# Analysis of filters

1. May 13, 2015

### ranju

1. The problem statement, all variables and given/known data
In the given filter network , we have to find the characteristic impedance Z0T
And the author found it as Z0T= √Z12/4 + Z1Z2
But I didn't get this , how this expression came up..!!!
I found Z0 by considering Z1/2 in parallel with Z2 & the resultant is in series with Z1/2... & a different expression is coming but not this one..!! Please explain..

2. Relevant equations

3. The attempt at a solution
I found Z0 by considering Z1/2 in parallel with Z2 & the resultant is in series with Z1/2... & a different expression is coming but not this one..!! Please explain.. I have got know that it is characteristic impedance of particularly T-network , but how this came up??

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Last edited: May 13, 2015
2. May 13, 2015

### rude man

I doubt the author came up with that. It's dimensionally wrong.

3. May 13, 2015

### The Electrician

If you use LATEX your expression for ZOT will show up properly. The expression you show should be:

$\sqrt{\frac{Z1^2}{4}+Z1 Z2}$

which is correct.

under the heading "Relation to characteristic impedance". If you're still having trouble deriving ZOT, ask again here.

4. May 14, 2015

### ranju

I am doubtful in the derivation only , the circuit I'hv attached according to that how Z0T is coming out as stated by the author..??

5. May 14, 2015

### Staff: Mentor

You'll have to show the details of your attempt (show the algebra) so helpers can see what you've tried and where things might be going astray. Helpers will not provide a solution for you.

6. May 14, 2015

### The Electrician

Under the heading "Measurement" on the page I referenced: http://en.wikipedia.org/wiki/Image_impedance

you will find the expression for the image impedance $Z_{i1} = \sqrt{Z_{SC} Z_{OC}}$.

Can you calculate ZSC, the impedance at the input port with the output port short-circuited, and ZOC, the impedance at the input port with the output port open-circuited?

As explained on that page, for a symmetric finite network such as yours, the input image impedance is the characteristic impedance, so calculate the input image impedance for your network. What do you get for this calculation? Show your algebra.

7. May 14, 2015

### ranju

I have got it and the write expression..thanks a lot for your guidance..