zero potential line in microstrip design
This is a basic doubt which I suddenly got. While designing microstrip patch antennas, based on the transmission line method, we assume the same effective dielectric constant as for a microstrip of corresponding width. How is this justified given that one is a radiating structure and another is a guiding structure ? Please do respond with your thoughts.
-svarun
For microstrip antenna analysis, cavity model is widely and well adopted. The EM wave is assumed confined inside the cavity. For microtrip transmission line analysis, the radiated wave (free space and the fringing field) is less compared with the wave confined between the microstrip line and the ground. That is reason for both of them, the effective dielectric constants are same, which is effect by the subsrate properties.
Regards.
in transmission line analysis we consider an effective ε for the enviroment and in fact we utilize a kind of equivalence , but there are obvious difference between an Antenna problem & a stripe transmission line problem .
this defference in a simple expression can interpreted as :
in the antenna problem we expect the effective ε be more similar to the free space permitivity , but in the circuit problem we expect that the effective ε be more similar to the substrate permitivity .
in fact in former problem we like that the energy to propagate and in the latter case we like that the energy consentrate in the substrate.
Exactly what I am suggesting. Since the two physics are so different, how are we justified in using those expressions ? Any thoughts on this one ?
-svarun
Here is what I think, although I haven't checked the formula carefully. For rectangular p-atch, assuming only one cavity mode is significant and sufficient, you would find that the field distribution (of that mode) is separable (i.e. f(x)*g(y)*h(z)). f(x) would satisfy the transmission line equation in x, hence you can define an "effective epsilon". This is valid even for the higher order modes. It is not logical to infer inclusions like "xxx is radiating, xxx can't satisfy the transmission line equation".
two more cents. For ustrip structure, one side is dielectric and the other side usually air. So the effective dielectric constant has been introduced, which presents some intermediate value between εr and air that can be used to compute ustrip parameters as though the strip structure which is completely surrounded.
Then this value can be used to calculate the EM wave propagating phase velocity, wavelength, etc. No matter ustrip structure is used as transmissionline or antenna, the EM wave nature is exactly the same.
Regards,
I agree with asdfaaa mostly. However, I have one doubt. In the ananlysis of microstrip, the effective εr is calculated by assuming an infinite length of the transmission line. I understand that it is done by sloving the two dimensional laplace equation for static potential as existence of Q-TEM mode means you can define a unique potential, assuming the ground is at zero potential. Hence it takes into account only the fringing fields present along the width direction. However, the microstrip radiator being finite in both directions, will have an effective permittivity depending on the length too. Do any of you know of any reference which has modelled the radiator taking this also into effect ? Is it more accurate ? All thoughts are welcome.
for microstrip or any "waveguide", you can solve the eigenvalue problem (in 2D) "rigorously" to find the beta (propagation constant) of the eigenvalue, and define a effective epsilon accordingly. the effective epsilon would depend on the frequency, I think. You can do that not only for the quasi-tem wave, but also higher order waves. Obviously, you might not get a closed form formula.
For the cavity model of microstrip p@tch, I am not sure if the fringe effect on the two edges along the "width" direction (of a particular mode) is taken into account. I am afraid it is not in the original "cavity model". A natural idea is to define an "effective width" to account for the fringe effect. There might be some papers about it. Likewise, you could get an "effective length" for the remaining two edges (along the "length" direction of the relevant mode). To me, the fact that the patch has a finite "length" only means the "transmission line" is "loaded"/"terminated" at the two ends. But this doesn't prevent you from applying the "transmission line model". The point is that these "eigen modes" all satisfy the wave equations, and if you have a "separable solution", then the behaviour of the field along a "preferred propagation direction" can be interpreted using "transmission line model".
Thanks loucy. I understand your statements fully. I will sit over the weekend, work with pen and paper and convince myself.
-svarun
PS : I think, people should reduce their dependence on simulators and start working with pen and paper like in the pre -1990s.
well, its OK. I do think we first have to findout things with pen-paper.
by the way, I faced same thing in my special problem of Two-Segment Rectangular Dielectric Resonator Antennas TSDRAs.
we there applied weighted average method to gain effective heights and effective permittivities, and effective resonant frequencies. the fact is that this simple method is better than even best simulators. So, I do think that this is actually a FACT. so, please try to describe it with theory, and if you cant, improve your theory; try not to apply your theory to FACTS.
my oppinion by the way,
.m