To get resonance near 500 MHz using a 330pF capacitor, the inductor should be about 0.4nH (400pH).
So, I assume your inductance calculation is wrong.
Your calculation is right.
I used to design a coil like you and have the almost same results. In my case,radiation boundary is 2.5 meter from coil.
Your lumped capacitor is strange and different from mine.
Can you upload your HFSS file and I will check?
Thuan
Getting it to resonate, and making it an efficient antenna are two very different goals.
Just connecting 330pF would make for a very low overall impedance, in which the resonant Q would also be extremely low.
Not only that, the radiation of both E and H fields will be extremely inefficient because the physical dimensions are very small with respect to the wavelength.
For effective radiation or absorption, you need two things.
A reasonably high operating Q at resonance, where the resonant amplitude builds up.
And physical dimensions that can launch an effective amount of energy into free space.
The physical size of your ring are much more appropriate for the wavelength at 500 Mhz, where one complete wavelength is about 0.6 metres, or very close to the circumference of your ring.
At 13.56 Mhz, one complete wavelength is about 22 metres.
Put simply, such a small physical device is not going to either generate, or capture 22 metre long waves very efficiently.
Magnetic resonance coupling is an entirely different principle to the electromagnetic generation of radio waves.
What you are trying to do has more in common with a (tuned) electrical transformer.
The electric or E field is not relevant here.
The H or magnetic field becomes of of vital importance, because that is all there is.
To generate a strong magnetic field you need to enclose as large an area as possible with as many ampere turns as possible. And resonance is a very efficient way of multiplying the current for any given input power level.
A single turn will certainly work, but multi turns will work a lot better if at all physically possible.
Its a case of driving enough current through what you have at the transmitting side.
Is there any reason why you cannot enclose several turns into a single loop instead of just having one single turn ?
It dramatically raises the impedance and much higher circuit Q is possible.
It will raise efficiency at both transmitting and receiving ends.
Loop antennas are nothing new, they have been used for over a hundred years for radio direction finding at low to mid radio frequencies.
https://en.wikipedia.org/wiki/Loop_antenna
You will not be able to efficiently resonate the coil all by itself, except at 500 Mhz which is its own natural frequency, and requires no resonating capacitors to achieve that.
The further you try to pull it down in frequency by adding capacitors, just destroys the Q to the point that any resonance peaking effect will be difficult to measure.
So another different approach is needed.
The way a normal radio transmitter works is you have a tuned tank circuit within the transmitter, and then you couple that into the antenna. The antenna itself may or may not be resonant, but with the correct degree of coupling the antenna becomes an extension of the tuned circuit within the transmitter.
If the coupling is too loose, insufficient energy reaches the antenna.
If coupling is made too tight, the non resonant antenna damps out the resonance of the tuned circuit in the transmitter, and killing the free amplitude buildup that resonance provides..
When tuning a radio transmitter, there are two controls, "tuning" and "loading".
Both need to set optimally for maximum output into the antenna.
What I think you may need here is something similar. Your power source at 13.56 Mhz needs to resonate a pretty efficient tuned circuit, where resonant energy is allowed to build up to a significant level.
You then couple your radiating loop to that, such that you can get maximum current circulating around that loop at 13.56 Mhz.
The loop itself will not be resonant, but it draws resonant energy away from the actual correctly tuned resonant part, but not so much that it kills the resonant peak.
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