Distributing the Power

One of the results you get after having determined element currents and applying the mutual impedance matrix is the power flowing to or from each element. Given that the matching and delay network is lossless, this is the same power that must flow to or from the summing point at the radio. Further, you generally want to have a resistive 50 ohm termination for the radio to look at.   This is actually quite easy to achieve. The  network which determines the phase shift can also transform the resistive impedance of the antenna matching network to whatever is necessary to achieve proper power distribution.

Taking the easy case first, assume you want an even distribution of power. You would calculate the delay network to have an input impedance equal to 50*N ohms, where N is the number of elements. The figure below illustrates this for 4 elements.  Each network would be adjusted so that it looked like a 200 ohm resistive impedance. When all the 200 ohm impedances were paralleled, the impedance that the transmitter sees is 50 ohms.

4 way equal power division

However, in general, the power is not divided evenly. In this case, you need to adjust the input impedances so that two constraints are met:

The following diagram shows how this would be done where you wished two elements to receive twice the power of the other two. Note that the parallel combination of the load resistances adds up to 50 ohms, and that the power dissipated in each load resistor is distributed appropriately.

4 way unequal power division

The equation which determines the required load impedance for each element is:

Negative Source Impedances - Negative Element Power

In some phased array set ups, a condition where negative power is consumed by an element occurs; that is, an element actually absorbs power from the other elements. With a lossless matching network, this power can be fed to the other elements, so nothing is really lost. This is accomodated quite easily by assuming that the load impedance is negative.

pwrdiv.htm - revised 11 March 1999, Jim Lux
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