Damped LC filter for low pass (1500Hz) filtering

[popchops]

Hi Duncan,

I have built a bog standard +/-55V power supply using bridge rectifiers and 2x 10mF caps on each rail.

I would like to add a compact inductor of about 1.5uH on each rail, between and connecting the parallel caps, for the purpose of attenuating high frequency noise/ringing. I know that some additional measures are needed to make sure the LC filter is adequately damped. Is it possible to model this in PSUD?

Or is it too complex? Thx. POPS.

 

[AndrewT]

I think 1.5uH is too low to be effective.
Try 100turns of 0.6mm or 0.8mm diameter enamelled copper wound onto a 22mm bobbin with cheeks set to 15mm apart.
You may want to compare this to a low turns version on a scope to see how much the ripple is rounded by the increased inductance.

 

[popchops]

Hi folks,

I am using 2x 10mF capacitors on each rail of my conventional 55V 5A linear power supply.

I would like to install a 1-2 uH air core inductor on each rail between and connecting the caps to form an LC filter. Can't hope to impact 100Hz ripple but anything above 10 kHz (ringing etc) will be toast.

I know that damping the LC oscillator is critical to prevent instability at the corner frequency (1.0-1.5 kHz). A colleague suggested that the ESR of the cap (~29 milliOhms) could be sufficient for damping. Is it true? Or do I need an additional series RC in parallel with the filter cap?

Can anybody walk me through the calcs or recommend a free/cheap tool that will allow me the model the LC filter plus damper in the frequency domain?

Reactance of the inductor will be about 12-14 milliOhms at the corner frequency. DC resistance of the coil (using 80cm of 1.2mm copper) is about 12 milliOhms also.

Many thanks! Popchops.

 

[trobbins]

Popchops, did you calculate what the impedance of a capacitor would be at 15kHz?

How did that compare with their ESR?

From that comparison, how would describe what each capacitor looks like at 15kHz.

 

[popchops]

Thx Andrew. Even if I can achieve f0 around 1500Hz I will be satisfied if the ESR of the filter capacitor can be used to (over)damp the LC filter. If there is a simple but stable inductor alternative to RC filter then I want to try it. Otherwise I will use 1 or 2 cm of 1.2mm constantan resistance wire to add a few milliohms between capacitors.

Is anybody using the ever popular 10mF capacitors with a small inductor? I will definitely try increasing the diameter slightly & reducing length between cheeks. Would like to understand the implications for stability though at f0. The corner frequency will always be in the audible range (for all reasonable inductors) which is ok if I can be sure my LC is overdamped. Ta. Pops.

 

[DF96]

Taking the OP's figures (which I have not checked) seems to show that the Q of this 'filter' will be somewhere around 0.3 at the corner frequency. No extra damping is needed as the coil itself has sufficiently low Q even before the cap ESR is added too. Of course, this 'low pass filter' will not achieve very much apart from giving the owner a warm glow. On a positive note, the inductor will do no harm.

 

[popchops]

Popchops, did you calculate what the impedance of a capacitor would be at 15kHz?

How did that compare with their ESR?

From that comparison, how would describe what each capacitor looks like at 15kHz.

Corner frequency is 1.5 kHz not 15 kHz. Sorry.

I double checked data on the capacitor, as follows (http://www.mouser.com/ds/2/427/101102phrst-101634.pdf)

Max ESR at 100 Hz = 27 milliOhms
Max Z (impedance) at 20 kHz = 19 milliOhms

So... I'm not exactly sure what ESR to expect from the capacitor at 1500 Hz. Something between 19 and 27 milliohms? Thanks again.

Pops.

 

[AndrewT]

Have you seen the rely from Duncanamps to your original enquiry?

 

[popchops]

Taking the OP's figures (which I have not checked) seems to show that the Q of this 'filter' will be somewhere around 0.3 at the corner frequency.

