# Reciprocity applied to complementary antennas

• Loren Booda
In summary, reciprocity states that if Antenna 1 is driven with a current i1 whichinduces a voltage v2 at the terminals of antenna 2, then if antenna 2 is driven with i1, antenna 1 will have v2 volts at the terminals.
Loren Booda
Does reciprocity, the rule that electrical specifications of an antenna are essentially the same for receiving and transmitting [Wikipedia], apply to the following situation:

Antenna Y transmits with power PY which antenna Z receives as power PZ. Does this mean if that antenna Z transmits with power PY, antenna Y receives it as power PZ? The antennae are assumed linear and well behaved.

I'm no antenna expert, but I believe that if the input Z of your two antennas are the same, then your statement will hold. The more general way that I've seen reciprocity derived (Stutzman & Theile, section 1.7) is in terms of the drive current into one antenna and the open circuit output voltage out of the other antenna:

Voc,a / Ib = Voc,b / Ia

If the two antennas have different input impedances at the drive frequency, then I think that your power statement may not hold. Like I said, though, I'm no expert on antennas...

berkeman,

Yours, the best explanation yet. One neat "power law" and more general than my original assertion, as you outline. Thank you.

Luckily, I'm an actual antenna expert.

Reciprocity is more interesting than that.

It says that if Antenna 1 is driven with a current i1 which
induces a voltage v2 at the terminals of antenna 2, then
if antenna 2 is driven with i1, antenna 1 will have v2 volts
at the terminals.

This rather remarkable statement holds regardless of z1 and z2
and regardless of the material configurations around or between
the antennas. Only linearity and isotropy is required.

What is amazing about this is that the transmitting and receiving
current patterns of any given antenna are not generally the same, and
reciprocity can be shown not to be a statement of energy
conservation.

Last edited:
Thanks, Antiphon. This may be what I had seen originally, years ago. Do you have any Internet references for the relation?

Loren Booda said:
Thanks, Antiphon. This may be what I had seen originally, years ago. Do you have any Internet references for the relation?

Berkeman's Theile reference is a reliable textbook.

As far as the internet goes, I cannot find a single technically correct reference.
Most of them are flat out wrong and state that it means that an
transmitting antenna has the same characteristics as a receiving antenna, etc.
I will edit this post if I find one.

As I mentioned the current patterns are different on an antenna which is
transmitting than for the same antenna when receiving. Reciprocity would
not be so unusual if this were not the case.

Edit: The Navy has a decent link- start on page 42 of the slide show.
http://www.nps.navy.mil/Faculty/jenn/EO3602/Vol2v1.3.pdf

BTW, this is an oustanding executive summary slide show about antenna theory.
I can recommend it to anyone looking for a decent antenna theory reference
without having textbooks handy.

Last edited by a moderator:
Excellent reference, Antiphon - I appreciate your homework.

## 1. What is reciprocity applied to complementary antennas?

Reciprocity is the principle that states the characteristics of an antenna do not change when it is used for transmitting or receiving. In the context of complementary antennas, this means that two antennas with complementary geometries can be used interchangeably for transmitting and receiving signals.

## 2. How does reciprocity benefit complementary antennas?

Reciprocity allows complementary antennas to be used in symmetrical systems, where the same antenna can be used for both transmitting and receiving. This simplifies the design of the system and reduces the number of antennas needed.

## 3. Are there any limitations to the application of reciprocity to complementary antennas?

Yes, reciprocity is only applicable to antennas with complementary geometries. Antennas with different geometries, such as a dipole and a loop antenna, cannot be used interchangeably for transmitting and receiving.

## 4. What are some common applications of reciprocity in complementary antennas?

Reciprocity in complementary antennas is commonly used in wireless communication systems, such as in Wi-Fi networks, cellular networks, and satellite communication systems. It is also used in radar systems and radio astronomy.

## 5. How is reciprocity in complementary antennas experimentally verified?

Reciprocity in complementary antennas can be experimentally verified by measuring the antenna's characteristics, such as radiation pattern, impedance, and gain, when used for transmitting and receiving. If the measurements are the same, then reciprocity is confirmed.

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