Calculating values for a capacitance multiplier

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Hi!

First off, I am a bit of a novice when it comes to building power supplies, and my research area is definitely not in audio. I have a specification to get a very low output voltage ripple on a high voltage power supply and have stumbled across the use of a capacitor multiplier to do this. I am not even sure if these circuits would be applicable at high voltages, but the student in me is intrigued about how the circuits are obtained and I'd like to do some simulations to understand their working, and see if they are applicable.

While doing some research online I see a lot of recommended circuits, which use a large array of different capacitor configurations and values, with no explanation on how these values were reached considering the output voltage, input voltage, frequency of the supply, etc. Is there any such guide for this online, or can someone give me some general hinters?

Thanks!
J :D
 
Depending on the voltage and output current, a double-sided Cockroft-Walton voltage multiplier is often useful. It sounds to me that your interest is more of academic nature for understanding the operation rather than for a particular practical application?

Yes, you are correct. Although it is hoped in a couple of years I can build the supply. The output that requires the very high attenuation (50mV) is a 5kV output, with 50W of power, so 10mA of current. I also wish to switch at a high frequency (currently 180kHz).

I will look into your suggestion - I have only heard of the standard CW multiplier. I doubt it could achieve this low ripple value, though? I was thus looking for maybe "active" filtering techniques to further reduce to acceptable levels.

The application is for a travelling wave tube, which is very noise sensitive, btw.

Thanks for your suggestion!
 
The capacitance multiplier just uses a simple, single transistor amplifier to multiply a capacitance by the beta of the transistor. You can derive the effective capacitance by measuring the time to discharge an RC circuit.

HV -- Pete Millett uses cap multipliers in some of his tube based amplifiers -- with MOSFETs, you could also use a bipolar transistor (like the horizontal deflection transistors still lurking around.)

In high voltage circuits using switch-mode techniques, a cap multiplier is not necessary.

EDIT -- 50mV on 5kV is "Herculean" -- PSRR of -100dB but possible -- check out this application note (and Figure 11) by (the late) Jim Williams: High Voltage Low Noise DC-DC converters

https://www.analog.com/media/en/technical-documentation/application-notes/AN118fb.pdf
 
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Yes, you are correct. Although it is hoped in a couple of years I can build the supply. The output that requires the very high attenuation (50mV) is a 5kV output, with 50W of power, so 10mA of current. I also wish to switch at a high frequency (currently 180kHz).

I will look into your suggestion - I have only heard of the standard CW multiplier. I doubt it could achieve this low ripple value, though? I was thus looking for maybe "active" filtering techniques to further reduce to acceptable levels.

The application is for a travelling wave tube, which is very noise sensitive, btw.

Thanks for your suggestion!

50mVeff ripple on 5KV should be possible if you need only very little current. You can reduce the ripple with a shunt regulator at the multiplier output.
 
The capacitance multiplier just uses a simple, single transistor amplifier to multiply a capacitance by the beta of the transistor. You can derive the effective capacitance by measuring the time to discharge an RC circuit.

HV -- Pete Millett uses cap multipliers in some of his tube based amplifiers -- with MOSFETs, you could also use a bipolar transistor (like the horizontal deflection transistors still lurking around.)

In high voltage circuits using switch-mode techniques, a cap multiplier is not necessary.

EDIT -- 50mV on 5kV is "Herculean" -- PSRR of -100dB but possible -- check out this application note (and Figure 11) by (the late) Jim Williams: High Voltage Low Noise DC-DC converters

https://www.analog.com/media/en/technical-documentation/application-notes/AN118fb.pdf

Hmm, this makes for really interesting reading. However, my primary side voltages can be as high as 300V, so I don't think these techniques would help me too much here as I won't be able to use the outlined control chips (?)
 
50mVeff ripple on 5KV should be possible if you need only very little current. You can reduce the ripple with a shunt regulator at the multiplier output.

Yes! This is exactly what I was thinking. I am struggling to find any references that use a shunt regulator at such a large output voltage. I am quite a novice at SMPS design (I am only in my first year of study - don't worry, no experiments for a long while yet) and am struggling to find anything of the sort that could help me in my application - do you know of any, could you point me in the right direction, possibly?:)
 
Pick up a copy of Horowitz and Hill "The Art of Electronics" -- a good chunk of the section on power supply design is devoted to high voltage regulators. You can put the regulator in the ground return path, but this isn't without risk.

