# full bridge rectifier transfer function

#### suzuki

Joined Aug 10, 2011
119
Hi,

having some difficulty putting this altogether so i thought i would ask here.

i want to find the transfer function of a full wave rectifier (four diodes in bridge configuration). Mathematically speaking, i believe this is the equivalent of passing a signal through an absolute value, so i tried to model it as such in simulation.

However, since the absolute value is non-linear, i'm not sure if i can use the frequency domain, bode plots etc for the purpose of analysis. So my question is, what other ways can i model my full bridge rectifier?

tia

#### steveb

Joined Jul 3, 2008
2,436
Hi,

having some difficulty putting this altogether so i thought i would ask here.

i want to find the transfer function of a full wave rectifier (four diodes in bridge configuration). Mathematically speaking, i believe this is the equivalent of passing a signal through an absolute value, so i tried to model it as such in simulation.

However, since the absolute value is non-linear, i'm not sure if i can use the frequency domain, bode plots etc for the purpose of analysis. So my question is, what other ways can i model my full bridge rectifier?

tia
This is a tricky subject.

Are you trying to find the transfer function of input voltage to load current to determine the power factor or loading conditions that a rectifier puts on an AC source? Or, are you interested in the transfer function from input voltage to output voltage?

Either way, it is nonlinear, as you said. You are asking the right questions because you have to be very careful in trying to define a transfer function and if you want to transform to the frequency domain in a meaningful way.

A few issues come up. For one, you might be interested in a large signal transfer function, and this might depend on amplitude. Or, you might be interested in what small AC signals might do when riding on top of the main large signal.

I'm guessing you want to find the voltage transfer function for large signals. If so, the first issue is to define what you mean by "transfer function". One possible definition is to look at the Fourier components of the output voltage and compare only the fundamental frequency of the output to the input. Is this definition useful to you? If not, you have to use another definition.

#### suzuki

Joined Aug 10, 2011
119
hi,
thanks for your response. just to clarify, my overall goal of this task is to determine the transfer function (of the plant) such that i can design a control loop to regulate the plant output voltage. i want to be able to determine and achieve specific crossover frequencies, as well as phase margins.

my input is an ac signal, which passes through a resonant network and is then rectified by the diode bridge to get a dc output. i also wanted to do the rectification at this stage, since i could more easily compare a dc setpoint value with my output voltage (to get my error signal).

As for the transfer function, i *think* what i want is the effects small ac signal riding on top of the dc signal, since this is usually how we obtain the bode plot, and this should give us a relationship between vout and vin. My other reason for thinking i need the small signal and not the large signal method as you suggested, is that i dont think my output voltage would have a fundamental frequency as it is a dc signal. Or, unless you meant "output voltage" as the the voltage before entering the rectifier, but im not sure if that would be useful in my case (since i want my control loop to compare a dc setpoint as stated above).

I guess the thing that is still confusing me is that, any time we look at the dc output voltage, we must already passed through the non-linear rectifier, but i cannot treat it simply as just doing a "absolute value" of my transfer function.

hopefully this gives some clarification on my overall objective, please let me know if you need any more information, as your help is most welcome and appreciated.

#### tgotwalt1158

Joined Feb 28, 2011
110
Hi Suzuki!
I have drawn full rectifier with input and out put waveforms. Please have a look at the attached drawing. Obviously the input is sine wave and the out put is composed of +ve half cycle plus absolute value of the negative half cycle. If you could transform both the waves in mathematical form, you will get the transfer function, which is a tricky part, at least for me for the time being. I hope this will help up to some extent.

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#### steveb

Joined Jul 3, 2008
2,436
hopefully this gives some clarification on my overall objective ...
Yes, most definitely it does. This is still a tricky task, but I think you can do it with some thought. I don't have the direct answer off the top of my head, but I would use the typical linearization approach used with nonlinear circuits.

Basically, you want to think of the large signal as creating a type of fixed bias point at any point in time. Think of that point as the operating Q-point similar to when you bias a transistor circuit with DC. Even though this so-called bias point is not fixed, it can still behave as a fixed point for high frequency small signals that might get through your system and cause instability/oscillations. Once you have the bias point, you can think of the forward biased diodes as having a dynamic resistance at that operating point, and then you can make an equivalent AC linearized circuit for small signals. The AC circuit will have parameters that vary in time, depending on where you are biased on your large AC signal that is driving the rectifier.

One issue is whether you need a more advanced high frequency equivalent circuit for a diode. This depends on the diode type and on how high a frequency you are interested.

