Switch mode DC transformer equations?

[Mzzed]

I would like to know if there are any general equations (such as the AC transformer equations) that describe a switch mode DC transformer. By this i mean a constant frequency DC signal (50% duty cycle) that ranges from 0V to some max voltage on the primary coil and outputs some higher voltage on the secondary coil which has a larger number of turns. Would the regular AC transformer equations work for this situation? (ie: Vprimary/Vsecondary = Nprimary/Nsecondary)

I know I could go back and derive some equation(s) using the relevant physics but that seems like much more work than is needed.

 

[anorlunda]

I think your best approach would be Fourier analysis. The DC square wave can be represented as the sum of sinuousoids of different frequencies. You can use AC equations for each frequency and superimpose. A possible flaw is saturation of the core which is nonlinear. But if that isn't a problem you're OK.

You may only need a few frequencies to approximate the accuracy you need.

But we don't know what you are trying to accomplish, so we can't be sure if that approach will suit your needs.

 

[sophiecentaur]

I would like to know if there are any general equations (such as the AC transformer equations) that describe a switch mode DC transformer.

Looking around on Google, (limited timescale, of course) I can only see examples of switch mode power supplies / regulators that use Inductors, rather than Transformers. Would you particularly want to use a transformer for this purpose?

 

[berkeman]

I would like to know if there are any general equations (such as the AC transformer equations) that describe a switch mode DC transformer. By this i mean a constant frequency DC signal (50% duty cycle) that ranges from 0V to some max voltage on the primary coil and outputs some higher voltage on the secondary coil which has a larger number of turns. Would the regular AC transformer equations work for this situation? (ie: Vprimary/Vsecondary = Nprimary/Nsecondary)

I know I could go back and derive some equation(s) using the relevant physics but that seems like much more work than is needed.

Transformers are not good at transforming square waves. You usually tune the transformer characteristics (material, magnetizing inductance, leakage inductance, winding capacitance, etc.) for the passband of your signals.

If you are wanting to get a higher DC voltage out, look at Flyback topology DC-DC converters with transformers, or even simpler is just a Boost DC-DC converter with an inductor, if you don't need safety isolation between the input and output voltages.

How high of an output voltage do you want to generate? What is your DC input voltage? What output current do you want to support?

 

[Windadct]

Stumbled upon this from OnSemi the other day... pretty comprehensive.

 

[berkeman]

Stumbled upon this from OnSemi the other day... pretty comprehensive.

Very nice! It even shows the 2-stage PFC topology. Nice find!

 

[anorlunda]

Part of the wonderful thing of PF is that we have multiple experts and diverse experts. My background is analysis. I read the OP as just a fun analytical challenge without regard to any practical application. The others replied with an eye toward practical circuits, then PWM in DC-AC converters. Think how diverse those viewpoints are.

I really hope the OP comes back to see the answers. ping @Mzzed

 

[davenn]

Stumbled upon this from OnSemi the other day... pretty comprehensive.

Thankyou and saved

 

[Mzzed]

Thanks all for the replies and help! I decided that since a transformer only really 'cares' about the change in magnetic flux over time and not the currents/voltages in either of the coils, the regular transformer equations should be fine for my application (a voltage booster IC for scavenging power from extremely small power sources) since AC and switched DC are essentially the same thing in terms of the magnetic flux produced.

 

[berkeman]

Sounds good. Can you say a bit about what you have found about the forward rectifying voltage of silicon diodes versus the small voltages produced by your scavenging circuits?

 

[Mzzed]

Sounds good. Can you say a bit about what you have found about the forward rectifying voltage of silicon diodes versus the small voltages produced by your scavenging circuits?

I'm not fully sure I understand what you mean, but if I understood you correctly, the transformer was used by the voltage booster IC which switched the current in the secondary coil where the current in the primary coil is coming from a small solar panel. The initial change in magnetic flux is caused by the connection of the solar panel to the primary i would guess, then capacitors in conjunction with some sort of transistor in the IC would resonate and continue the switching the current. The switched current was passed through the transformer to step it up to a higher voltage and this is then regulated by the IC to produce a constant voltage output of 5V.