Cockcroft-Walton Voltage Multiplier Problem

[jegues]

Homework Statement

Hello all,

I am attempting to preform some analysis on the Cockcroft-Walton Voltage Multiplier circuit.

Homework Equations

The Attempt at a Solution

I am using PSCAD to simulate the circuit, but the use of any other circuit simulator should provide the same results.

Attached is a picture of the circuit, and my PSCAD file.

First off, I build the circuit within PSCAD and input all of my source and component values. After doing so I have come across a number of problems, some of which I've attempted to fix and others for which I am clueless.

Problem 1: For my "Single Phase Voltage Source" I put in a voltage of 1kV because I desired a voltage with an amplitude that varies from +1kV to -1kV. When I had displayed the source output on the graph it looked at though the source was fluctuating between ~+/-1.4kV. Why is this, and how do I achieve my desired amplitude of 1kV? (For now I simply used trial and error to achieve a AC source of ~1kV amplitude, it required and input of ~0.72kV)

Problem 2: The circuit is not providing the correct output voltage, and I can't figure out why. I haven't changed anything within the diode settings except not to use the snubber circuitry. Furthermore, I measured V2p and V3p and found them to be identical waveforms to Vo. Ideally, Vo should sit somewhere around 2*n*Vs, where n is the number of stages. Since I used n=3 stages, I expect a voltage slightly below 6kV, but I am seeing a voltage of a mere 1kV. What is going on here?

Problem 3: Assuming I can get the circuit functioning properly, I want to make numerous measurements by varying one variables (i.e. f, C, load resistance etc...) and holding the others constant. Assume I had 3 different values for each variable that I wanted to test, this would leave me with 27 (3*3*3) circuits to reconfigure and measure. Is there a way where I can test all the different combinations of parameters while only building one circuit and have PSCAD tabulate the results for me? (Or something similar to make my life easier?)

Any insight/suggestions/comments/corrections on either of these problems would be greatly appreciated!

Thanks for your time!

Cheers!

 

[gneill]

1. The supply voltage discrepancy looks suspiciously like a peak versus rms issue. Does the voltage supply definition expect the voltage parameter to be rms?

2. If your load resistance is too small the capacitors will be bled dry during discharges and their voltage won't build up over the cycles. There's an effective time constant determined by the capacitors and load resistance (and the source resistance, but I see you've set that very small indeed). Try starting with a larger load resistance (maybe a few megs) or a higher source frequency to shorten the discharge times.

3. I'm not familiar with PSCAD so I can't help with any programming capabilities it might have. Sorry.

 

[jegues]

1. The supply voltage discrepancy looks suspiciously like a peak versus rms issue. Does the voltage supply definition expect the voltage parameter to be rms?

2. If your load resistance is too small the capacitors will be bled dry during discharges and their voltage won't build up over the cycles. There's an effective time constant determined by the capacitors and load resistance (and the source resistance, but I see you've set that very small indeed). Try starting with a larger load resistance (maybe a few megs) or a higher source frequency to shorten the discharge times.

3. I'm not familiar with PSCAD so I can't help with any programming capabilities it might have. Sorry.

Hello gneill,

First off thank you for your response!

The issue with the source voltage was an rms issue indeed, I have corrected this now!

Furthermore, your suspicions about the capacitors bleeding dry due to the small load at the output it also correct!

Here are the results I obtain with a larger load of 1MΩ.

Do you know how the RC time constant is calculated for a such a circuit? In other words, how did you know a load of 1MΩ would be suitable?

EDIT: My goal from this simulation was to compare the theoretical equations described in the table below to the simulation results.

However from the simulation I measure a ΔV = 140V & 2δV = 38V, but from the Kuffel equation with all the capacitors all equal to C I calculate a ΔV = 26.4V & 2δV = 7.2V which is quite the discrepency.

Why is this?

Cheers!

 

[gneill]

Hello gneill,

First off thank you for your response!

The issue with the source voltage was an rms issue indeed, I have corrected this now!

Furthermore, your suspicions about the capacitors bleeding dry due to the small load at the output it also correct!

Here are the results I obtain with a larger load of 1MΩ.

Do you know how the RC time constant is calculated for a such a circuit? In other words, how did you know a load of 1MΩ would be suitable?

Cheers!

You're welcome, I'm glad I could help.

Regarding the time constant, I haven't tried to do a detailed analysis of the circuit; it looks like it might be a pain though, what with the diodes changing things at various times for different parts of the circuit. But I made a guess (educated?) based on the last stage. A 10μF capacitor and a 1kΩ load would yield a time constant of only 0.01s. A 60Hz supply (I guessed you'd use 60Hz) has a period of 0.017s. I figured that's too close for comfort. Bump the load up to a meg and the time constant looks more like 10s so you'd hardly notice the leakage.

 

[jegues]

You're welcome, I'm glad I could help.

Regarding the time constant, I haven't tried to do a detailed analysis of the circuit; it looks like it might be a pain though, what with the diodes changing things at various times for different parts of the circuit. But I made a guess (educated?) based on the last stage. A 10μF capacitor and a 1kΩ load would yield a time constant of only 0.01s. A 60Hz supply (I guessed you'd use 60Hz) has a period of 0.017s. I figured that's too close for comfort. Bump the load up to a meg and the time constant looks more like 10s so you'd hardly notice the leakage.

Hello again gneil,

I have updated my previous post with more questions in the edit please take a read and let me know what you think.

Also, my source frequency was actually 500Hz.

Cheers!

 

[gneill]

Hello again gneil,

I have updated my previous post with more questions in the edit please take a read and let me know what you think.

I'll take a look and see if anything occurs to me.

Also, my source frequency was actually 500Hz.

Ha! Looks like I ran into a bit of luck then! Nothing succeeds like success

 

[gneill]

I've looked at what you posted in your edit above. While I can't explain the values that you've measured in your simulation, I can say that when I do my own simulation (using LTSpice) with a load resistance of 1MΩ and a source frequency of 500Hz, I'm seeing a ΔV of about 27V and a 2δV of about 7.1V (making δV about 3.5 V).