Finding the resonant frequency of a resonant circuit such as an antenna trap is usually done by coupling a source and power sensor very loosely to the circuit.
A modern solution is an antenna analyser or one port VNA, it provides both the source and the response measurement from one coax connector.
Above is a diagram from the Rigexpert AA35Zoom manual showing at the left a link (to be connected the analyser) and the trap (here made with coaxial cable.
The advantage of this method is that no wire attachments are needed on the device under test, and that coupling of the test instrument is usually easily optimised.
Why / how does it work?
So, what is happening here? Lets create an equivalent circuit of a similar 1t coil and a solenoid with resonating capacitor.
The two coupled coils can be represented by an equivalent circuit that is derived from the two inductances and their mutual inductance. The circuit above represents a 1µH coil and a 10µH coil that are coupled such that 3% of the flux of 5% of the flux of one coil cuts the other (they are quite loosely coupled, as in the pic above.
The resonant frequency of the 10µH coil and 100pF capacitor can be calculated to be 5.033MHz… and this is the value we want to find from our measurement.
Above is a plot of the magnitude of S11. You can see that the cursor set to the theoretical (ie known) resonant frequency coincides almost exactly with the minimum |S11|, and therefore almost exactly with the theoretical (ie known) resonant frequency.
Lets increase the coupling.
Above, the equivalent circuit with the same coils but 9% flux coupling (the coils have been moved closer together).
Above, we have a deeper response, but note the minimum |S11| is now further away from the cursor which is at the theoretical (ie known) resonant frequency.
Too much coupling causes interaction with the test object.
How can you determine how much is too much coupling?
One approach is to simply couple up tightly and find the response, and loosen the coupling until the frequency for minimum response stops moving.
So where do you measure |S11|?
Your instrument may display S11 labelled as the complex reflection coefficient, or it may display the magnitude of the complex reflection coefficient, or it may display Return Loss (which is -|S11|).
VSWR is related to |S11|, minimising VSWR is akin to minimising |S11| (or maximising Return Loss).
Use whatever feature your analyser offers.
Some analysers will not show a useful response for very loose coupling, eg they may not indicate VSWR greater than say 10. You really need to explore the instrument and manual to find if there is a way to display extreme VSWR, even if only at one frequency.
There is good reason why some analysers might not show extreme VSWR. If the inherent resolution of the instrument is poor (eg analysers with 8 bit ADCs), then it may not have sufficient accuracy to usefully display extreme VSWR.
Sometimes it is just that the designer didn’t really understand the instrument applications in the real world.
Of course this technique will not work on a trap that is substantially enclosed in a shield that prevents magnetic coupling.
Here is a measurement made of a parallel resonant circuit at 1.8MHz using a 60mm diameter 1t coil of 2mm copper wire connected directly to an AA-600.
Above is a ReturnLoss scan. It is not possible to expand the scale any more… did I mention that designers often do not understand real world applications. Nevertheless we can see that the middle of the peak in the response is at 1.813MHz where ReturnLoss is 0.34dB (equates to 51.6).