Reciprocity applied to complementary antennas

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Discussion Overview

The discussion revolves around the application of reciprocity in antenna theory, specifically whether the power received by one antenna when another transmits can be reciprocated when the roles are reversed. Participants explore the implications of reciprocity in linear and well-behaved antennas, as well as the conditions under which it holds true.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions if reciprocity applies such that if Antenna Y transmits power PY to Antenna Z, then Antenna Z transmitting power PY back to Antenna Y would result in the same power PZ being received.
  • Another participant suggests that reciprocity may hold if the input impedances of the antennas are the same, referencing a more general derivation involving drive current and output voltage.
  • A participant with expertise in antennas elaborates that reciprocity states if Antenna 1 is driven with a current, it induces a voltage at Antenna 2, and vice versa, regardless of the input impedances or surrounding materials, provided linearity and isotropy are maintained.
  • Concerns are raised about the common misconception that transmitting and receiving antennas have identical characteristics, emphasizing that current patterns differ between transmitting and receiving modes.
  • References to literature and internet resources are shared, with one participant noting the difficulty in finding technically correct online references about reciprocity in antennas.

Areas of Agreement / Disagreement

Participants express differing views on the conditions under which reciprocity applies, particularly regarding input impedances and current patterns. There is no consensus on a definitive interpretation of reciprocity in the context discussed.

Contextual Notes

Some participants highlight limitations in common understandings of reciprocity, particularly regarding the assumption that transmitting and receiving characteristics are the same, which remains unresolved in the discussion.

Loren Booda
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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.
 
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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.
 

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