# How to solve Cuk converter look alike circuit?

#### kunx2

Joined Jan 6, 2020
11
I got no idea to solve this circuit.
plz help.

#### drc_567

Joined Dec 29, 2008
784
Laplace transforms ...

#### WBahn

Joined Mar 31, 2012
25,318
Laplace transforms ...
Not going to be that simple -- Laplace transforms are for linear circuits and that diode makes it nonlinear. Also, modeling the switch with a transform isn't going to be easy.

#### WBahn

Joined Mar 31, 2012
25,318
I got no idea to solve this circuit.
plz help.
View attachment 196200
This is a sufficiently advanced problem that you should have at least some ideas on how to start doing something one it.

Can you explain qualitatively what the circuit does and how it does it?

What kind of model are you using for the diode?

What if the problem was simplified and just asked you to find Vo(t) after the switch is closed (and remains closed)?

#### drc_567

Joined Dec 29, 2008
784
The provision in the problem data for a duty cycle seems to imply that the input signal is a pulsed waveform. Given that the diode is shown as reverse biased, seems to make it non-conductive, given the on/off pulse input signal.
... One question is whether the input switch can be modeled as a form of the Heaviside Function, as defined here:
see 1-Uc(t) definition

#### kunx2

Joined Jan 6, 2020
11
This is a sufficiently advanced problem that you should have at least some ideas on how to start doing something one it.

Can you explain qualitatively what the circuit does and how it does it?

What kind of model are you using for the diode?

What if the problem was simplified and just asked you to find Vo(t) after the switch is closed (and remains closed)?
The circuit is kind of DC converter.
As the switch turn on and off the current in inductor would likely to be continuous and cause the voltage to raise or drop.
THE diode is ideal one(forward bias voltage drop is zero).

#### MrChips

Joined Oct 2, 2009
20,372
I would attempt to solve it first with the diode omitted.

#### MrAl

Joined Jun 17, 2014
7,196
Not going to be that simple -- Laplace transforms are for linear circuits and that diode makes it nonlinear. Also, modeling the switch with a transform isn't going to be easy.
Hi,

Actually it does look like Laplace Transforms can be used here which is true of most converters anyway and this looks like a converter circuit or at least should act like one.
The trick is that the switch itself is not 'modeled'. Instead, the circuit is divided up into switch 'modes' where each mode comes from a different state of the switch. That would provide the time equations. Since they give values for all of the components, it should not be too hard to find the Inverse Laplace Transform.

However, since they are asking for the input/output relationship i would think that it would be easier to write a set of ODE's and then use averaging techniques. That should be a lot less work too.

This is an interesting circuit in any case, looks almost like a Cuk and wondering if it could be a type of Cuk or maybe there is another name for it. I dont know yet if the output can be anything given a variable switch duty cycle like a real converter but im going to look into it.

I have to agree though that this circuit should not have been one that was just thrown at the student from out of nowhere but the student should have been prepared for this kind of thing. It looks like one of the modes could be third order.

#### MrAl

Joined Jun 17, 2014
7,196
I got no idea to solve this circuit.
plz help.
View attachment 196200
Hi,

First, "I NEED HELP" is a really bad choice of thread title. It is obvious that anyone who posts here needs help and you are supposed to use a more descriptive title.

But as to the solution, what techniques have you learned in the past, such as averaging techniques or something? What kind of converters have you analyzed in the past?

#### kunx2

Joined Jan 6, 2020
11
Hi,

First, "I NEED HELP" is a really bad choice of thread title. It is obvious that anyone who posts here needs help and you are supposed to use a more descriptive title.

But as to the solution, what techniques have you learned in the past, such as averaging techniques or something? What kind of converters have you analyzed in the past?
I have learned how to solve boost,buck and cuk converter.
We draw the figure of current and voltage with straight line.(using L*ΔI/Δt = V)
I don't know if it is averaging techniques.

sorry for the title.But, it seems that I cant change the title as I post the thread.

#### MrChips

Joined Oct 2, 2009
20,372
It may resemble a Cuk converter but the diode is turned around to trick you.

#### MrAl

Joined Jun 17, 2014
7,196
I have learned how to solve boost,buck and cuk converter.
We draw the figure of current and voltage with straight line.(using L*ΔI/Δt = V)
I don't know if it is averaging techniques.

sorry for the title.But, it seems that I cant change the title as I post the thread.
Hello,

Well then maybe you could show some work with what you did with the Cuk or maybe the boost and buck too. That way we know what method is acceptable for you.
At least show the work for the boost but since the Cuk is somewhat similar that would be good to show your work for also.

