Aperture coupled circular patch antenna

Hi all,
I'm designing aperture coupled circular patch antenna and i have the following questions:
1- in many papers i found out that the stub length (Ls) should be less than λeff/4. WHY? i know that the stub is given by -jZoc Cot(βLs) but where does λeff/4 come from?
2- i need a paper giving the equivelant circuit for the aperture coupled circular patch. All the papers i have are dealing with rectangular patches.


Regards,
Hassan

Hi Hassan,
Basically you need a short circuit at the end of the transmission line to get the proper termination. How do you get this ? By using a open circuited transmission line of quarter wave length. You set β=2Π/λ and Ls= λ/4 in the formula you have given and you get the stub impedance referred at the center of the slot as 0.

Now why λeff ? Well . the fields on the microstrip are in part in air and in part in the substrate. In order to work with a homegeneous medium you need to use an effective permittivity being defined. You will find the formula for this in many references ( Example : Chapter on microstrip antennas in Balanis ). Since the strip is now lying in a homogeneous medium of permittivity εreff the λ/4 length will become λ0/√εreff , where λ0 is the free space wavelength.

Finally why less than λeff/4 ? The fields at the edge of a microstrip strip line do not abruptly go to zero. ( They would vialate Gauss's law if they did ). There will be some fringing fileds. Hence the actual electrical length would be greater than the physical length. To get an electrical length of λeff/4 you need a stub length of slightly less than λeff/4. Again formulas are available to calculate the fringing length. Hope this helps.

-svarun