I remember a simple rule in electromagnetic theory that when we scale the frequency by a value alpha and scale the dimension of your antenna or scatterer by a/alpha, the properties of that device does not change.
I want to know how practical is this rule and if all of the electromagnetic properties like radar cross section, radiation pattern, impedance, normalized bandwidth, S-parameters will be unchanged by this rule?
theoretically you are right.
Practicality is more difficult because often material properties do not scale so well. So with dielectrics the permittivity changes with frequency and so do its losses - this has an impact on s-parameters, bandwidth and also on gain/efficiency of the antenna.
Also dielectric substrates for printed antennas have fixed thicknesses - you cannot easily scale the substrate thickness by factor 10 because typically you would not have a substrate so thick or thin. This often means that for high frequencies you then have relatively thicker substrate which results in problems with surface waves.
Similarly, with metals - if you scale too much towards high frequency you might have problems with things like skin effect.
Next thing is that you typically do not scale ports because you have for instance a standard SMA connector. For a smaller antenna the connector itself then plays more important role and "disturbs" the performance.
So to keep it short if you want to scale just a little bit - e.g. factor less than 2, it will pretty much follow the theory.
If you scale more the scaling works but you have much more effects that have an additional impact so simple scaling gives you a good start to your antenna design but it needs some fine tuning.
I inferred from your answer that for microwave waveguide slot antenna such as edge slot slot array, we can use this scaling rule because there is not substrate and skin effect problem and all physical dimension can be well scaled. however port scaling may still be a problem. is any other problem than port or probe scaling ?
I wonder If there exist an standard procedure and chain of devices like port/probes that let us build and measure in S-Band in place of X-Band ? i am not practically experienced in this field however It might be a standard SMA port replacements for addressing scaling from S-Band and X-Band to each other.
Actually the cost of building an S-Band edge-slot array antenna is much cheaper than in X-band with the same radiation pattern.
if you are considering moving from X- to S-band there will be some problems with losses as the waveguide loss does depend on frequency due to the skineffect - at higher frequency the current flows through smalle cross-section.
If you want to build a waveguide slot array I guess the port will not really matter. In both cases people would tend to stick with SMAs because they are very cheap.
This is not exactly my field but in principle to build something in S-band as a proof of concept is possible. I do not see any direct problems and it should work well in terms of radiation pattern ... but not in terms of efficiency. However, you will still need to build the x-band thing eventually but you are right that building first prototypes in S-band would save you costs whilst providing enough information for a proof of concept.
thank you very much. I wonder if the skin effect on a waveguide antenna is such important that may change the results ! can we observe this skin effect in numerical solvers EDA tools like HFSS or CST ?
we are building the waveguide slot array for proof of the results we have gained in simulation in our article. would you recommend to do follow this dimension scaling for our article ?
most of the CNC technicians in our zone stating that using very thin drill size for the corner of the slots is the cause of the high cost. can we use any alternative method to neglect the cost of small drill size for the corner of the slots?
I am not expert on manufacturing these antennas but I could try to play in CST with shapes of the corners of the slots. I could imagine that if the corner is not "so sharp" it might not change the performance too much because it is kind of the centre of the slot that is "the main" radiator. But this is just a guess. I never designed slot waveguide antenna and all my knowledge about it is theoretical.
Skin effect, I think, mainly impacts the loss of the waveguide. The losses in waveguides or in transmission lines from the same material scale with square root of frequency (this is what I remember from my undergraduate).
So I think that it has some impact on the overall efficiency. So depending where in the S and X band you plan to operate it may change it a lot or a little.
It is irrelavant for your proof of concept but something to keep in mind if your design requires high efficiency.
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