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Ash Small

Mon Jul 23 2018, 05:56AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

I think I have a question...

As I understand it, the way this filter works (based on the LTSpice simulation and experimental observation) is that the first capacitor in the filter acts as a power factor correction capacitor, matching the phase angles of the source (transformer) with the load (inductive/reactive notch filter). I've done some googling, and there is mention of rectifiers requiring PFC as well, but not got my head around that yet, although there's a full wave rectifier involved here.

All this was trial and error as far as the PFC bit was concerned, I didn't have a clue where to start with the maths, it's not simple, involves a transformer, rectifier, two capacitors and a choke, not to mention the rest of the filter, two more inductors and chokes.

My instict tells me the first capacitor matches the ripple power to the notch filter, but not to the rest of the circuit, so all the ripple ends up in the notch filter and, from the simulation results, none gets into the rest of the filter.

Is it fair to say that, under these circumstances, with the correct PFC, the notch filter displays negative resistance to the ripple?

2Spoons

Mon Jul 23 2018, 09:09PM

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM
Location:
Posts: 615

No. Negative resistance implies an inverse relationship between voltage and current. That is not what is happening.

Ash Small

Tue Jul 24 2018, 06:33AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

2Spoons wrote ...

No. Negative resistance implies an inverse relationship between voltage and current. That is not what is happening.

Thanks. So this is just a case of the first capacitor doing the power factor correction thing for the phase angle difference between an inductive source and inductive load?

2Spoons

Tue Jul 24 2018, 10:51PM

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM
Location:
Posts: 615

I'd be inclined to think of it in terms of impedance matching, rather than PFC. Makes more sense for a filter.

hen918

Wed Jul 25 2018, 01:08PM

Registered Member #11591 Joined: Wed Mar 20 2013, 08:20PM
Location: UK
Posts: 556

The transfer function for Ash's filter (unladen) is below, where s is jw, the complex angular frequency. It's not in standard form, but should still be useful.

Vou/Vi = (C2*L2*s^2+1)/(1+C1*C2*C3*L1*L2*L3*s^6+((((L2+L3) *C3+C1*L2)*C2+C1*C3*L3)*L1+C2*C3*L2*L3) *s^4+((C2+C1+C3)*L1+C2*L2+C3*L3)*s^2)

The equivalent series impedance is:
Z = (C1*C2*L1*L2*L3*s^4+(((L2+L3)*C2+C1*L3) *L1+C2*L2*L3)*s^2+L1+L3)*s/ (1+C1*C2*C3*L1*L2*L3*s^6+(((C3*L3+L2*(C1+C3)) *C2+C1*C3*L3)*L1+C2*C3*L2*L3)*s^4+((C2+C1+C3) *L1+C2*L2+C3*L3)*s^2)

So with a load R, The output voltage will equal:
Vo = Vi*R*(C2*L2*s^2+1)/ (C1*C2*C3*L1*L2*L3*R*s^6+C1*C2*L1*L2*L3*s^5+(((C3* L3+L2*(C1+C3))*C2+C1*C3*L3)*L1+C2*C3*L2*L3) *R*s^4+(((L2+L3)*C2+C1*L3)*L1+C2*L2*L3) *s^3+((C2+C1+C3)*L1+C2*L2+C3*L3)*R*s^2+(L1+L3) *s+R)

These were found using Norton / Thevenin transforms to simplify the circuit, then Maple mathematics software to simplify the equations.

Ash Small

Wed Jul 25 2018, 11:49PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

hen918 wrote ...

The transfer function for Ash's filter (unladen) is below, where s is jw, the complex angular frequency. It's not in standard form, but should still be useful.

Vou/Vi = (C2*L2*s^2+1)/(1+C1*C2*C3*L1*L2*L3*s^6+((((L2+L3) *C3+C1*L2)*C2+C1*C3*L3)*L1+C2*C3*L2*L3) *s^4+((C2+C1+C3)*L1+C2*L2+C3*L3)*s^2)

The equivalent series impedance is:
Z = (C1*C2*L1*L2*L3*s^4+(((L2+L3)*C2+C1*L3) *L1+C2*L2*L3)*s^2+L1+L3)*s/ (1+C1*C2*C3*L1*L2*L3*s^6+(((C3*L3+L2*(C1+C3)) *C2+C1*C3*L3)*L1+C2*C3*L2*L3)*s^4+((C2+C1+C3) *L1+C2*L2+C3*L3)*s^2)

So with a load R, The output voltage will equal:
Vo = Vi*R*(C2*L2*s^2+1)/ (C1*C2*C3*L1*L2*L3*R*s^6+C1*C2*L1*L2*L3*s^5+(((C3* L3+L2*(C1+C3))*C2+C1*C3*L3)*L1+C2*C3*L2*L3) *R*s^4+(((L2+L3)*C2+C1*L3)*L1+C2*L2*L3) *s^3+((C2+C1+C3)*L1+C2*L2+C3*L3)*R*s^2+(L1+L3) *s+R)

These were found using Norton / Thevenin transforms to simplify the circuit, then Maple mathematics software to simplify the equations.

