# A query about "Theory of reciprocity" for antenna

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#### g86

##### Full Member level 4 Look at the linear array of two antennas below. first element is a power divider and its output ports are connected to antennas. Power divider S-para are given below the figure.

<figure>
port 1(input) =<port 2and 3 --- [connected to antennas 1 and 2]
</figure>

(S11=0, S22=-6dB, S33= -6 dB and S32=-6dB)[no isolation R]

Normally we use equal and unequal power dividers for antenna arrays. When the antenna is transmitting and the input port of power divider is fully matched, power will appear at antennas and will be radiated. But at receiving mode the input impedance at output ports are not matched (we know for a equal power divider S22 or S33= -6 dB) so all power will not appear at port 1.

My question is how we can apply "Theory of reciprocity for these arrays". Are they really good radiators and bad receivers.

I am more confused when amplitude taparings are there in a large planer array.

:!: :idea: :?:

#### flatulent special case

For your power combiner, this is a special case where the signals coming in to ports 2 and 3 have a special amplitude and phase relationship that allows all of the power to go to the port 1. Therefore the S22 and S33 return loss values are much better and the receiving efficiency is the same as the transmitting efficiency.

On the tapering of the arrays, the usual thing to do is to feed the left/right elements equal distance from the center from the same power divider. Unequal dividers are used to make the taper.

In one sense the tapered array is less efficient than a uniform array because the peak gain is less. But all of the power coming in from the transmitter goes into space. As far as as beam patterns, the tapered array has a lower peak but a broader beam width so the total energy radiated is the same.

#### g86

##### Full Member level 4 Re: special case

It is true that the power will appear at port 2 and 3 with same amplitude and phase and we may assume that odd mode is not present were equal power dividers are used. I think you also suggested the same thing.

But in case of an array where power tapering is present i.e. unequal power divider is present to get desired sidelobe level, there good isolation can not obtained even if power appears in same phase and amplitude. Some power at port 2 must appear at port 3 and the array can not be used as a good receiver. Here I am still confused! :?: :idea: :!:

flatulent said:
For your power combiner, this is a special case where the signals coming in to ports 2 and 3 have a special amplitude and phase relationship that allows all of the power to go to the port 1. Therefore the S22 and S33 return loss values are much better and the receiving efficiency is the same as the transmitting efficiency.

On the tapering of the arrays, the usual thing to do is to feed the left/right elements equal distance from the center from the same power divider. Unequal dividers are used to make the taper.

In one sense the tapered array is less efficient than a uniform array because the peak gain is less. But all of the power coming in from the transmitter goes into space. As far as as beam patterns, the tapered array has a lower peak but a broader beam width so the total energy radiated is the same.

#### flatulent beginning to understand

I am now beginning to understand your question. One way of looking at it involves a directional coupler and what happens to the power that goes into the coupled port.

If you use the peak gain of the arrays, the tapered one is not as efficient (peak gain) as the uniform one in both transmit and receive.

I will have to think upon this one.

(after thinking a while) The notcoupled power gets into the coupler internal resistor.

However, you have losses with a uniform array off axis because the phase of the two inputs to a combiner are off and some of the energy goes into the balancing resistor.

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