# ideal rectifier in series with ideal inductor

Joined Feb 17, 2016
5
Hi all,

Lets consider we have ideal bridge diodes rectifier that converts the positive-negative sinewave to ideal positive-positive signal (like the dashed positive-positive wave on the right of the schematic).

V1 220 V AC L1 = 50miliHenry
R1 = 50 Ohm

Can anyone tell what will be the current and power factor (most important) from the source .
many thanks to all.
BR.

Joined Feb 17, 2016
5
i need to know more specific the power factor of the circuit.

#### AnalogKid

Joined Aug 1, 2013
9,941
The drawing is incorrect because the rectified voltage waveform is not a sine-squared wave, which is what is shown. That notwithstanding, you can sketch in the current wave based on the capacitor's voltage wave in red, then take the cosine of the angle between the positive zero-crossings of the voltage and current waves. Note that to really old farts the power factor of this circuit is not defined, because the original definition of power factor involved two continuous waveforms such as sinewaves. The grossly discontinuous current waveform makes this ambiguous - do you look at the phase angle between the voltage and current positive peaks, zero crossings, or what? The "modern" definition came about because of the current waveform harmonic distortion caused by the discontinuous diode action. The "power factor" at the zero crossings captures effects of this more accurately than that of the positive peaks.

ak

#### dannyf

Joined Sep 13, 2015
2,197
Can anyone tell what will be the current and power factor (most important) from the source .
You can do so with simulation but not through formula: most textbooks are wrong about the current waveform through the diode in a rectifier set-up -> it is not half sine. Instead, it is much more like a sharp pulse.

Unless you specifically want it that way, the inductor is in the wrong place.

Joined Feb 17, 2016
5
yes i want it in series with rectifier.
what do you think the power factor be?
just from rough calculation.

Joined Feb 17, 2016
5
lets consider the ideal diodes case and consider rectified sine-wave after rectification of course even with spiked signal the circuit will have some power-factor

#### KL7AJ

Joined Nov 4, 2008
2,229
yes i want it in series with rectifier.
what do you think the power factor be?
just from rough calculation.
The reactance of the inductor is 19 ohms. You can pretty well consider that as being just in series with the load resistor, and work from there.

#### wayneh

Joined Sep 9, 2010
17,166
If you can tell me what the sine wave on the rectifier looks like, I can tell you what the output looks like. I worked out the analytical solution for a full wave bridge plus capacitor.

I realize the input depends on the output, and I can't imagine how to calculate this without using a numerical, iterative approach.

Dang, KL7AJ beat me with a good start.

#### crutschow

Joined Mar 14, 2008
29,485
Here's a simulation of the circuit with a 500 ohm load (you also stated 50 ohms so I'm not sure which is correct).
As you can see, the inductor current is a series of quasi half-sine pulses, so I'm not sure how you would calculate the power factor.  #### Attachments

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#### dannyf

Joined Sep 13, 2015
2,197
I worked out the analytical solution for a full wave bridge plus capacitor.
Try us.

#### wayneh

Joined Sep 9, 2010
17,166
Try what? But I used the wrong word, it's not an analytical solution. I don't believe there is one. It's a quickly-converging spreadsheet iteration. What I meant to convey is that it doesn't make the usual simplifying assumptions and is a rigorous solution.

#### WBahn

Joined Mar 31, 2012
26,398
The drawing is incorrect because the rectified voltage waveform is not a sine-squared wave, which is what is shown. That notwithstanding, you can sketch in the current wave based on the capacitor's voltage wave in red, then take the cosine of the angle between the positive zero-crossings of the voltage and current waves. Note that to really old farts the power factor of this circuit is not defined, because the original definition of power factor involved two continuous waveforms such as sinewaves. The grossly discontinuous current waveform makes this ambiguous - do you look at the phase angle between the voltage and current positive peaks, zero crossings, or what? The "modern" definition came about because of the current waveform harmonic distortion caused by the discontinuous diode action. The "power factor" at the zero crossings captures effects of this more accurately than that of the positive peaks.

ak
Aside: @AnalogKid: What would happen if power factor was simply defined as the ratio of real power to reactive power? Seems like that is what would fall of the definitions of complex power.

#### crutschow

Joined Mar 14, 2008
29,485
Try what? But I used the wrong word, it's not an analytical solution. I don't believe there is one. It's a quickly-converging spreadsheet iteration. What I meant to convey is that it doesn't make the usual simplifying assumptions and is a rigorous solution.
Sort of a poor man's spice? #### WBahn

Joined Mar 31, 2012
26,398
Sort of a poor man's spice? Perhaps we should call it ExSpice. #### wayneh

Joined Sep 9, 2010
17,166
I guess. I'm not sure how spice would do it but I guess it just iterates over a lot of time points. My calculation requires iteration only to calculate the points where conduction ends and the output curve switches from a sine wave to an RC decay curve, and then where conduction begins again. Spice might even consider things like diode switching time, so is maybe more accurate.

And since LTspice is free and Excel is not...

#### AnalogKid

Joined Aug 1, 2013
9,941
As you can see, the inductor current is a series of half-sine pulses, so I'm not sure how you would calculate the power factor.
Thanks to the inductor, the current pulses are somewhere between sine-squared and the normal fast-attack/rounded decay kind in cap-input supplies.

PF is the cosine of the phase angle between the voltage and current zero crossings. The series inductor is an improvement over the standard cap-input.

ak

#### crutschow

Joined Mar 14, 2008
29,485
I guess. I'm not sure how spice would do it but I guess it just iterates over a lot of time points. ...............
Exactly.
It iterates over thousands of points and adjusts the iteration time interval in response to how rapidly things are changing in the circuit. Thus a rapidly changing circuit (such as those with high frequency signals), takes longer to simulate for a given time interval then one with lower frequency signals.
It also uses all the parameters in the part models it has in calculating all the node voltages and currents with respect to time.
These models are quite complex for most semiconductor devices which makes the simulation of those devices fairly accurate.

#### crutschow

Joined Mar 14, 2008
29,485
Okay.
Using this calculation for the power factor on my LTspice simulation in post #9 I came up with an apparent input power of 213W and a real real power of 159W, giving a power factor of .746.

LTspice allows calculation of the RMS power and the apparent power directly from the graphs with the build-in waveform arithmetic, which is a very handy feature.

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#### WBahn

Joined Mar 31, 2012
26,398
PF is the cosine of the phase angle between the voltage and current zero crossings. The series inductor is an improvement over the standard cap-input.
I'm not convinced that this gives the correct PF for nonlinear loads. At the very least, in the general case the very notion of "zero crossings" is very ambiguous - there might be a multitude of zero crossings over the course of one cycle and they may not be uniformly spaced).

I think the definition of power factor is, fundamentally, the ratio of real power to apparent power.

#### crutschow

Joined Mar 14, 2008
29,485
.................
I think the definition of power factor is, fundamentally, the ratio of real power to apparent power.
That's the definition I used in my calculation.