You can use a Maida regulator and a high voltage triode as the pass element.

There are also a number of papers on high voltage printed circuit design -- once you go over a few hundred volts special design techniques are necessary, special PCB materials etc.

I've had the power supply for photo-multiplier tubes blow up -- it's not a pleasant experience.
 
Pick up a copy of Horowitz and Hill "The Art of Electronics" -- a good chunk of the section on power supply design is devoted to high voltage regulators. You can put the regulator in the ground return path, but this isn't without risk.

You can use a Maida regulator and a high voltage triode as the pass element.

There are also a number of papers on high voltage printed circuit design -- once you go over a few hundred volts special design techniques are necessary, special PCB materials etc.

I've had the power supply for photo-multiplier tubes blow up -- it's not a pleasant experience.

A "Maida" regulator, can't say I've heard of that. Since it's regulated, can it still be used with an SMPS which is primary side controlled?

Yep, I have to look at the transformer design also, so I am already aware of the issues with insulation at these voltages. Something I am always reminded of by my supervisors.

By pass element do you mean, instead of the transistors in the Maida regulator? Could high voltage rated MOSFETs like Silicon carbide, possibly be used?
 
Hmm, this makes for really interesting reading. However, my primary side voltages can be as high as 300V, so I don't think these techniques would help me too much here as I won't be able to use the outlined control chips (?)

You can use a little regulator like the Supertex/Microchip LR8N3 for the chips . It can stand off 450V and is used for aux supply in off-line switchers. See figure 3-3 in the datasheet:
https://www.mouser.com/datasheet/2/268/20005399A-909415.pdf
 
Lots of comments … not much meat so far.

The OP's (eventually revealed) question was, “I need a 5 kV DC supply, 50 mV or less ripple, and will be using 100 kHz or higher operating frequency. What capacitance values to use, and what topology to implement?”

Cockroft-Walton generators are essentially half-wave rectifier stacks. See Cockcroft& - Wikipedia for a darn-good write up. It isolates the 'gotchas', namely high ripple (the opposite of your requirement). In the middle of the article, this chestnut:
In practice, the CW has a number of drawbacks. As the number of stages is increased, the voltages of the higher stages begin to "sag", primarily due to the electrical impedance of the capacitors in the lower stages. And, when supplying an output current, the voltage ripple rapidly increases as the number of stages is increased (this can be corrected with an output filter, but it requires a stack of capacitors in order to withstand the high voltages involved). For these reasons, CW multipliers with large number of stages are used only where relatively low output current is required. The sag can be reduced by increasing the capacitance in the lower stages, and the ripple can by reduced by increasing the frequency of the input and by using a square waveform.
But these seem to be your conditions. Relatively low current … 50 ma … and rather high frequency AC input … 100+ kHz.

One of the other points the article makes is that for practical high voltage supplies, a step-up transformer limits the number of stages of the Cockroft-Walton, and reduces both the ripple-on-load issues, and the limit-of-practical current business.

So, rectify line A/C. Use full-wave-bridge diode configuration. Assuming 120 VAC operation, charge up a 250 V rated capacitor of pretty large value. Now you have about 170 VDC.

From there, feed a 4 MOSFET H-bridge 100 kHz switch. Now you have 330 Vpeak-peak to transform up. (This is important for the safety angle, too). Driving a 2:1 wired, hi-volt potted ferrite homebrew transformer, the output is over 600 VPP. Cool!

Follow up with a CW stack. The implementation will require Vreverse-breakdown silicon rectifiers rated over 1,500 V blocking. Not cheap to buy, but easy to make, by putting 3 ea, 1,000 PIV garden-variety diodes in series. Don't forget to put 1,000 kΩ resistors in parallel with each diode, too. Makes them last a whole bunch longer. You will need capacitors that are equally high-volt rated. The maximum voltage each is required to handle is VPP of the driving AC. Again, read article.

So… values.

Illinois Capacitor / CDE brand, 10 µF, 350 V, axial leads, $1.30 ea, qty 10 (you'll need a bunch). Basically, stepping up 600 VPP to 5,000 V requires 2 ea at each stage in series (700 VMAX), plus 2 more for the non-ground-leg sets at each stage. So…
5,000 ÷ 600 = 9 stages.