Thinking quickly, one thing I'm wondering about is whether your small AC signals will do a 180 degree phase shift on the negative half-cycles. My intuition says that it might do that, but I guess I'd have to work out the math to be sure.

Hopefully you can work this out. This week, I'm actually working in a remote location on a project for my job. This means my internet access is very limited and my time is limited too because we are working 16 hours per day. If you have any issues, hopefully others can guide you if you think this approach might be useful to you, and I'll also check in here periodically.

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#### Harry Hutchinson

Joined Jan 11, 2018
6
This is a tricky subject.

Are you trying to find the transfer function of input voltage to load current to determine the power factor or loading conditions that a rectifier puts on an AC source? Or, are you interested in the transfer function from input voltage to output voltage?

Either way, it is nonlinear, as you said. You are asking the right questions because you have to be very careful in trying to define a transfer function and if you want to transform to the frequency domain in a meaningful way.

A few issues come up. For one, you might be interested in a large signal transfer function, and this might depend on amplitude. Or, you might be interested in what small AC signals might do when riding on top of the main large signal.

I'm guessing you want to find the voltage transfer function for large signals. If so, the first issue is to define what you mean by "transfer function". One possible definition is to look at the Fourier components of the output voltage and compare only the fundamental frequency of the output to the input. Is this definition useful to you? If not, you have to use another definition.

You mentioned determining "loading conditions that a rectifier puts on an AC source", where can I find information on that subject, in particular, the loading conditions presented by a full bridge diode rectifier? All help gratefully received, Regards, Harry

#### MrAl

Joined Jun 17, 2014
10,883
You mentioned determining "loading conditions that a rectifier puts on an AC source", where can I find information on that subject, in particular, the loading conditions presented by a full bridge diode rectifier? All help gratefully received, Regards, Harry
Hi,

It would help if you could specify what exactly you are trying to calculate.

#### OBW0549

Joined Mar 2, 2015
3,566
You mentioned determining "loading conditions that a rectifier puts on an AC source", where can I find information on that subject, in particular, the loading conditions presented by a full bridge diode rectifier? All help gratefully received, Regards, Harry
Whenever you reply to a post, it's a good idea to check the date on the post and click on the person's username in the sidebar; this will bring up a popup with basic information on that person. In this case, steveb, the person to whom you are asking your question, is long gone from AAC and hasn't even logged in here in more than five years so it's very unlikely he'll see your message.

Usually, rather than resuscitating an ancient thread like this one (we call that "necro-posting"), it's best to start your own thread. The way you've done it here, we're likely to get a bunch of people coming in here attempting to help suzuki, the fellow who started the thread (who, likewise, hasn't been around AAC in over four years).

#### MrAl

Joined Jun 17, 2014
10,883
Hi,

Wow this is an old thread, and evern Steveb has not been here since 2012.

I replied mostly because this has been an interesting topic for me since the early 1980's or late 1970's.
The main thing of interest is that with any output cap the circuit transfer function is really a partial differential equation and so is not like most transfer functions that have well defined impedances or assumed impedances.
The diodes only conduct for part of the cycle, and so when they start and stop has to be solved for, which is unlike most other circuits we see around here which have externally defined start and stop times.

With no cap though, and that is as per one of the drawings in this thread, then we default to the simplest case where we have a transfer function which can be given in terms of unit steps and sine terms. That's the only case i think that gets really simple like other transfer functions. Of course that assumes resistive load only, and simple diode models like an ideal diode or similar. So we get a transfer function like:
pi*a/(a^2*s^2+pi^2)*coth(a*s/2)

where 'a' is the half cycle period.
Unfortunately, that is for resistive loads only.

#### Harry Hutchinson

Joined Jan 11, 2018
6
Hi,

Wow this is an old thread, and evern Steveb has not been here since 2012.

I replied mostly because this has been an interesting topic for me since the early 1980's or late 1970's.
The main thing of interest is that with any output cap the circuit transfer function is really a partial differential equation and so is not like most transfer functions that have well defined impedances or assumed impedances.
The diodes only conduct for part of the cycle, and so when they start and stop has to be solved for, which is unlike most other circuits we see around here which have externally defined start and stop times.

With no cap though, and that is as per one of the drawings in this thread, then we default to the simplest case where we have a transfer function which can be given in terms of unit steps and sine terms. That's the only case i think that gets really simple like other transfer functions. Of course that assumes resistive load only, and simple diode models like an ideal diode or similar. So we get a transfer function like:
pi*a/(a^2*s^2+pi^2)*coth(a*s/2)

where 'a' is the half cycle period.
Unfortunately, that is for resistive loads only.
hi MrAI