Stepped impedance Low pass filter

Hi im kinda new at the microwave filters. i jus need some help with this:

design and optimize a stepped impedance low pass filter using a microstrip transmission line with a cut-off frequency of 2.5 GHz. The filter must have more than 20dB insertion loss at 4 GHz with a reference impedance of 50 Ohms.

how do i find the values for Hi and Low impedance and the width of the line?
What formulas do i need to use ?


Thank you.

By reading some filter design books..
Or, you may use a filter design synthesizer program to make it...

i have read some but i still dont understand.. any suggestions ?

i suggest that u can see the book go to this link
**broken link removed**

---------- Post added at 03:07 PM ---------- Previous post was at 03:06 PM ----------

in that book only examples r given how to design sir filter

This is a classic engineering problem. The task involves using available materials to achieve an end result. So, one sets about this in a logical engineering fashion. A set or questions one might ask themselves, and some possible answers:

Q: what media do I want
A: Microstriip on duroid 0.25 mils thick

Q: What do I know how to design
A: I know how to get the element values for a lumped lowpass filter (i.e. the L's and C's) to meet my design goals. The filter schematic would be series L, shunt C, series L....series L.

Q: How do I use that to get a "stepped impedance" filter design
A: I know from the very old "telegrapher's equation" that a transmission line can be modelled as a ladder of series L and shunt C elements, distributed along its length. I know that the specific L and C values per length are dependent on the "characteristic impedance" of the line. And I know that if I have a short length of transmission line (short being << quarterwavelength), it sort of works like a lumped L-C network.

Q: so how do I proceed
A: By inspection, I decide that the short piece of transmission line approximating a lumped inductor would work best with a high characteristic impedance. Similarly I conclude that the short piece of transmission line approximating a capacitor would look mostly like a low characteristic impedance line. I then design the L's and C's for a lumped element lowpass filter, being careful to add a few poles beyond the bare minimum to meet my rejection spec--since a distributed circuit will not be as good as a lumped circuit. I then take my list of series L's and shunt C's, and figure out the lengths of series high Z line and lengths of series low Z line to approximate them. In this, I use practical impedances (for the forementioned duroid, maybe the highest Z I can get is 120 ohms, and the lowest Z I can get is 15 ohms, before the line width get impractical). I then cascade all those short line lengths, and reoptimize to get things better.