9 × (2 ⊕ 2) = 36 capacitors. 10 µF, 350 V.
9 × (2 ⊕ 2) = 36 rectifiers. 1000 VPIV[/sub
72 ea, 1 MΩ, ½ watt resistors.
OK. Now… what about ripple. The stack of 9 ea., 10 µF caps in series is about what, 1.1 µF or so. Remembering ΔV = IΔt/C for constant current, at 100 kHz, Δt is only 10 µs. 10×10⁻⁶ sec. So,
ΔV = IΔt / C
ΔV = 0.050 amp × 10×10⁻⁶ sec ÷ 1.1×10⁻⁶ farad
ΔV = 0.454 V​
Not bad! Nowhere near your 0.050 V requirement, but still encouragingly close. Factor of 10 away.

Here's where the fun is. Since you've already (presumably) figured out how to make the 100 kHz hand-wound ferrite transformer, the same skills will allow you to make a 0.1 henry choke. Another 18 capacitors, 18 bleed resistors … and you now have a CLC power supply. The voltage drop will be minimal, but the ripple will drop 25× or better.

Voilá. A 50 mA, 5 kV supply. Shunt regulation could have worked, but passive components tend not to blow up at the least opportune times. While shunt regulators also tend to be pretty robust, there are quite a few less-than-helpful ways they fail.

Just saying,
GoatGuy ✓
 

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For commercial economy, your Raw DC should aim for 2%-5% ripple. Any lower value can be gotten by filtering the raw DC.

"Commercial" and "economy" mean different things in different times and places. GoatGuy seems to have figured 0.01% ripple at the raw DC point, in part because e-caps have become very cheap, and mostly by changing from 50/60Hz to 100kHz.

A single R-C stage after that would get your 50mV goal. Some voltage is lost. Say you can lose 5%, or 250V, at 10mA. This is a 25k resistor (2.5+ Watts). Another 1.1uFd cap-string after that would give WAY more ripple reduction than you need. (You could even reduce 25k to 1k for less DCV loss.)

Your project is halfway between two once-common power supplies. An oscilloscope needs 2,000V at 2mA. This was commonly got from a HV winding and a single tube diode (not worth putting more money in it). TV sets needed much higher voltage and current. The required cap-size would hold enough energy to be lethal. Also costly. Also there was already a high-frequency power amp in the box (H-sweep). Most TV sets took another winding on the 17KHz coil to a diode and cap. The high frequency allowed a small cap and less stored charge (less lethal).
 
Lots of comments … not much meat so far.

The OP's (eventually revealed) question was, “I need a 5 kV DC supply, 50 mV or less ripple, and will be using 100 kHz or higher operating frequency. What capacitance values to use, and what topology to implement?”

Cockroft-Walton generators are essentially half-wave rectifier stacks. See Cockcroft& - Wikipedia for a darn-good write up. It isolates the 'gotchas', namely high ripple (the opposite of your requirement). In the middle of the article, this chestnut:
In practice, the CW has a number of drawbacks. As the number of stages is increased, the voltages of the higher stages begin to "sag", primarily due to the electrical impedance of the capacitors in the lower stages. And, when supplying an output current, the voltage ripple rapidly increases as the number of stages is increased (this can be corrected with an output filter, but it requires a stack of capacitors in order to withstand the high voltages involved). For these reasons, CW multipliers with large number of stages are used only where relatively low output current is required. The sag can be reduced by increasing the capacitance in the lower stages, and the ripple can by reduced by increasing the frequency of the input and by using a square waveform.
But these seem to be your conditions. Relatively low current … 50 ma … and rather high frequency AC input … 100+ kHz.

One of the other points the article makes is that for practical high voltage supplies, a step-up transformer limits the number of stages of the Cockroft-Walton, and reduces both the ripple-on-load issues, and the limit-of-practical current business.

So, rectify line A/C. Use full-wave-bridge diode configuration. Assuming 120 VAC operation, charge up a 250 V rated capacitor of pretty large value. Now you have about 170 VDC.

