For many years, the capabilities of long-range wireless power have been talked about and with increasing interest. The technology is proven and is already being used today in many industries like manufacturing, building automation and hospitality. An assortment of other, short-range wireless charging technologies are on the market, including Qi (inductive coupling) and magnetic resonance. However, the focus of this article will be on the various methodologies for RF-based wireless power for powering devices over distance.

**WIRELESS POWER OVER DISTANCE**

RF wireless power is a technology that enables power to be sent over distance using radio waves. A transmitter uses an antenna to generate an RF field which propagates toward a receiver’s antenna. The receiver captures a portion of the RF field and uses an RF to DC converter to produce usable DC to power electronics or recharge batteries. RF wireless power can be implemented in various ways and many design decisions impact the performance of the system. When all variables are considered, RF wireless power networks offer a way to remove wires and batteries from many of the devices we encounter every day.

Wireless power transmission using RF in the far field can be described using the Friis equation:

where P_{R} is the received power, P_{T} is the transmitted power, G_{T}( θ_{T},φ_{T}) is the angular dependent transmitter antenna gain, G_{R}( θ_{R},φ_{R}) is the angular dependent receiver antenna gain, λ is the wavelength, r is the distance between the transmit and receive antennas, Γ_{T }is the transmit antenna reflection coefficient, Γ_{R} is the receive antenna reflection coefficient, p̂_{T} is the transmitter antenna polarization vector and p̂_{R} is the receiver antenna polarization vector. Generally, the transmitter and receiver are assumed to be matched, have the same polarization vectors and are in the main radiation beam, which simplifies the equation to:

This equation shows the received power is inversely proportional to the distance squared, which means if the distance doubles, the received power reduces by 4x. This can be understood considering the power is spreading over the surface area of a sphere with area A=4πr^{2}.

Another factor in RF wireless power transfer is the received power is proportional to the square of λ or inversely proportional to the square of the frequency. This means a low frequency signal will provide more received power than a higher frequency signal, assuming all other variables are the same. For example, consider an amplifier delivering 1 W of RF power to a transmitting antenna with a gain of 4, i.e., 4 W EIRP. A dipole antenna at a fixed distance at 915 MHz will receive about 7x more power than a dipole antenna at 2.4 GHz:

and about 40x more power than a dipole at 5.8 GHz:

This difference in power is because the effective area of the antenna is reducing as frequency increases. The dipole antenna, typically λ/2 long, gets shorter as frequency increases, reducing the physical capture area of the antenna.

However, the power density, S, is independent of frequency:

Equation 3 shows the radiated power spreads over the surface of a sphere independent of frequency, and the effective area of the antenna, also known as capture area, determines the amount of received power. This explains why a λ/2 dipole antenna at 5.8 GHz captures less energy than a λ/2 antenna at 915 MHz under identical conditions.

The effective area of an antenna, A_{e}, is directly proportional to its gain:

Higher gain antennas can be used to increase the capture area, but high gain antennas come at the cost of directionality. Depending on the application, precise antenna directionality is not always advantageous. One way around this potential burden is using multiple antennas and RF to DC converters to increase the overall capture area. However, this solution also increases the cost of the receiver because of the additional hardware. This shows why it is important to outline performance and project expectations prior to designing the system.

The Friis equation is only valid in the far field, so determining the boundary between the near and far field is important. One common method is to determine where the parallel ray approximation begins to break down, i.e., where the wave exiting the transmit antenna can be approximated as a plane wave impinging on the receiving antenna. A plane wave means the receiving antenna sees a constant amplitude and phase across its aperture (see **Figure 1**). Typically, a phase error of π/8 or 22.5 degrees across the receiving aperture is considered an acceptable approximation for a plane wave, which yields the common boundary between the near and far fields given by:

where D is the maximum dimension of the transmitting or receiving antenna or array, r is the distance between the transmitting and receiving antennas and λ is the wavelength.