How can I Calculate input impedance of radial stub

i everybody

How do I Calculate input impedance of radial stub that has angle, radial or length, wide of input part?

That is very important for me.

Please give me a simple formula.
RADIAL STUB.gif
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the input impedances is given in the two references below. The formula can hardly be described as simple since it involves infinite series having terms with Bessel functions, but that is only to be expected when dealing with a radial line geometry.

References:

[1]. F. Giannini, R. Sorrentino and J. Vrba, "Planar Circuit Analysis of Microstrip Radial Stub," IEEE Trans. vol. MTT-32, pp. 1652-1655, Dec. 1984. See equs. (3) - (6).

[2]. F. Giannini, M. Ruggieri and J. Vrba, "Shunt-Connected Microstrip Radial Stubs," IEEE Trans. vol. MTT-34, pp. 363-366, March 1986. See equs. (1) - (5).

two refrences have tedious formulas, and I want to write a paper and must put in it a simple and clear formula for calculating input impedance of the radial stub.

I do not need very accurate formula.

Please help me.
BEST REGARD

ALI REZA

Better than any formula is to use an EM simulator.

you are right.
but I want to write a journal paper and I cannot do not put any formula .
I need very it.