Blog The Filter Wizard Remastered

Design a fast-settling bias voltage filter with high ripple rejection

Zeroes have value
To get the most stopband attenuation for a given passband bandwidth, you need a filter with stopband zeroes. These are the features that look like “notches” in the response at particular frequencies. Such filters are often loosely called “elliptic” filters, but that term only actually applies to a specific type of filter having flat passband and stopband response and the maximum possible number of ripples in both bands. Stopband zeroes help to “pull” the stopband response down quickly. The tradeoff is that the stopband rejection doesn’t become indefinitely larger as frequency rises, but ends up bouncing around, ideally staying below some defined minimum level, in our case 60 dB.

Standard tables exist for some filters like this but in that case, they are not only not “dissipated” (the term to describe passive filters designed for inductors with loss) but are also only given for doubly-terminated networks, which is no use to us here, as discussed in “Lowpass Filters that Don’t”.

So I gave an Excel Solver spreadsheet the job of fitting a 5-pole DC-free filter circuit (or rather, the prototype uses to develop the filter) to a response that tracks the Gaussian amplitude profile out to 9.5 dB at the standard ‘normalized’ cutoff frequency of 0.159 Hz, and that is then down at 60 dB at slightly less than twice that frequency. It worked!

When scaled and transformed into our final filter, we end up with the circuit of Figure 7. The schematic doesn’t show the surge protection diodes or TVS devices that you really should use in any circuit like this, to prevent the enormous voltage switch-on surges from damaging the low voltage-rated op-amp inputs).

DC-free lowpass filter
Figure 7. This is the DC-free filter derived from our “Million Monkeys” optimization.

Stopband zeroes are introduced into the prototype with a small capacitor across each inductor, which translates into a small resistor in series with the input to our almost-D-element. Despite the approximations inherent in trying to form stopband zeroes with this filter structure, we easily reach the stopband requirements. I tried several values of ‘dissipation factor’ and ended up with one that gave nice round numbers in the final filter. The Excel result and its simulated response are shown in Figures 8 and 9.

filter response Excel plot
Figure 8. The Excel plot of the fitted prototype filter response fits the constraints.
comparison of filter response
Figure 9. The new filter’s response plotted alongside single-pole and 5-pole Gaussian.

The settling behavior, shown in Figure 10, is a bit “nervous” in comparison to the Gaussian filter but still easily beats it, at 58 ms to less than 0.1%. If you’re happy with 1% settling, it is much faster than the Gaussian version (18 ms versus 46 ms).

filter response ringing reduced
Figure 10. How the new filter compares to the 5-pole “Gaussian to 12 dB” filter.

We haven’t completely conquered that boosting at the amplifier outputs, as Figure 11 shows, though it’s much better controlled, and we’ll be able to cope with our 1 VPP of 120 Hz ripple with no problem. More intervention in the optimization process could probably improve this and perhaps trim a little more total capacitance off (maybe also compensate for any ESR effects). Nevertheless, the capacitors shown add up to only 137 µF, not far short of a 100x reduction in comparison to the single-pole case. We might actually get it to fit!

filter frequency response peaks
Figure 11. There’s still a little peaking at the op-amps, but it’s not nearly so bad.

Will it actually work? Figure 12 shows the op-amp output voltages and currents when running on a ripple waveform on 1 VPP created by a full-wave rectified power supply feeding a 1000 µF reservoir cap and a 1.37 kΩ load. The voltage swings are well inside the 5 V supply rail (the non-inverting inputs are biased at half the supply voltage, of course) and the required output current is safely inside the 25 mA rating of the op-amps I used. And the ripple level on the output is too small to show on that scale of graph. So, yes, I think it will!

filter op-amp output current
Figure 12. The final op-amp voltages and currents are now well-controlled.

Are there other ways of doing this? I’m happy to receive homework submissions and will publicize the best one. But I don’t yet know where I’d start if I couldn’t solve the problem this way.

Happy (rapid, low-capacitance) bias filtering!

[1] Williams & Taylor, “Electronic Filter Design Handbook”, McGraw-Hill
[2] Zverev, “Synthesis of Filters”, Wiley

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5 comments on “Design a fast-settling bias voltage filter with high ripple rejection

  1. didymus7
    November 7, 2019

    ‘our bias voltage can tolerate 100 W source impedance’ – 100 Watt source impedance? Am I misunderstanding something here?

  2. Tucson_Mike
    November 12, 2019

    A common word processor issue is to convert the ohm symbol to W, that happened here and is very common. Unfortunate as W makes some sense, but not in the context of the text.

  3. kendallcp
    November 21, 2019

    Yes – this one escaped both Martin and I when proof-reading for publication. It almost caught us out again so we’re much more careful now with these symbol additions!

  4. Measurement.Blues
    November 21, 2019

    The “100 W” instances are now 100 “Omega.” Can’t show the special character in a comment. I once worked with a desktop publishing system (Ventura) that mapped upper-case Omega to V. No better from a EE perspective.

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