How to test a low-impedance filter circuit? - Page 1
Forum section: electronics / projects

author: jmw
author_rank: Frequent Contributor
timestamp: August 02, 2019, 08:17:38 pm
content: 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...

author: IconicPCB
author_rank: Super Contributor
timestamp: August 02, 2019, 11:24:15 pm
content: Minimum insertion loss resistive pad?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: August 02, 2019, 11:59:44 pm
content: 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.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  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

author: Someone
author_rank: Super Contributor
timestamp: August 03, 2019, 12:05:42 am
content: Quote from: jmw on August 02, 2019, 08:17:38 pmWhy 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.

author: jmw
author_rank: Frequent Contributor
timestamp: August 03, 2019, 01:32:56 am
content: 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'sFundamentals of Power Electronicsas a starting point.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: August 03, 2019, 04:31:04 am
content: Al poly ESR should be at least ballpark right. I'm not aware that it changes much (unlike electrolytics which vary with temperature).Although the aging mechanism is, I think, moisture seeping into the polymer, and then what, decomposing it, I don't know; does it lower conductivity so ESR rises, or does it act to disconnect areas so ESR rises while C falls, roughly proportionally?Now; you've plotted the transfer function v2/v1, but that's not necessarily what we want. (But, again, it's not clear what's needed, lacking a model of the power converter.) Traditionally we measure the response of a filter as the insertion loss. For that, we use V1 = 2, Rs = 50, and first test with an RL = 50. Which is of course a simple 50% resistor divider, so we measure 1V at the load. Then we put the filter between Rs and RL, and measure the output voltage again (not the gain; or, half the gain to Vs(O/C), if you like).The impedance of, like, the last bit, 2.2uH to 44uF, is 0.22 ohms, but ESR is 0.015 ohms, so the Q there could be quite high. ESR closer to 0.2 would be better.Polymers are available in a range of ESRs; generally lower ESRs than tantalums (the staple of "bulk cap with known ESR"), but they have a lot of overlap; this should be doable.The 1uH + 990uF is very low indeed, of course, but 3m ohm ESR is quite low, too, in fact Q = 1 falls at merely 10nH. So 1uH is a lot higher, though it's only noticeable against very low source impedances.The fact that all these values are fairly mismatched, makes it inconvenient to try and force it into a prototypical filter; really I should be looking for the most important loops. The source end should be inconsequential -- it rolls off with L1 (sans the 47R/12R pad) at 8MHz. So we can ignore L1 at lower frequencies. (A good hint that you may want another cap in front of it -- one of those 330uF's perhaps?)The next loop is the 330's to L2 to the 22's. This has a total equivalent of 44uF + 990uF = 42uF , so resonates with Zo = 0.23 ohm at Fo = 16.5kHz. Loop ESR is 38m ohm, so Q ~ 6. Capacitors in series ("+") use the parallel formula... I have no notation for "series" other than the plus sign.When you have a resonant loop, any tap along it acts in a similar way; in effect we have a cap divider, which in turn acts as an RF impedance transformer, and we have a super low impedance on the left, and a modest impedance on the right. It acts parallel resonant, so we expect an impedance peak at V2 of around 0.23 * 6 = 1.4 ohms (at Fo).You can measure port impedance by setting the other sources to zero, and placing a current source from GND to V2, of magnitude 1. V(V2) = (1A) * Z(V2) = Z(V2), so you read off ohms directly.Since there's an impedance peak there, we might seek to shunt it; but we know better than to simply add more capacitance, because we'll just keep doing the same thing over again. If we use an R+C, with R ~ 0.2 ohm, and C >> 44uF (typically >= 2.5 times more), we'll end up with a deliciously flat impedance over the transition band.You might also consider moving over C1 like I hinted earlier, then changing C3 to a damper (more ESR and C).Back to the load again -- do you have any insight into it, at this time? Is it going to have a bunch of input capacitance like most converters? If so, we can model that; we could even model the converter's input resistance, which might range from positive to negative, depending.If it's cap-input, consider putting a choke towards it. Which basically swaps around the filter, which solves the not-terribly-useful-L1 situation, and also gives you something to reason about, if you choose to shorten the filter instead (honestly, I'd be surprised if more than a CLC is needed, unless this is super sensitive, MIL or something).Don't forget that common mode is often a worse offender than differential. You've got a damn fine filter here for differential, but it's all for naught if there's a 100MHz spike blasting straight over that common ground wire!Tim

