Analysis of Filters: Calculating Characteristic Impedance Z0T

[ranju]

Homework Statement

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..

Homework Equations

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??[/B]

 

[rude man]

Homework Statement

In the given filter network , we have to find the characteristic impedance Z0T
And the author found it as Z0T= √Z12/4 + Z1Z2

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

 

[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.

Have a look at this page: http://en.wikipedia.org/wiki/Image_impedance

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

 

[ranju]

I am doubtful in the derivation only , the circuit I'hv attached according to that how Z_0T is coming out as stated by the author..??

 

[gneill]

I am doubtful in the derivation only , the circuit I'hv attached according to that how Z_0T is coming out as stated by the author..??

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.

 

[The Electrician]

I am doubtful in the derivation only , the circuit I'hv attached according to that how Z_0T is coming out as stated by the author..??

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 Z_SC, the impedance at the input port with the output port short-circuited, and Z_OC, 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.

 

[ranju]

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