From there, feed a 4 MOSFET H-bridge 100 kHz switch. Now you have 330 Vpeak-peak to transform up. (This is important for the safety angle, too). Driving a 2:1 wired, hi-volt potted ferrite homebrew transformer, the output is over 600 VPP. Cool!

Follow up with a CW stack. The implementation will require Vreverse-breakdown silicon rectifiers rated over 1,500 V blocking. Not cheap to buy, but easy to make, by putting 3 ea, 1,000 PIV garden-variety diodes in series. Don't forget to put 1,000 kΩ resistors in parallel with each diode, too. Makes them last a whole bunch longer. You will need capacitors that are equally high-volt rated. The maximum voltage each is required to handle is VPP of the driving AC. Again, read article.

So… values.

Illinois Capacitor / CDE brand, 10 µF, 350 V, axial leads, $1.30 ea, qty 10 (you'll need a bunch). Basically, stepping up 600 VPP to 5,000 V requires 2 ea at each stage in series (700 VMAX), plus 2 more for the non-ground-leg sets at each stage. So…
5,000 ÷ 600 = 9 stages.

9 × (2 ⊕ 2) = 36 capacitors. 10 µF, 350 V.
9 × (2 ⊕ 2) = 36 rectifiers. 1000 VPIV[/sub
72 ea, 1 MΩ, ½ watt resistors.
OK. Now… what about ripple. The stack of 9 ea., 10 µF caps in series is about what, 1.1 µF or so. Remembering ΔV = IΔt/C for constant current, at 100 kHz, Δt is only 10 µs. 10×10⁻⁶ sec. So,
ΔV = IΔt / C
ΔV = 0.050 amp × 10×10⁻⁶ sec ÷ 1.1×10⁻⁶ farad
ΔV = 0.454 V​
Not bad! Nowhere near your 0.050 V requirement, but still encouragingly close. Factor of 10 away.

Here's where the fun is. Since you've already (presumably) figured out how to make the 100 kHz hand-wound ferrite transformer, the same skills will allow you to make a 0.1 henry choke. Another 18 capacitors, 18 bleed resistors … and you now have a CLC power supply. The voltage drop will be minimal, but the ripple will drop 25× or better.

Voilá. A 50 mA, 5 kV supply. Shunt regulation could have worked, but passive components tend not to blow up at the least opportune times. While shunt regulators also tend to be pretty robust, there are quite a few less-than-helpful ways they fail.

Just saying,
GoatGuy ✓


Some very good information here and exactly what I was looking for, thank you.

As of currently, my topology is a half-bridge LCC converter, fed by a buck-converter to achieve regulation (the main bridge is fixed frequency). This, mostly because I have to achieve high power density and I believe the reduction in number of switches/control IC's and chips etc would be beneficial.

For this reason also, I have been told it usually undesirable to have inductance on the secondary side, due to the high voltages and therefore large sized inductances that will exists in the filter. Although I understand LC circuits give much better attenuation. This is the reason I was looking into capacitance multiplier/active filters/regulation in the secondary side.

Another issue is that I have a second output, which is at 3kV, which has a higher output current of 200mA, which doesn't require as much regulation. But I assume this higher current may mean the Cockroft Walton is not as applicable (I've only seen it in X-ray type, or plasma type supplies which have very small currents).

Anyway, you have gave me plenty to start working on. I will look into the use of CW multipliers.
 
............Another issue is that I have a second output, which is at 3kV, which has a higher output current of 200mA, which doesn't require as much regulation. But I assume this higher current may mean the Cockroft Walton is not as applicable (I've only seen it in X-ray type, or plasma type supplies which have very small currents)................

For a 600W output, I would not consider using a CW multiplier. The capacitors will be huge and expensive. As you do not have the same ripple demands, I would consider fly-back eventually in parallel.
NB: If you are only in your first year of study (university I assume), you have set your ambitions high.
 
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For a 600W output, I would not consider using a CW multiplier. The capacitors will be huge and expensive. As you do not have the same ripple demands, I would consider fly-back eventually in parallel.
NB: If you are only in your first year of study (university I assume), you have set your ambitions high.

Lol! Unfortunately, I am not the one who set my ambitions! I am a first year PhD student, but I did not propose this project. I simply took it on following my previous studies when it was advertised.

What I believe you are proposing is two or more flyback converters which are connected in parallel at the output? Kind of like an interleaved configuration?
 
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