#### kunx2

Joined Jan 6, 2020
11
Hello,

Well then maybe you could show some work with what you did with the Cuk or maybe the boost and buck too. That way we know what method is acceptable for you.
At least show the work for the boost but since the Cuk is somewhat similar that would be good to show your work for also.

here is what I did to solve a boost converter

And this one is the job done to the buck converter

Looks like it add inductor and capacitor to the buck circuit.

#### MrAl

Joined Jun 17, 2014
7,196
here is what I did to solve a boost converter
View attachment 196249
And this one is the job done to the buck converter
View attachment 196251

Looks like it add inductor and capacitor to the buck circuit.
Hi,

Ok great, and yes that is averaging, however, we still need to see your work on the Cuk. Those two circuits can both be solved by assuming the switched state of the diode, while the Cuk may require that you solve for that too. So i'd like to see how you worked out when the diode is on and when it is off so you can write the averaging expressions. Perhaps you were able to come up with some reasoning that allows you to assume the diode state.
So seeing the work you did on the Cuk would help a lot here.

#### kunx2

Joined Jan 6, 2020
11
Hi,

Ok great, and yes that is averaging, however, we still need to see your work on the Cuk. Those two circuits can both be solved by assuming the switched state of the diode, while the Cuk may require that you solve for that too. So i'd like to see how you worked out when the diode is on and when it is off so you can write the averaging expressions. Perhaps you were able to come up with some reasoning that allows you to assume the diode state.
So seeing the work you did on the Cuk would help a lot here.
I found that cuk is kinda different from boost and buck,as I solve it with capacitor current rather than inductor one.

I am wondering if I can apply the same thing to my problem.

#### MrAl

Joined Jun 17, 2014
7,196
I found that cuk is kinda different from boost and buck,as I solve it with capacitor current rather than inductor one.
View attachment 196300
I am wondering if I can apply the same thing to my problem.
Hello again,

Ok that's interesting. With the Cuk your work shows that the diode switching states are synchronized with the actual switch switching states. That means that you can choose whether the diode is on or off based on the switch switching state and that means we have two distinct modes of operation:
1. Switch on, Diode off.
2. Switch off, Diode on.
This makes it easy to solve using several methods.

How
However, in this new circuit, the subject of this thread, the diode switch state is only partially sync'd to the switch state. We actually end up with three different modes of operation:
1. Switch on, Diode off.
2. Switch off, Diode on.
3. Switch off, Diode off.

So it looks like when the switch is off you will have to find a way to determine when exactly the diode is on and when it turns off . It seems clear that the diode turns on when the switch first turns off, but it is then not as clear when the diode turns off.
So the main question is, can you determine when the diode turns off when the switch is off?
(That would be some time during mode 3).

#### kunx2

Joined Jan 6, 2020
11
Hello again,

Ok that's interesting. With the Cuk your work shows that the diode switching states are synchronized with the actual switch switching states. That means that you can choose whether the diode is on or off based on the switch switching state and that means we have two distinct modes of operation:
1. Switch on, Diode off.
2. Switch off, Diode on.
This makes it easy to solve using several methods.

How
However, in this new circuit, the subject of this thread, the diode switch state is only partially sync'd to the switch state. We actually end up with three different modes of operation:
1. Switch on, Diode off.
2. Switch off, Diode on.
3. Switch off, Diode off.

So it looks like when the switch is off you will have to find a way to determine when exactly the diode is on and when it turns off . It seems clear that the diode turns on when the switch first turns off, but it is then not as clear when the diode turns off.
So the main question is, can you determine when the diode turns off when the switch is off?
(That would be some time during mode 3).
Ya. My classmate found the diode act like what u said using mathlab simulation.
I am trying to determine when the diode turns off now.

Last edited:

#### kunx2

Joined Jan 6, 2020
11
I got stuck here as I don't know how to determine when the diode turns off.

#### MrAl

Joined Jun 17, 2014
7,196
I got stuck here as I don't know how to determine when the diode turns off.
View attachment 196326
Hi,

I cant read that it is too blurry.

Does it help if you assume that the diode turns off when iL1 first becomes equal to iL2?