Antenna reciprocity: directivity/gain

[amp2]

Hi,

I read in my courses that antennas are reciprocal so they should have the same directivity and gain when transmitting and receiving. So if I have two transceivers (operating at sub-GHz) one with a pcb trace antenna and the other with a commercial stick dipole, and assuming the transmit power is identical in both transceivers and the path loss being same, will the received power rssi in both transceivers be identical? In theory and in practice?
   

[indeterminatus]

Interesting question, also keen to learn the answer to this!

[rubidium]

For starters, the receive and transmit gains will easily differ simply if the polarization of the arriving wave is not exactly that of what is being transmitted. Think about it.  Let's say I have 2 identical receivers each driven by identical dipole antennas. Off at infinity I have a single transmitter. As I rotate one of the receive dipoles with respect to the other, certainly I am going to experience received signal strength differences between the 2 receivers.

Further differences will depend on the antenna. Certainly if the antenna is comprised of multiple elements that can be independently weighted, then there is the latitude to have independent transmit and receive patterns. Certainly modern radars (my world) do this to impose sidelobe control on receive to suppress intentional interference, while generally just letting the transmit side go without so-called tapering.

[fourfathom]

All else being equal?  I can't prove it, but YES.

[ejeffrey]

Hi,

I read in my courses that antennas are reciprocal so they should have the same directivity and gain when transmitting and receiving. So if I have two transceivers (operating at sub-GHz) one with a pcb trace antenna and the other with a commercial stick dipole, and assuming the transmit power is identical in both transceivers and the path loss being same, will the received power rssi in both transceivers be identical? In theory and in practice?
 

Loss is non-reciprocal but in a trival way and that can include path loss as well as loss in the antenna itself.  In any case, as long as the antennas are passive, have no ferrites, and everything is time invariant, this is true,  |S21| = |S12|.  This is a single mode analysis, if you have multiple modes you need to consider each pair of modes independently.

This doesn't mean the link works just as well in either direction because it only applies to the transferred signal, the two antennas may have very different susceptibility to third party signals such as interference and noise.  For instance, a satellite dish can have a very good received SNR even with weak received power because the background noise it sees is generally deep space with a noise temperature of 2.725K.  Try to run the link in reverse and the SNR will be worse because the background noise is blackbody radiation of the earth, plus any in-band terrestrial noise sources.

[E Kafeman]

Passive power path loss in both directions are identical. Anything else will break a number of physical laws.
Path loss includes antenna directivity and efficiency.

>and assuming the transmit power is identical
Tx power is not related to path loss. Same for received RSSI, it is not related to path loss.
Path loss is an attenuation value, normally expressed unitless in dB.

If both Rx and Tx stages are ideal for both transceivers and same impedance matching, yes, RSSI will be same in both directions as attenuation in both direction are same.
A less good receiver or low Tx power due to impedance mismatch will result in lower RSSI reading but it is not related to pathloss which is a constant value and same in both directions.

If properties of Tx power, receiver noise floor and actual modulation protocol needed SNR, can a link budget be calculated.
Path loss is a part of calculated link budget.

[radiolistener]

If we don't take into account material property change due to a high power for TX, the path loss will be identical.

if your transmitter works with very low power (some mW), you can assume that path loss in both direction will be the same. But if you apply high power into antenna, it may change material properties in the near field region of antenna and it can affect signal loss. So, it may depends on environment in the near field region of antenna.

[E Kafeman]

>If we don't take into account material property change due to a high power for TX, the path loss will be identical.

Antenna path loss, |S12|=|S21|, will always remain same in both directions or else do we need a new physic.
If changing nearfield environment parameters during Tx or disconnect antenna during Rx does not affect path loss! It is a misunderstanding what antenna path loss is.
Antenna path loss is normally calculated from one antenna port to another antenna port. No need for any formal transceiver at all.
It is a variation of Friis equation. A sub part is Free Space Path Loss, which not include antenna directivity and assumes isotropic free space spread.
Antenna path loss can include non free space loss.

Power as an absolute parameter and local reflection loss are used when calculating link budget where TX power, Rx sensitivity, different amount of Tx and Rx reflection losses in antenna feeding are all parts of this calculation. Link budget parameters will affect resulting RSSI and RSSI can be different in different direction due to differences related to active circuit such as variations in Tx power which only will affect opposite transceiver indicated RSSI value.

