
(bottom plot) that you see in your filter’s output.

The most dramatic effect of higher Q values is the settling time, as
seen in the bottom plot of Figure 2. The curve with a Q of 5 has considerable
ringing compared to the Q with a curve of 0.707.

The two filter systems in Figure 3 have differing maximum Q values. The
filter with a higher Q value demonstrates more ringing with a step stimulus at
the input of the filter.

Figure 3: Comparing the step
response of second- and sixth-order 0.5 Chebyshev low-pass filters

In Figure 3, the input signal for these filters is a 0.5V square wave. The
maximum Q factor with the left-hand curve is 0.8547. The initial overshoot is
approximately 0.15V above the final settling voltage value of 0.5V. This curve
quickly settles to its final value with very little ringing.

The Q factor for Figure 3’s right-hand curve is equal to 6.513. The initial
overshoot is approximately 0.23V overshoot. This curve, with a higher Q factor,
takes a little longer to settle, with eight visible cycles. As you design
filters using WEBENCH
Filter Designer, you will find the maximum Q value for the particular filter
you choose to design.

So how high can Q become before it causes problems? In our industry, the
consensus is that Q should be less than 10. But, beyond that, assess the
characteristics and requirements of your circuit. From there, you can decide
what is the maximum acceptable Q for your system.

Additional resources

Find out about TI’s OPA124
precision op amp.

Begin designing today with the WEBENCH
Filter Designer.

“Q
– Quality Factor Tutorial” from Radio-Electronics.com.

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