# Hi Circuits Geeks! Have you ever seen something like this ? (Passive AC Circuit Problem)

#### hto nanny

Joined Dec 16, 2017
4
Hi All about Circuits ! I need help to resolve this circuit. I'm looking for the tension Va. I ve tried to solve it by hand but when i try to plot the step response on matlab, it says that this is an improper system. Can any one give me the analytic equation of Va(t)? Best reguards

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#### WBahn

Joined Mar 31, 2012
25,899
Since you've tried solving it by hand already, please post you best attempt at doing so. We can't possibly tell you where you've made a mistake unless you show us your work.

#### MrAl

Joined Jun 17, 2014
7,656
Hi,

Another unclear thing is if that 170mF cap is connected to that 15H inductor.
There are no dots at all on the picture so i would assume that it is without more information.
That puts the two inductors in parallel and the two caps in parallel.
If this is not the case, you should say so.

LATER:
I took another look at this and i can see that if the nodes as mentioned above are NOT connected together, this can get pretty complicated. We probably get a 6th order denominator for example so the response is quite complicated, such as a lump with sine ripples on it.
If the nodes in question ARE connected, then the network gets much simpler.
Do you need the time response, or just the transfer equation for example.

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#### hto nanny

Joined Dec 16, 2017
4
Hi @MrAl ,
Yes the dots are connected, but what's really bugging me is that courant source in parallel with the resistance.
I've managed to turn that to a voltage source (thevenin )in serie with the same resistance.
Later, i need just the transfer function since this is for a control system design.
Thank you for your help, i really appreciate it!

Hi,
Another unclear thing is if that 170mF cap is connected to that 15H inductor.
There are no dots at all on the picture so i would assume that it is without more information.
That puts the two inductors in parallel and the two caps in parallel.
If this is not the case, you should say so.

LATER:
I took another look at this and i can see that if the nodes as mentioned above are NOT connected together, this can get pretty complicated. We probably get a 6th order denominator for example so the response is quite complicated, such as a lump with sine ripples on it.
If the nodes in question ARE connected, then the network gets much simpler.
Do you need the time response, or just the transfer equation for example.

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#### WBahn

Joined Mar 31, 2012
25,899
Hi @MrAl ,
Yes the dots are connected, but what's really bugging me is that courant source in parallel with the resistance.
What is bugging you about it?

I've managed to turn that to a voltage source (thevenin )in serie with the same resistance.
If you've managed to turn it into a thevenin equivalent, then what is bugging you about it?

Later, i need just the transfer function since this is for a control system design.
Thank you for your help, i really appreciate it!
A transfer function implies and input and an output. Your output is presumably Va. What is your input?

#### hto nanny

Joined Dec 16, 2017
4
Hi @WBahn
This is my best attemp

Since you've tried solving it by hand already, please post you best attempt at doing so. We can't possibly tell you where you've made a mistake unless you show us your work.

#### WBahn

Joined Mar 31, 2012
25,899
Hi @WBahn
This is my best attemp
Thank you.

I'm still unclear what the input is for the transfer function you are trying to end up with.

Look at your first equation.If (Vs-Va) is the voltage across the inductors, then that means that the reference node (i.e., "ground") must be the bottom node in the schematic. But if (Vth-Va) is the voltage across the 758 ohm resistor, then that means that the top right node must be the reference node. So your equation is not self-consistent.

Also, if you would track your units properly, you would see that every term in your first equation has units of current except the last one, which has units of voltage. How can you add currents and voltages? Answer: You can't. So that would have been a big red flag telling you that your very first equation was wrong and any further work based on it is a pure waste of time.

Try simplifying the circuit before setting up your equations.

You might also consider what possible impact a shorted current source can have on the rest of the circuit.

#### WBahn

Joined Mar 31, 2012
25,899
You might also consider what possible impact a shorted current source can have on the rest of the circuit.
And note that, if you don't consider this, it will still all work out. If you take the time to set up your node equation carefully, this will become apparent.

#### MrAl

Joined Jun 17, 2014
7,656
Hi @MrAl ,
Yes the dots are connected, but what's really bugging me is that courant source in parallel with the resistance.
I've managed to turn that to a voltage source (thevenin )in serie with the same resistance.
Later, i need just the transfer function since this is for a control system design.
Thank you for your help, i really appreciate it!
Hello again,

Ok so there is a dot connecting both inductors and both capacitors. I did not want to assume that because it makes a sort of trick network.

I drew the dots in to show the network in a little more clear fashion. Note the current source is clearly shown as being shorted out.

You effectively end up with one inductor and one capacitor and one resistor and the response is across one cap, (with resistor) so your transfer function will be second order. You should make sure you get that kind of transfer function.

The network drawn clearly with node dots is shown in the attachment.

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#### MrAl

Joined Jun 17, 2014
7,656
Hello again,

Originally i was thinking that there was no dot in the center there so i went about solving it like that and realized this is a good exercise in dealing with higher order transfer functions so i went ahead and solved it and checked it with a simulator. Note however this is NOT what the OP was asking about, so this is a side note for those that want to try to solve the more complicated network where there is no dot in the center. The new schematic is shown in the attachment (with jumper in the center) along with the solutions in the frequency and time domains for Va shown as F(s) and f(t).
It turned out to be interesting with an interesting time response.
The time domain solution may be simplified a little more.

EDIT: Fixed syntax and simulation scaling.

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