What would be the most suitable way to measure the quality factor of high-Q coils under the following conditions?
Specifications
- Frequency: 5 MHz to 15 MHz, the target application is wireless charging
- Coil type: air core, constructed using hollow copper tubes, size is around 15 cm
- Range of the measurements: Inductance \$L\approx 1 \mu H\$, Quality factor \$Q> 1000\$ (estimated from the simulations) and resistance \$R=\frac{\omega L}{Q}\approx 30~m \Omega\$ (at \$5 MHz\$)
What I have: VNA, low-frequency LCR meter (only up to 1MHz), other laboratory equipment such as Oscilloscopes, DC supply, etc. I don't have access to an Impedance analyser working at the target frequency range.
My approach: I first measure coil inductance at low frequency using the LCR meter and then add series capacitor (NP0 type - resistance of the capacitors is expected to be negligible) to tune the coil to the desired frequency. Next, coil impedance is measured using VNA (impedance parameters). Finally, use curve-fitting to estimate the coil resistance. Currently, estimated resistance is more than three times the expected values.
Identified problems in my approach are 1. Coil resistance is very small and the input impedance is not matched with the VNA at the resonance, therefore, I am not sure how accurate is the reading. 2. In this method, I cannot directly get the frequency response as the resistance is a function of the frequency - This also affects the curve fitting.
The Question: Is there any better way to measure high-Q coils accurately. I came across a book from Matlab, which I don't have access I am not sure if there is any useful information there.