author: coppercone2
author_rank: Super Contributor
timestamp: August 03, 2019, 08:17:19 am
content: 4 quadrant supplies should be able to test low impedance things

author: jmw
author_rank: Frequent Contributor
timestamp: August 03, 2019, 07:31:58 pm
content: Quote from: T3sl4co1l on August 03, 2019, 04:31:04 amSo the converter is a boost in DCM; there's no input cap other than C4/C5 in the filter. In DCM, the input port looks like the converter's inductor in series with a resistance which is the average model of the switch network. When the converter is at regulation, that resistance tends to zero and you just see the inductor. In the Middlebrook extra-element theorem analysis, Z_d = 16 ohm + (15 uH)sand Z_n = (15 uH)s. There's some load and output cap influence on that 16 ohm resistance factor but it's so small it just looks like a flat 16 ohm out to 170 kHz. That's why I was trying to keep the output impedance of the filter under 15 uH (+ DCR of about 40 mohm for the inductor I'm using).

author: T3sl4co1l
author_rank: Super Contributor
timestamp: August 04, 2019, 01:58:27 am
content: Ah, so those are the converter input capacitors. Excellent.Tim

author: jmw
author_rank: Frequent Contributor
timestamp: August 04, 2019, 07:53:54 pm
content: I tried some ideas with damping. Picking higher ESR capacitors is a problem since they'll reduce HF attenuation unless I bypass them. There's already a quite bit of capacitance here, enough that I'll have to consider the inrush transient later, so I tried parallel R+L. I replaced C4/C5 with a single 100u to adjust for the frequency shift from damping, and 200m DCR for the damping L means I can use chip inductors with that spec since there's about 10:1 ratio between the DC in L1/L3 and L2/L4. Rough Q estimate is 1.5 for the first section and 2.2 for the second section so the output impedance peaks around 130 mohm and stays under the (15 uH)s] line, even though it does get close near the resonant peaks.I'm still confused by what you said about testing this with both 50 ohm sources and loads. This isn't for traditional RF signal filtering, it's for the conducted EMI from the converter's pulsating current draw. Shouldn't the closest simulation look like hooking a AC current source to V2 and measuring at V1 connected to a 50 ohm || 50 uH load (assuming that's our LISN spec)?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: August 05, 2019, 01:20:59 am
content: Yes, quite. The 50/50 ohm test is the general case, unless we know something more specific, which we do in this case. An AC current source at the load side would be a more correct model here.Again, the input isn't doing much (2u rolls off with 50 ohms at >>10kHz), but if you don't mind the use of more inductors, that Q doesn't sound bad, yeah.Inductors are usually the more annoying part of a design, so one tends to prefer a CLC(LC..) format, with RC damping.Also, have you considered simply making a longer filter? You'll get better attenuation with those 330uF's spread out amid, say, three 0.47uH's. Probably don't even need to be 330, unless there's a hold-up spec you're supporting (in which case, don't forget the diode on the front end, to prevent other loads from discharging it faster!).Tim

author: jmw
author_rank: Frequent Contributor
timestamp: August 06, 2019, 03:09:23 am
content: You're right, below 4 MHz that 2 uH isn't doing much when in series with 50 ohm. Now I understand what you meant by the transfer function isn't everything: the textbook of course doesn't mention the measurement is taken at the LISN port with its 50 ohm impedance at frequency!