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How to test a low-impedance filter circuit?

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jmw:
I'm designing an input filter for a power converter and the output impedance of the filter needs to stay comfortably under the input impedance of the converter, which looks like a 15 uH inductance at its operating point. Staying under 15 uH is a squeeze, but this one seems to be a good start: -75 dB at 100 kHz when I put in some reasonable figures for ESR and DCR.

But if I want to build this and test it out with a function generator and scope, it's going to load a 50 ohm source in the place of V1 too much to get a clear picture of the transfer function. How can I characterize this circuit if I build it?



The filter's input impedance will clobber a 50 ohm source...

IconicPCB:
Minimum insertion loss resistive pad?

T3sl4co1l:
You've committed a few errors; but, they aren't at all obvious without experience/theory in the RF domain, so I'm not blaming you!

The trick is this: a network of purely reactive components (L/C) is meaningless.  It stores energy, but there's no power source or sink.  You need resistance to do that.

Traditionally, the source has 50Ω, and the load does too, unless you have a more accurate model of the system attached to it (example, an offline power supply has a capacitance from primary to secondary, which is also the offending noise source).

Nontraditionally, EMI filters are sometimes also tested with oddball impedances, like 1/100Ω differential, which gives a closer fit to a filter that's terminated either with the low impedance mains (relevant at low frequencies), or into a bulk filter cap (after the rectifier, true while the rectifier is conducting of course).  Schaffner often provides these data.

EMI is measured with a fixture (a Line Impedance Stabilization Network (LISN), or Coupling Decoupling Network (CDN)) that sets the source impedance to something convenient.  For mains, it's typically 50uH coupled to 50Ω; for automotive, 5uH or thereabouts.  I once created my own that was a well damped 1~3uH, giving good isolation from the "DC" port, and a reasonably stable response regardless of the impedances at the "DC" and EUT ports.

If you're working to a test like this, then you must use a 50Ω source.  Or load.  Whichever.  (More generally, there's a source at both ends, and you look at the voltages and currents at both ends, using superposition -- that is, one source active, the other zero, then vice versa.  A passive filter like this is reciprocal -- you'll always get the same results out either way, so you only really need to test one direction.)

Now, you mention ESR in the text, but I don't see any labeled on the schematic, so I'm just going to assume...they're all zero?  Pet peeve about LTSpice, it hides necessary information by default. |O  Show all components separately on the schematic, or enable the labels at least.

As for output impedance of the filter -- we can bring these two points together.  Resistance is necessary, but it doesn't have to be at the formal start and end of a filter.  Done carefully, we can stick it in the middle just as well, and then not care whether the input and output are any goofball impedance.  (For certain restrictions on what kind of filter we'd have, of course.  Good luck getting a sharp and flat Butterworth this way!)  Or, if we're targeting a certain source or load resistance, over a certain frequency range, we can add series and shunt resistance to dominate over the filter's impedance in that range.

To implement this, we might use series L || R and parallel R+C elements.

So, the ESR in your capacitors will help quite a bit with this, if it's in the right range.

What range should we choose?  The quantity Zo = sqrt(L/C) has units of impedance.  When the filter's total L and C are plugged in, that's more or less the characteristic impedance (assuming similar impedances for the two ports, i.e. a more-or-less symmetrical filter).  If we stick such a resistance in the middle of the filter, there's two halves of filter hanging off it in parallel, so we need to use R = Zo/2.  Likewise for a series branch between filter halves, they act in series and we use R = 2*Zo.  Probably some combination would be used (a lossy inductor and a lossy capacitor), and the combined losses of both mean we don't need quite as much for each (i.e., closer to Zo for both).

The most important part for crafting good EMI filters, is we don't need to use pure resistance.  We can keep the R+C bypassed with capacitance, or the L||R seriesed with L -- giving good HF attenuation -- as long as the pure reactive component is much smaller than the lossy component.  Your 22uF caps might be rearranged as one 10uF and three 10uF + ESR, giving a maximum Q of, uh, probably 1 or 2, at the transition frequency.

You may want to use a fairly generous [lossy] input capacitance, because the source inductance may be poorly defined -- for example if this is an automotive application, that CDN already burns 10uH of your limit (five each for plus and minus), and some meters of cable will further raise that up (loose cables are, very roughly, about 1 uH/m).

The key thing though, is with a low Zo and good damping (generous R+Cs), you can use arbitrarily much inductance, without compromising the converter's input impedance. :-+

Tim

Someone:

--- Quote from: jmw on August 02, 2019, 08:17:38 pm ---But if I want to build this and test it out with a function generator and scope, it's going to load a 50 ohm source in the place of V1 too much to get a clear picture of the transfer function. How can I characterize this circuit if I build it?
--- End quote ---
Why do you think a scope won't see the signal? Up to 100kHz you'll still have less than the theoretical 140dB attenuation which should be easily seen if you drive the input with a 20Vp-p 50 ohm source.

jmw:
Thanks Tim - you raise a number of things! Eventually this goes at the input of the converter and it gets measured through a LISN. I built my own 50 uH/50Ω LISN for DC supplies, it's a single high-frequency ferrite coil without damping and taps, so it's not totally flat after 20 MHz ... but I'll deal with that later.

Though first I kind of want to build this filter on its own with real components and see how close it comes to the simulation. The caps I picked out were Al-Poly and is the datasheet ESR figure accurate at frequency? Only one way to find out... but here's the schematic with the ESR and DCR broken out. If I put in a resistive pad as suggested by IconicPCB then measuring V2/V1 gives the transfer function I was looking for, so maybe I'll try and see the same on my scope's frequency response analysis setup.

I know just a tiny bit about damping with parallel R+C, series R||L, and parallel R+L, but given how close the ESR/DCR are to the reactances in this filter in the 1 kHz - 100 kHz range, I thought adding that wouldn't help much. It seems the total ESR here is pretty close to the total sqrt(L/C). As a friend would say, "I understand some of those words" when reading your reply, so it's a good reminder to do some more reading - I was using the "Input Filter Design" chapter of RW Erickson's Fundamentals of Power Electronics as a starting point.


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