Filter DC voltages outside your supply rails
Most filter configurations introduce DC offset error due to the offset voltages of the
amplifiers used. We saw, in “Lowpass filters That Don’t”, an approach that can mitigate this to some extent. In the final circuit presented there (shown again as Figure 1 below) the heavy lifting of frequency response management is done by an active “sidechain”, and the main signal just passes along a resistor network from input to output. The only contribution to offset error comes from amplifier input leakage currents dropping voltage across this resistor network. In modern MOS amplifiers these leakage currents are tiny (at least at room temperature).
Figure 1: A DC-coupled lowpass D-element filter with low offset voltage.There are some use cases that this configuration still doesn’t support, though. One is where you can’t rely on the amplifier input currents being low enough to neglect. This might be the case, even with MOS amplifiers, if the filter is inside a seismic sensor sitting at the bottom of a very deep hole in the ground. The other case might not seem like a legitimate case at all at first glance. That’s where the voltage you want to filter is outside the supply voltages that you have available to run your active circuitry. For instance, say you’ve got a high-value bias voltage of tens or hundreds of volts, and you’re trying to lowpass-filter it to remove some ripple, but you only have a 5 volt power supply on your circuit board. Attenuating the voltage to ‘fit’ is out of the question, since you want the filtered voltage to be the same value as the input – just cleaner.
It seems obvious to consider using a higher order filter to solve this problem. If the ripple frequency is quite low, a passive filter may require inconveniently large inductors. There’s more about passive approaches, and picking an actual filter response, in the next article. Right now let’s concentrate on inductorless solutions – i.e. active filters.
Can we use the D-element ladder filter technique shown in figure 1 to create a suitable high order filter? Well, not as it stands. You can see from the schematic that the amplifiers are connected to the input voltage through a resistive path, and this sets the static voltage at each of the op-amp terminals. There’s no practical way round that. What we need is a D-element topology that doesn’t actually ‘see’ the DC voltage that it is attached to. And, while we’re at it, wouldn’t it be a good idea if it used fewer amplifiers? (Op-amp manufacturers need not answer that question). To get us started, let me reintroduce you to a filter configuration with which you may well be quite familiar:
Figure 2: The ever-popular multiple feedback bandpass filter.
Think about what’s happening at the point labeled J in Figure 2. Can you see by
inspection what the frequency response at that point will look like, referred to the input? Well, we know that the voltage at the amplifier output has a bandpass characteristic. And we can also see that the block formed by C2, R2 and amplifier is just a differentiator, with a +6 dB per octave rising slope. So, the voltage at J, when multiplied by this +6 dB/octave slope, looks like a bandpass. For that to happen, J’s voltage must actually have a second order lowpass response with respect to the input, as shown in Figure 3:
Figure 3: Voltages at nodes out and J in Figure 2. V(j) is a lowpass response.
Figure 4: A sideways look at figure 2, showing the ‘hidden’ D-element.
We can chain a bunch of these together to get an RDC ladder filter, as shown in figure 5:
Figure 5: Stringing our new circuits together to make a higher order filter.
What’s more, you can see that we’ve only had to use one amplifier for each branch in the filter. Figure 5 is a seventh order filter and it uses only three amplifiers instead of the six required by the regular singly-terminated D-element design in Figure 1.
This might all seem rather theoretical and lacking in “how do I use this?” information. Next time I’ll describe a worked example of a higher order filter for a high bias voltage that’s well outside available DC power supplies, using this approach to meet tight component size and settling time constraints that simply can’t be met by just “slapping a capacitor on”. This will also involve a deeper look at how cutoff frequency, stopband rejection ands settling time interact, and how we can optimize the values in these nonstandard circuits for best performance. Meanwhile, why not look sideways at some of your other circuits?
Happy (DC-free) filtering! / Kendall.
To view the Filter Wizard's archive of spells click here
P.S. Check out my Cypress blog at www.cypress.com/go/thefilterwizard - you can also email me from there.
About the author:
Kendall Castor-Perry is a Principal Architect at Cypress Semiconductor,doing mixed-signal system analysis and design for the new PSoC platform. Kendall uses decades of experience in analog engineering, filtering and signal processing to capture signals across many domains, extract the information from them and do something useful with it.
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