Differential filter design

There's a good guide here:

Two questions I have about applying filter-design software to this process:

The series elements are scaled by 1/2 vs the single ended topology. Does this change at all if the inductors are coupled on a common core?

Single-ended filter design software you usually have to specify a source and termination impedance. How would you work this if what you're after isn't maximum power transfer between specified terminations but maximum power available into arbitrary load, like a class D audio amplifier, say.

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Re Class D amps, I only have general response. My advice may be obvious, or out of date now. But I recall my former colleagues who designed amps would: (1) design around a known *range* of speaker impedance and parameters. (2) simulate on computer the circuit using well-known speaker models. (3) bench-test circuit using a "loudspeaker simulator" (passive RLC network) so you don't have to blow up a lot of expensive drivers. Have multiple simulators, e.g. "2-ohm", "4-ohm", etc., to suit the application. (4) finally bench test on actual loudspeakers, long term, with a suite of "stress test" signals. Cheers, Rich S.

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Rich S

Yes, of course. In case of full coupling, you must halve the inductances /again/ to maintain the same response. This is because the effective impedance in one branch is now the sum of the single-side inductance and the mutual inductance, which has to remain the same.

Filter responses are calculated for a given source and load impedance. If you drive a filter from the wrong impedance, or terminate it into a value for which it wasn't designed, the shape of the response will change. This has nothing to do with maximum power transfer.

I suppose a class D amplifier is essentially a zero-impedance source, so the filter should be designed for that. Such filters always start with a series component, obviously.

Jeroen Belleman

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Jeroen Belleman

Got it, thought it might be something like that.

Right, completely arbitrary impedance would be silly, speaker impedance aren't completely arbitrary.

I think that may have been my sticking point, have to well-define something. a parallel initial element doesn't make sense as while the output stage has some low output impedance it's not well-defined.

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There's no reason a class-D audio amp should have a differential output filter, and lots of reasons why it shouldn't.

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John Larkin

Just a motivational example, man. Motivational example. this is an educational exercise

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Eh, it was just a motivational example. I don't have much interest in building audio amps myself but just had questions about the differential topology and how it works when it's done that way.

There is no way to "match" into an arbitrary load impedance makes sense, the termination is in a range.

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Coupling is covered by others.

So, in the article, they completely ignore common mode, which is peculiar. Their motivating examples seem to have low CMV at the source, maybe they're ignoring it for that reason.

So, first of all -- there are many reasons for choosing differential mode signaling. They do not give much motivation here. They do mention susceptibility and emissions, and cancellation of even distortion.

They also mention "double the signal level", and better linearity and SNR, which are rather weak to me: you're also doubling the output stages, so you get as much noise from them regardless. I suppose you aren't doubling the input stages in comparison to regular op-amps, which use differential input stages pervasively, whether or not you're using them single-ended. But that's very easily solved by not using op-amps at all (e.g., use an MMIC), or making a single-ended one (feedback around a common-emitter/source transistor, say).

Some stronger reasons include:

Cost of the media. Losses. 100 ohm twisted pair, and 300-600 ohm twin lead, typically are cheaper, and have lower losses than coax.

Availability. You can't construct coax on a PCB very easily, but diff is free. Coax requires special connectors; diff can be transmitted on any old headers.

Noise rejection. For CM noise within the CM range of the receiver, rejection is very good. Beyond there, signal quality degrades aggressively (typically, CM current forward-biases the input ESD clamp diodes, shorting out the diff signal in part or whole).

Note that coax can be connected differentially, too, to the same benefit! But this is rarely done. Probably because designers are creatures of habit?

Isolation. When the signal can be transformer coupled, single-ended signals must use shielded transformers: expensive, and poorer performing. Differential signals can use simple twisted-pair windings. (Both can be improved with CMCs, of course.)

Alternative functions. We can put whatever we want on the common mode, assuming that we have a return path for it, and that we don't mind it may be noisy. PoE is an excellent example: we don't care that it's noisy because we only want DC, and we have four pairs in a CAT5+ cable to choose from.

