# How to measure the power emitted from an HF antenna in near-field WPT?

I'd like to estimate the power density from a 13.56 MHz power source in a near-field WPT (wireless power transfer) scenario. Using a spectrum analyzer with a receiving antenna will give the E-field measurements, while for near-field WPT the magnetic coupled resonance is the used method (non-radiation). So, I suppose I cannot use spectrum analyzers to measure what I want. I'm wondering if there is any measurement method to measure the power (in dBm) emitted from a source to be harvested by a loop antenna in near-field concept. Any advice would be highly appreciated.

• Although I really like Glenn's answer, this is not about amateur radio usage at all, and not about general radio theory that can be applied to amateur radio; it's about non-radio EM fields, to be specific. Hence, electronics.stackexchange.com would be the right place to ask. – Marcus Müller Dec 5 at 15:05
• @MarcusMüller According to the guidelines in the Tour and Help - what's on topic and acceptable here, questions unrelated related to amateur radio are not specifically disallowed. The wording in the Tour is "Don't ask anything about anything not directly related to amateur radio OR the science and technology of radio". HELP further expands on that. ... – Mike Waters Dec 5 at 22:19
• @MarcusMüller Please feel free to add your opinions in this new Meta question. – Mike Waters Dec 5 at 22:22

WPT (wireless power transfer) is typically performed using flat, multi-turn coils (inductors) as antennas. In some cases, the coils are self resonant based on their parasitic capacitance and self inductance in order to avoid the losses in a typical matching network. Due to the close proximity of the two coils, the mutual inductance must also be considered.

The amount of power that can be transferred is heavily influenced by ensuring that the input impedance of the transmitting coil is a conjugate match for the ZO of the transmitter and that the load impedance, ZL is a conjugate match for the overall system. Because the mutual impedance factors into this condition, it is typical that the system is first modeled in order to reduce the unknowns prior to commencing construction.

Because the system is closely coupled, the load impedance of the receive antenna should also be included in the modeling exercise. Unlike a radio link with identical antennas in their far fields, the mutual inductance factor often causes the optimum load impedance of the receive antenna to be different than the transmitting coil input impedance even though the coiled antennas are identical.

Specific to your question as to how to measure the transferred power, place a high impedance RMS RF voltmeter across the load resistor on the receiving coil and apply Ohm's law to resolve the power:

$$P=\frac{E_{RMS}^2}{R} \tag 1$$

Alternatively, you may use an oscilloscope. In this case, the observed voltage will be peak to peak. To calculate power:

$$P=\frac{E_{p-p}^2}{8R} \tag 2$$

The power term can then be converted to dBm:

$$dBm=10\log\left(\frac{P}{.001}\right) \tag 3$$

If you are interested in a fairly easy read, and the basic math, regarding WPT you may enjoy the practical academic paper by Minfan Fu, Tong Zhang, Xinen Zhu and Chengbin Ma entitled A 13.56 MHz Wireless Power Transfer System Without Impedance Matching Networks, to which the above diagram is credited.

• Thanks for your instruction. In my opinion, that is exactly what a spectrum analyzer would do to measure the power density. So, do you think I can use a spectrum analyzer to measure the transferred power? Just like in far-field WPT, just connect an antenna to the analyzer and I can get the power density. – Minh Lam Dec 6 at 8:10
• @MinhLam "In my opinion, that is exactly what a spectrum analyzer would do..." That is true only to a certain extent. In a power transfer application, the receive antenna load will dissipate more power than an SA can handle and the impedance of the load will likely not be the typical 50 ohm input of an SA. So the SA must be in high impedance mode and the reported dBm therefore must be transposed based on the actual load impedance. – Glenn W9IQ Dec 6 at 8:17