If Q = XL/ESR then Q = 12mR / 27mR = 0.45. But this ESR is @ 100 Hz. Corner frequency = 1/(2*pi*LC^0.5) = 1300 Hz. What 'ESR' should I expect?

If damping factor = 1/2Q then zeta = 1.1. Lovely.

No extra damping is needed as the coil itself has sufficiently low Q even before the cap ESR is added too. Of course, this 'low pass filter' will not achieve very much apart from giving the owner a warm glow. On a positive note, the inductor will do no harm.

I've got to use something to connect the capacitors - why use a straight bit of copper when I can use a coil? Cheap thrills. Zero additional component count.

Thank you.

 

[AndrewT]

I use a twisted pair to connect the two poles of the capacitor to the next stage.

 

[trobbins]

The impedance of 10mF at 1.5kHz is 10 milliohm. The capacitor ESR appears to be significantly more that that. In effect the capacitance acts like a resistance around and above that frequency. So there effectively is no LC circuit to resonate, especially if the impedance of the choke is dominated by its ESR.

What is your aim with a pi filter - to effectively constrain power supply charging pulses to one of the capacitors, and to constrain audio currents from the amplifier to the other capacitor?

 

[popchops]

Hi Duncan,

I am expecting some high frequency ringing > 15kHz to be introduced by the bridge rectifier diodes. I haven't measured/observed this yet. I wanted to equip one half of the power supply with R or L between filter caps and then do back to back comparison.

So the objective with the 1.5uH inductor is to give 40dB/decade attenuation above 1500Hz. That's the dream.

My actual capacitors (Vishay 101 63V 10mF 35mmx80mm) have no quoted ESL figure. Equivalent Epcos capacitors (not the special low inductance type) are 20nF ESL. So I am expecting something in the tens of nanofarads.
But what I really want to do is model this, considering the coil resistance and ESL/ESR of the caps. Can PSUD or LTSpice do this (freq domain)?
Or is there a test I can do to verify the gain at the resonant frequency? Input a sine wave to the amp? Sounds risky. THANKS! Pops.

 

[duncanamps]

Hi Duncan,

I am expecting some high frequency ringing > 15kHz to be introduced by the bridge rectifier diodes. I haven't measured/observed this yet. I wanted to equip one half of the power supply with R or L between filter caps and then do back to back comparison.

So the objective with the 1.5uH inductor is to give 40dB/decade attenuation above 1500Hz. That's the dream.

My actual capacitors (Vishay 101 63V 10mF 35mmx80mm) have no quoted ESL figure. Equivalent Epcos capacitors (not the special low inductance type) are 20nF ESL. So I am expecting something in the tens of nanofarads.
But what I really want to do is model this, considering the coil resistance and ESL/ESR of the caps. Can PSUD or LTSpice do this (freq domain)?
Or is there a test I can do to verify the gain at the resonant frequency? Input a sine wave to the amp? Sounds risky. THANKS! Pops.

Ah, OK. This is way beyond what PSUD can do and LTSpice in the time domain sounds like a much better option.

One of the things you can do with SPICE based runs is take the FFT (Fast Fourier Transform) response of one of the outputs, this will show the amplitude and frequency of any unwanted signals on the output.

However, it will depend on the accuracy of the models to be meaningful, and that includes inductive effects of the capacitors.

 

[popchops]

What is your aim with a pi filter - to effectively constrain power supply charging pulses to one of the capacitors, and to constrain audio currents from the amplifier to the other capacitor?

Hi trobbins and thanks.

No - to modify the ripple cycles requires a large inductor and energy storage starts to get scary. It's important for me that my output voltage does not overshoot by more than 8%. A large inductor can do that.

So my ambitions are limited to LP filtering noise (inc. ringing) above the corner frequency ~1300 Hz. Advantage of LC vs RC filter is the steeper 40db/decade roll-off. -40dB attenuation @ 13kHz is quite attractive to me, especially for the price of 20 turns of bent metal (gives ~1.5uH).