This could be done with pairs of coax as well, but it's probably a bit rude to put "hot" voltages on shields that are ordinarily assumed to be grounded?

As for the filter circuit:

The full circuit includes stray capacitances to ground (which affect the differential values in the filter, too!). The parallel equivalent of those capacitances, acting against the leakage inductance of the coupled (diff mode) inductors, give a CM filter of some cutoff and impedance.

Note that, if the inductors are inverse coupled, the leakage becomes the critical diff-mode spec, and CM inductance instead can be very high. So you can, very effectively, craft very different responses and impedances for DM and CM.

If you have much CM noise to filter, and it's present at frequencies feasible to filter, well there you go, that's part of your filter spec! The CM filter prototype will probably be different, reflecting the different spectrum, and because you can't make accurate assumptions on the source port impedance. Namely, a lossy network is preferred, to act to stabilize the source impedance.

For loose cables, you can broadly assume a CM impedance of 100-200 ohms, but with peaks and valleys due to random resonances (because it's a transmission line in somewhat-free space). Ferrite beads help flatten out those resonances, and further stabilization (R+C to ground and R||L in series) furnishes something you can confidently filter against.

Which by the way, relates to the class D amp example: the two sources are both nearly zero ohms. Note that we don't need to model this differentially, because this is the same whether expressed as normal mode, CM or DM.

We can possibly save a little cost by using a weak DM filter: the speaker won't care if it's eating a few volts of 200kHz or whatever. But we still need a strong CM filter to meet emissions (assuming this is an amplifier block).

Or conversely, if this is an integrated speaker, the wiring can be much shorter, and the speaker frame can be grounded, allowing much tighter control over emissions. The CM filter might be much simpler, or perhaps even nothing at all. Yes, they actually get away with that sometimes!

Anyway, the fact that the source impedance is effectively zero, means we must design with a one-port-shorted prototype. And really, the other port isn't much better (the speaker impedance is... well, anywhere on the right half-plane, there's that :^) ), so we probably want a lossy network to stabilize the impedance.

So, the basic form of this filter might be:

. +--/\/\--+ R1 . L1 | | . Amp o---ccc--+------+-+--ccc---+---o Speaker . | | L2 . | === C2 . === C1 | . | > R2 . | > . GND _|_ _|_

The L1-C1 section can be as many LC(LC..) as needed to get desired attenuation, and can end with a series branch (L) too. The R+C and R||L sections provide termination even when the load is open or shorted. (Open is the higher priority, as speakers are generally inductive at high frequencies. However, beware of the piezo tweeter!)

(Note that, when there's an R+C in parallel with a C, the R+C's capacitance needs to be several times larger, so that the R is dominant in the transition band.)

We can apply this with as many CM and DM stages as needed to meet the above-discussed attenuation requirements.

Oh and, note that the CM filter in this case, is shorted one side and /open/ on the other (the speaker isn't grounded or anything) -- what fresh hell is this? :) Obviously, filtering is _meaningless_ without CM termination, and an R+C is obligatory, if you're going to do a CM-DM type filter here.

But also, yeah, more reasonable to take the simpler case -- an H-bridge is nothing more and nothing less than two half-bridge stages, and you would filter those with normal-mode filters. Why make it more complicated by imagining it any other way? :)

Which does assume the usual case -- the H bridge is just driven balanced, in the usual "bridge tied" way.

When this isn't the case, it can be different. Consider phase shift PWM: this is used in SMPS, and delivers a CM voltage of full rail-to-rail switching, almost all the time! This is quite an EMI burden, and some heavy filtering will be desirable. The filtering can be done on the AC or DC side, preferably not much on AC (direct inverter output) due to the added leakage inductance reducing power output. But given the magnitude, it might be required on the AC side, just for basic functional operation (i.e., 400V of switching noise is likely to confuse the controller!).


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Tim Williams

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