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Conduction angle equation?

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Posted on August 29, 2019 at 12:33:28
Lee of Omaha
Dealer

Posts: 1800
Location: Omaha NE
Joined: September 8, 2006
 Does anyone know of equations to predict conduction angle of a power transformer given configuration (such as C-L-C) with all needed values known and a load resistance? I can find equations for predicting ripple, but nowhere can I find equations to predict conduction angle.

I'm familiar with the equation for critical inductance for a choke input filter, and I know that PSUD2 exists (only runs in Windows, which I don't use). I don't think PSUD2 models conduction angle, anyway (if I'm wrong please let me know and I'll get a Windows computer).

If anyone can help, that would be appreciated.

If no one has any leads, we're going to install three identical capacitors, then hook up 1, 2, and then 3 of them, measure behavior using a 'scope, and note transformer temperature rise, and attempt to write an equation empirically.

Thanks!

 

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RE: Conduction angle equation?, posted on September 7, 2019 at 15:38:01
Lee of Omaha
Dealer

Posts: 1800
Location: Omaha NE
Joined: September 8, 2006
 We only have three data points, so I haven't figure out an equation. Still, I think this should be of use to those trying to design or modify power supplies with lots of stiffness that are still easy on the power transformer.

Configuration: C1-L1-C2-L2-C3-RL. We varied C1. The fixed values are:

L1-10 H
C2-110uF
L2-2.5 H
C3-220uF
Rl-about 2000 Ohms

We first used a "0" uF input capacitor (choke input). The conduction angle was 100%, but the output from the power supply never reached full B+.

With a 10uF input capacitor (motor run due to the very high AC component) the conduction angle was about 33%. B+ was normal.

With a 20uF input capacitor (2 x 10uF motor run) the conduction angle was about 25%. B+ was normal.

So our rule of thumb for the present is to use a small motor run as input followed by a nice choke and then a final C-L-C filter. Stiff as hell output, but still easy on the power transformer.

 

7 mV!, posted on September 14, 2019 at 14:03:54
Lee of Omaha
Dealer

Posts: 1800
Location: Omaha NE
Joined: September 8, 2006
 We tested power output and measured hum on our highly modified Dynaco ST-70. About 14 watts per channel (triode) and a not-so-whopping 7 mV RMS! We used a variation on C-L-R-C-D-C. If I did the math right, that's about -96dB. Just filtering, no regulation.

 

RE: Conduction angle equation?, posted on October 22, 2019 at 12:32:02
John Elison
Audiophile

Posts: 23900
Location: Central Kentucky
Joined: December 20, 2000
Contributor
  Since: January 29, 2004
 Is there a schematic I can look at. Perhaps you can point me to a URL with a schematic of what you're talking about. It seems to me that you should be able to use Ohm's Law with complex numbers to determine phase angle. Anyway, I'm very ignorant of what you're trying to do, so if you could point me to a URL online that shows me how C1-L1-C2-L2-C3-RL are connected, I might be able to figure out how to calculate phase angle.

Thanks,
John Elison

 

RE: Conduction angle equation?, posted on October 26, 2019 at 13:38:49
Lee of Omaha
Dealer

Posts: 1800
Location: Omaha NE
Joined: September 8, 2006



John,

We're trying to develop an equation that let's us predict conduction angle (actually RMS current in the secondary) to minimize power transformer heating due to I^2*R losses aka copper losses.

See attached photo for approximate schematic. We got the conduction angle to about 25% or 90 degrees. And while conduction angle should correlate well with RMS current, I'd love to have an explicit equation.

I think the analytic answer requires solution of integrodifferential equations, which are beyond me.

If you can help, you will benefit our entire community.

Thanks for any help you can provide.

 

RE: Conduction angle equation?, posted on October 29, 2019 at 23:19:32
John Elison
Audiophile

Posts: 23900
Location: Central Kentucky
Joined: December 20, 2000
Contributor
  Since: January 29, 2004
 Sorry, I can't help you. To me that looks like a DC power supply so I guess I don't understand why you're concerned about phase angle, assuming that's what you mean by conduction angle. At any rate, it's beyond my abilities.

Sorry!
John Elison

 

RE: Conduction angle equation?, posted on October 30, 2019 at 14:19:46
Lee of Omaha
Dealer

Posts: 1800
Location: Omaha NE
Joined: September 8, 2006
 John,

Thanks for trying. Conduction angle is the term for the percent of time the power transformer conducts. The greater the angle the lower the I^2R heating in the windings. I think the math is quite complex, so we may do more work in trying to approximate an equation empirically.

 

PSUD2, posted on December 25, 2019 at 19:23:39
Tre'
Industry Professional

Posts: 17298
Location: So. Cal.
Joined: February 9, 2002



gives a graph showing one diode only. If you look at the time and do the math you can calculate conduction angle.

Tre'
Have Fun and Enjoy the Music
"Still Working the Problem"

 

RE: PSUD2, posted on December 25, 2019 at 19:29:14
Tre'
Industry Professional

Posts: 17298
Location: So. Cal.
Joined: February 9, 2002



Critical inductance choke input. Again, one diode only. Fill in the other diode and you see constant conduction.

Tre'
Have Fun and Enjoy the Music
"Still Working the Problem"

 

RE: Conduction angle equation?, posted on December 26, 2019 at 05:16:22
stellavox
Audiophile

Posts: 413
Joined: June 23, 2004
 Hey Lee,

A wild shot.

If you're experiencing some kind of problem with heating in a transformer at your location, could the actual cause be DC offset on your incoming power line? Remember reading about this and suggested methods to eliminate it on the web.

Charles

 

RE: Conduction angle equation?, posted on January 4, 2020 at 09:26:12
Lee of Omaha
Dealer

Posts: 1800
Location: Omaha NE
Joined: September 8, 2006
 I've never heard of DC on an AC power line. But in this case that wasn't the issue, as adding a critical input capacitor solved the problem.

 

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