Charging pulses will be unaffected @ 100Hz, although you could say that re-supply between capacitors would be restricted at >1300 Hz. I don't see this as a problem though.

So - am I crazy? What's the catch? Popchops.

 

[abraxalito]

I would like to install a 1-2 uH air core inductor on each rail between and connecting the caps to form an LC filter. Can't hope to impact 100Hz ripple but anything above 10 kHz (ringing etc) will be toast.

I'd suggest upping the inductance by winding your coil around a powdered metal toroid. A hi-flux core would be the ideal choice.

Can anybody walk me through the calcs or recommend a free/cheap tool that will allow me the model the LC filter plus damper in the frequency domain?

AC analysis from LT spice will do the trick nicely -Linear Technology - Design Simulation and Device Models

 

[Mark Johnson]

I've successfully eliminated rectifier-induced ringing in the transformer secondary, through a combination of selecting the right diode, and adjusting the RLC resonant circuit to be critically damped. The ringing data I took on 48 different diodes, including Schottkys, 35 amp bridges, HEXFREDs, ultrafast diodes, soft recovery diodes, silicon carbide diodes, etc., is tabulated in this article in Linear Audio magazine: (link). The magazine charges EUR 0,99 for a soft-copy.

But perhaps that's not the type of ringing you seek to remove.

The few times I've included LC filtering in a raw DC line, I found that connecting a resistor in parallel with the inductor was effective. Overdamping the inductor's self-resonance, to the tune of zeta=25 (Q=0.02), made for an extremely smooth and well behaved frequency response in SPICE, and no misbehavior on the bench. Capacitor ESR and inductor series resistance were sufficient to overdamp the system at its much lower "natural frequency" , 1/sqrt(LC).

 

[popchops]

However, it will depend on the accuracy of the models to be meaningful, and that includes inductive effects of the capacitors.

Sorry - again! I meant to type 20 nH not 20 nF. ESL is of the order of tens of nano-Henrys.

 

[Mark Johnson]

The impedance of the LC circuit at its resonant frequency (sometimes called its "characteristic impedance") is given by sqrt(L/C). If L=1E-6 and C=1E-2 then the characteristic impedance is 10 milliohms. The series resistance of the inductor and the ESR of the capacitor are much greater than 0.01 ohms, making this an overdamped RLC circuit with no oscillatory ringing at all.

 

[popchops]

The few times I've included LC filtering in a raw DC line, I found that connecting a resistor in parallel with the inductor was effective. Overdamping the inductor's self-resonance, to the tune of zeta=25 (Q=0.02), made for an extremely smooth and well behaved frequency response in SPICE, and no misbehavior on the bench. Capacitor ESR and inductor series resistance were sufficient to overdamp the system at its much lower "natural frequency" , 1/sqrt(LC).

Now that's what I'm talking about.

I initially assumed I would need a resistor in parallel (inside the coil perhaps) equivalent to the reactance at the resonant frequency. For me this would be about 12 milliOhms. It's manageable even at 5A max throughput.

Would a lower resistance give greater damping? Are you saying that the resistor was not needed for damping, but added anyway to increase damping? Thanks Mark.

 

[DF96]

Advantage of LC vs RC filter is the steeper 40db/decade roll-off.

You will not get second order rolloff. At best you will get first order rolloff, as the cap will look like a resistor. At a sufficiently high frequency the cap will look like an inductor so no further rolloff at all.

I am not convinced that you need to filter these frequencies - much better to avoid generating them in the first case by careful design of the rectifier circuit. However, if you want a filter then you need to use appropriate component values: larger inductor and smaller capacitor.

You need to think about the effect of a coil carrying charging pulses. This will spray an AC magnetic field around. Most people think about using twisted pair to connect capacitors (as AndrewT suggests) in order to minimise magnetic induction; you seem to want to maximise it!