Help with Microstrip-Length Formula

[SaabFAN]

Hello

I have been struggling since friday evening to understand the Formula given in a lecture-manuscript to calculate the length of a piece of Microstrip that is part of a filter.
One of the Formula in question is this one:

I have managed to find the real world counterparts of all the Variables, except
From digging through wikipedia-articles and other sources, the small Omega-Letter with a small c could be the cutoff-frequency, or the circular frequency, but using those values does not yield 11,04mm of length.
Could you guys tell me what this variable is and does in the circuit, or where my error lies? I'm rather new to this particular field of electronics and do this only as a hobby.

btw. This is the presentation where the slide is from:http://ntuemc.tw/upload/file/20110321102525847f2.pdf

[KJDS]

A little light background reading of the mathematics of microstrip lines

https://fenix.tecnico.ulisboa.pt/downloadFile/3779573460329/design%20of%20coupled%20microstrip%20lines.pdf

Alternatively,

http://www.awrcorp.com/products/optional-products/tx-line-transmission-line-calculator

uses the same equations.

[nctnico]

I think the images above come from a book called 'Microstrip filters for RF/Microwave applications'. The design of these filters and the formulas used are explained in greater detail then these slides. I highly recommend to buy this book if you want to get into microstrip filter design.
The wc is the radians per second at the filter's center frequency.

[SaabFAN]

Thx for clearing that up, nctnico.

Btw. I just looked for that book: 140€ on Amazon! Why are books covering this topic so damn expensive?

[T3sl4co1l]

I'm not entirely sure where the slide is going, but it looks like it's calculating microstrip in terms of lumped equivalents (using the transform theorem).  Then, w_c should be the characteristic frequency of that segment, which is general will be a small ratio away from the cutoff frequency.  How much depends on the type chosen (Butterworth/Chebyshev/..) and position in the filter.

But I might be wrong about that.  Assuming you have an instructor, ask them to be sure.

Thx for clearing that up, nctnico.

Btw. I just looked for that book: 140€ on Amazon! Why are books covering this topic so damn expensive?

Because almost no one has to design them?..

Tim