Antenna path loss is not including power as parameter in its unitless result but it describes a power ratio, how much power is reduced at receiving antenna  port from Tx antenna feeding port.
Path loss includes antenna directivity but not losses due to antenna imperfections in opposite to link budget calculation.

>But if you apply high power into antenna, it may change material properties in the near field region of antenna and it can affect signal loss.

We can change thousand of things around antenna nearfield when switching from Tx to Rx and we do that rather often. As an example, it is common that Rx and Tx have different antennas, switching from omni-directional to directive, change feeding point from horizontal to vertical polarization. Antenna path loss will however be same in both directions for a certain path.


>I read in my courses that antennas are reciprocal
Correct.

> will the received power rssi in both transceivers be identical?
Relative identical is possible but not exactly. Path loss is same in both directions but Tx and Rx will be different optimized relative antenna impedance and as there are assumed two different antenna types and by that different antenna-impedance can a few dB difference in respective RSSI be within normal variations.

[T3sl4co1l]

Note that you could have an environment like this:
https://en.wikipedia.org/wiki/Optical_isolator

The rotation might come from a variety of effects (most often, solutions of chiral molecules, like the phase rotation caused by sugar water; in outer space, magnetic fields and interplanetary/interstellar plasma can do the same), and polarization selection can come from acicular dust grains or specular reflections from dielectric surfaces.

Most of these should be fairly uncommon (there's little in the atmosphere that should effect polarization or rotation), or not in the same place (e.g., rotation from interplanetary plasma vs. specular reflections off the ocean?), but some very specific situations can probably still happen (weird reflection paths through atmospheric ducting I think could cause enough directions of rotation to effect polarization shift?).

Also, if the rx/tx aren't identical designs, they can have different receive or processing gain for example, so on top of other effects, they might still end up different.  Or two products of identical design, will be dissimilar due to manufacturing variation, perhaps far enough to change the RSSI noticeably (some LSBs)?

So, "yes, but also no", or more precisely: to what level of accuracy do you count as "identical", and to what degree of duplication are you stipulating?  (And, at what point does the list of stipulations become so long it becomes pointless to ask? )

Tim

[radiolistener]

>If we don't take into account material property change due to a high power for TX, the path loss will be identical.

Antenna path loss, |S12|=|S21|, will always remain same in both directions or else do we need a new physic.
If changing nearfield environment parameters during Tx or disconnect antenna during Rx does not affect path loss! It is a misunderstanding what antenna path loss is.
Antenna path loss is normally calculated from one antenna port to another antenna port.

When I talked about path loss, I mean power loss from one antenna port to another antenna port.

For example, let's take a look at the following setup:

Antenna 1: half-wavelength dipole in a free space with no third-party items or material in the near field region (just a vacuum).


Antenna 2: ferrite rod antenna.


So, the path loss for a high power TX will depends on direction. Because when you apply high power (for example 1 kW) to Antenna 2 it will change ferrite rod properties (magnetic saturation).

In such case |S12| is not equals to |S21| because ferrite rod properties (which is placed in the near field region) will be changed when you apply a high power to the ferrite rod antenna, but remains unchanged when you apply high power to the half-wavelength dipole.


In real world path loss is affected by a power transmission direction, just because real antenna consists of a real materials with non-linear behavior which depends on the power and also depends on a background electric or magnetic field strength, temperature, etc. So, the antenna properties will depends on applied power and/or environment conditions (such as background magnetic/electric field strength, temperature, pressure and other).

Of course, if you're using exactly the same antenna and exactly the same near field region configuration, then you can assume that |S12| = |S21|, because property changes will be equals for both directions. But in real world, there is almost always exists some difference for the near field configuration of both antennas. For example, backround magnetic field can be different for antenna 1 and 2 and it can affect a piece of ferromagnetic placed in the near field region of antenna which will affect the antenna properties.

By the way, I think S-parameters is not applicable here, because S-parameters are intended for a DUT with linear behavior, but effects I'm talking about leads to a non-linear behavior.

Another example, when you apply high enough power into transmission antenna which is placed in the air environment, the air state may be changed to a plasma, and path loss will be dramatically changed because the plasma is a good shield for electromagnetic fields and also it is a conductor, so the configuration of your antenna will be changed, include antenna directivity, gain, efficiency. Such effect of plasma can be used for plasma antenna, in which plasma is used instead of traditional metal conductors.

