# Help on very basic filter analysis

#### NiklasF

Joined Dec 29, 2008
5
I would like to know the behavior of a certain filter but I'm unable to get anywhere. I don't have any experience working with filters although I remember some theory from school.

The filter in question is a 1-phase AC filter, see attached picture. I would like to derive the transfer function and then draw the frequency response "by hand", back to basics so to speak.

The source is a high power converter (GigaWatts) and the load is approximately of the same size although varying. Can you guess the application?

Some help or guidance is much appreciated!

/Niklas

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#### NiklasF

Joined Dec 29, 2008
5
Oooh, thats embarrassing, MegaWatts!!! Sorry!

#### retched

Joined Dec 5, 2009
5,208

#### The Electrician

Joined Oct 9, 2007
2,957
Since you have shown V1 as a perfect voltage source, which implies zero internal impedance, the R1, L1, C1, C2, L2 branch is shorted by V1's zero internal impedance, and therefore has no effect on the power delivered to the load.

The R1, L1, C1, C2, L2 branch will draw current from V1, but, as I said, will have no effect on the power delivered to the load.

The transfer function will be just that provided by L3.

If some kind of signal is being generated at the load end of things, the filter could have an effect on injection of such signals back into V1. Is that what you're concerned about?

Otherwise, you will have to provide some series impedance in the V1 branch to make the situation more realistic, and then a more complicated transfer function will result.

#### Ghar

Joined Mar 8, 2010
655
To draw a frequency response by hand is pretty simple.
Resistors are horizontal lines, capacitors are lines sloping down and inductors are lines sloping up.
Series combinations become the largest of the component impedances while parallel become the smallest.

So for example, you can draw the parallel R L C from your shunt branch. At low frequency you will have sL, since it's the smallest (0 at DC). Eventually it will become R and then 1/sC. If R is very high the structure is more resonant and you may not have the flat R portion of the response, since sL and 1/sC intersect before reaching R. Otherwise the intersection points will be where R = 1/sC and R = sL.

You just build it up like that on the graph.

#### NiklasF

Joined Dec 29, 2008
5
http://forum.allaboutcircuits.com/member.php?u=14241The Electrician: Yes that makes a lot of sense. The source is a switched frequency converter with a transformer. The purpose of the filter is to attenuate harmonics from the converter perhaps also from the load to some extent.

I have tried to find some information in evaluating a parallel filter, this is probably useful:

The parallel RC circuit is generally of less interest than the series circuit. This is largely because the output voltage Vout is equal to the input voltage Vin — as a result, this circuit does not act as a filter on the input signal unless fed by a current source.
(http://en.wikipedia.org/wiki/RC_circuit)

How am I to draw the circuit so that I can evaluate this filter? I could use a current source in Spice but I would just be guessing! I would feel more confident in the solution if I could derive it by hand.

retched: Elsie seems to be quite useful. Although I would like to learn some of the basics and come to an answer myself.

Ghar: Yes thats the approach I would like to use but I find the circuit quite complex when you add all the parts together.

#### retched

Joined Dec 5, 2009
5,208
I agree, you should learn the basics. But having software to check your answers and to see WHY things are filtered the way they are, can be quite an education on its own.

The graphing and visuals involved in elsie are a nice way to SEE what is going on.

The math is where it is at, though.

#### NiklasF

Joined Dec 29, 2008
5
retched: Yes I agree with you. I will try Elsie and see what the outcome is.

I have already looked at the eBook. This is a very good source of information but I still need some help with this circuit though.

#### The Electrician

Joined Oct 9, 2007
2,957
How am I to draw the circuit so that I can evaluate this filter? I could use a current source in Spice but I would just be guessing! I would feel more confident in the solution if I could derive it by hand.
If V1 is a Megawatt converter, then you must be working for a company that can afford such a piece of equipment. They can afford to buy (or should already have on hand) a spectrum analyzer, and other equipment to determine the output impedance of the V1 source versus frequency.

Then you can add a series impedance to represent the source impedance to your spice model. And, of course, if you add that series impedance then you can evaluate the filter performance "by hand".

#### NiklasF

Joined Dec 29, 2008
5
Yes sure I could do that but this is more me being interested rather then a project at work. I just figured that I could get some sort of simple approximation without spending too much work and time (free-time that is! ).

#### The Electrician

Joined Oct 9, 2007
2,957
As I explained earlier, if you don't have an impedance in series with V1, then only L3 will have an effect of the power transfer to the load.

Maybe you can ask the manufacturer of the converter for an approximate output impedance.

If you can't get a value that way, then just insert some arbitrary impedance, and you can carry out the analysis.