## Active and Reactive Power

It might be useful to think about antenna systems, particularly phased arrays with multiple driven elements, in terms more familiar for power systems, that is, with active and reactive power. The usual antenna system has a single feed point, and a single feed line, and some matching components, so the natural model is to think of impedance matching, transmission line loss, and so forth. However, many antennas have significant reactive impedance, and the flow of reactive power through the system can result in surprising losses.

Consider, for example, an antenna with a feedpoint impedance of 50 + 30j ohms, fed from a transmitter with 50 ohm resistive output impedance and 100 Watts (this means the generator is putting out 70.7 volts into a 50 ohm load). What does this really mean as far as the feed line and matching components are concerned? Ignoring the "impedance transforming" effects of the feed line for a moment, we've got the following sort of circuit. The load is drawn in the parallel form because it will relate better to what we're doing later. With 70.7 volts out of the source, the total current through the load will be 1.21 Amps: 1.04 through the resistance, and -0.62j through the reactance (it's inductive, so the current lags the voltage). Note also that the apparent power (voltage times current) is only 85.75 watts.. providing a nice example of why you want source and load impedances matched.

We put in a matching network that "cancels" the 30j impedance of the antenna with a -30j impedance (a capacitor in this case). (by the way, it's really a -.00882j admittance (in parallel form) at the antenna and a .00882j admittance in the network.

An interesting thing is that in the feedline between transmitter (source) and the matching network, there is just the active power flowing. That power flows through the next segment of feedline, and is "dissipated" in the load resistance. The load resistance is a combination of the loss resistance of the antenna and the radiation resistance (where the power actually winds up being transmitted over the air).

Between the matching network and the antenna, though, there is also a "reactive" power flow, as charge/current moves back and forth between the inductance in the antenna and the matching capacitance in the tuner. No actual power is moving, because the current and voltage are 90 degrees out of phase. In fact, this current is the 0.62 Amps we calculated before. All well and good, IF the transmission line is lossless. Consider, though, what happens if the transmission line has some loss, represented here by a series resistance. (For most transmission lines at HF and VHF frequencies, dielectric loss is negligible, and most of the loss is due to the resistive loss in the conductors, so this is a reasonable model.)

The current for both the active AND the reactive power is flowing through Rloss B. And, because that current is greater than just the current for the active power, the system loss is greater. With, say, 1 ohm of Rloss B (corresponding to less than 0.1 dB loss, in the matched case), we'd be dissipating 1.5 Watts in RlossB. This, then, is why you want to do your matching at the antenna, not the transmitter, particularly if the mismatch is quite reactive.

antenna/phased/power.htm - 30 November 2002 - Jim Lux