I'll take your word for it Hen

Two Spoons, I never really saw impedence matching like that, but can see that it relies on the same principles as tuned length (1/4 wavelength) transmission lines. and the parallels with reflected signals. etc.

I just had this 'hunch', from the variation in the signal distortion waveforms I was seeing, that it was possible to 'tune' the system by finding the correct value capacitance, so that the whole 'ripple signal' ended up in the notch filter, or at least sufficient that the rest of the filter could eliminate what was remaining, or at least reduce it to levels that were negligible.

2Spoons

Thu Jul 26 2018, 02:08AM

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM
Location:
Posts: 615

Looking at the values you have I suspect you don't really have filter 'sections' as such - given all the impedances are in the same ball park I think there is probably a lot of interaction between the various elements.
From memory the rule of thumb for cascading passive filter sections would be to make sure each section has 10x the impedance of the one before it, otherwise loading of one section by another means you dont get the filter you were expecting.
Though that doesn't really apply to the design by trial process you are using!

Ash Small

Sat Jul 28 2018, 03:07PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

2Spoons wrote ...

Looking at the values you have I suspect you don't really have filter 'sections' as such - given all the impedances are in the same ball park I think there is probably a lot of interaction between the various elements.
From memory the rule of thumb for cascading passive filter sections would be to make sure each section has 10x the impedance of the one before it, otherwise loading of one section by another means you dont get the filter you were expecting.
Though that doesn't really apply to the design by trial process you are using!

I read that successive stages in a Butterworth filter typically have three times the capacitance of the preceeding section, but this, I appreciate, is to approximate to a flat passband.

I did initially mis-understand Butterworth filters, but when I started designing 'my filter', I guess I was basing it loosely on the type of filters with two capacitors and one choke that are usually found in tube amps, but with extra stages. (these are typically around 10:1)

Der Albi then suggested the notch filter, which I initially tried after the first stage, and noticed that I could distort the ripple in either direction, but couldn't eliminate it completely, so tried it after the rectifier in parallel with the first capacitor, where the ripple also has greater amplitude.

As mentioned previously, my understanding is that the first capacitor matches the phase angle of the source to the phase angle of the notch filter, thus providing a low impedence path for the ripple, which 'sees' the first 10mH choke as a much higher impedence.

I think on the sim some ripple was still getting through the first stage, but it was uVolts. This appears to be reduced to a nonaVolt or two by the final stage, however, I suspect I've come up against the limits of LTSpice in this instance.

I'm still preparing to wind a 0.4uH, 10mOhm choke, I've unwound a few, just need to get the kinks out of the wire

Dr. Slack

Sun Jul 29 2018, 06:43AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

A notch section in your filter can 'short out' one frequency. If you choose that to be the fundamental frequency of your ripple, then you can get a significant reduction in the pp output ripple, but only a reduction, because the harmonics get through unaffected.

A systematic way to design a lowpass filter with stop-band zeros (notches) is to do an elliptic design. Unfortunately, a power supply filter tends to have neither port well-matched, so a systematically designed filter will not behave as its prototype response, once placed in a power supply environment. The one thing that will be on specification though is the position of the stopband zero!

Ash Small

Sat Aug 04 2018, 06:43PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Well, I wound one, and it was a nightmare, I used second hand wire, which didn't help as it had work hardened by the time I'd straightened it out.

It could have been wound tighter, and came out at 0.12mH.

I worked out the value of caps needed to resonate at 100Hz, 21,100uF, and put these figures into the LTSpice simulation, and every permutation I tried came out worse than using no notch filter.

There is something about the values of 0.4mH and 6,330uF that just 'work' with the other values in the circuit.

With the 0.12mH and 21,100uF I just get loads of harminics, like millivolts, up to ten or twelve. With no notch filter I'm getting around 10uV ripple at the output, and with the 0.4mH and 6,330uF I'm getting a nanovolt or so.

For some reason, those particular values appear to block the harmonics. I don't understand why it appears to get worse with a notch filter with different value caps and choke, but the same resonant frequency.

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