Antenna path loss is not including power as parameter in its unitless result but it describes a power ratio, how much power is reduced at receiving antenna  port from Tx antenna feeding port.
Path loss includes antenna directivity but not losses due to antenna imperfections in opposite to link budget calculation.

it is not included for ideal antenna for which properties doesn't depends on the power. But in real world it depends on the power and antenna has limited working power limits for which it's parameter will be within specification. But when you exceed these limits it may leads to a significant change, include directivity change, gain change and efficiency change. And as result path loss change.


Another example is a transformer with core. When you don't exceed it's specification of the input voltage, it's parameters will be within specification. But when you reach some voltage limit, it leads to a core saturation and transformer parameters will be significantly different.

[ejeffrey]

>If we don't take into account material property change due to a high power for TX, the path loss will be identical.

Antenna path loss, |S12|=|S21|, will always remain same in both directions or else do we need a new physic.

That's not true.  |S12| == |S21| is a consequence of a system that is linear, time invariant, passive, and isotropic.  The first two are needed for S-parameters to even be well defined (although in some cases you can hack something that works anyway), active devices like amplifiers are rarely reciprocal, and devices made with magneto optical materials such as circulators are not isotropic.  These conditions are so widely applicable and useful that people tend to think of it as a fundamental law but forget that it comes with caveats.

[ejeffrey]

Another example is a transformer with core. When you don't exceed it's specification of the input voltage, it's parameters will be within specification. But when you reach some voltage limit, it leads to a core saturation and transformer parameters will be significantly different.

This is a particularly good example because a transformer by itself could be considered to be reciprocal.  The S parameters are power dependent but saturation happens the same forward and reverse.  But you have violated the rules of the proof which means you have no guarantees.  If you then cascade the  transformer with an attenuator (which is reciprocal) the cascaded network is longer even approximately reciprocal since a signal from one direction hits the transformer first and saturates it.  The same power from the other direction is attenuated first and doesn't saturate the transformer.

[E Kafeman]

When I talked about path loss, I mean power loss from one antenna port to another antenna port.

Yes that is how antenna path loss and Friis equation normally is defined. See https://www.antenna-theory.com/basics/friis.php

Because when you apply high power (for example 1 kW) to Antenna 2 it will change ferrite rod properties (magnetic saturation).

This is on the other hand not how antenna path loss i defined. Friis equation assumes a reciprocal system, which it is if measuring from antenna port to antenna port just as you wrote above.
Link budget is a better description for what you is trying to describe.
Only passive isotropic and reciprocal elements exist between antenna ports as we else would cause an unbalance of total amount of energy in universe depending on signal directions. That is not allowed.

By the way, I think S-parameters is not applicable here, because S-parameters are intended for a DUT with linear behavior, but effects I'm talking about leads to a non-linear behavior.

Yes you is talking about active non reciprocal  systems, not related to antenna path loss calculation. Please check Friis equation. Not even reflection loss is included as it is happening before antenna port and for same reason do it not neither exist any big Tx rig causing antenna elements to saturate. Just forget your mega power transmitters if it is transmission loss that is calculated.

For same reason in Friis equation is not a Tx modulation or transmission mode factor. For link budget however, assume that your ferrit is saturated to a big resistor due to a lot of power feed to it. It will affect Tx losses exactly just as much as Rx losses if it is duplex traffic.
For good reasons do we not include local malfunction or poor design in Friis equation. Traffic mode will neither be a part of path loss, but may affect link budget.

Another example, when you apply high enough power into transmission antenna which is placed in the air environment, the air state may be changed to a plasma,

Yes, just as I did wrote above.

Antenna path loss is not including power as parameter in its unit-less result but it describes a power ratio, how much power is reduced at receiving antenna  port from Tx antenna feeding port.
Path loss includes antenna directivity but not losses due to antenna imperfections in opposite to link budget calculation.

But when you exceed these limits it may leads to a significant change, include directivity change, gain change and efficiency change. And as result path loss change.

Yes, just as I did wrote above. It is NOT a part of antenna loss path and it is not anything included in Friis eqation and neither usable information for calculation of path loss.
It is a result of poor or malfunction in a local radio system if antenna system is degraded by its own Tx system.
Such things are of limited interest  when as example,  calculating wave propagation for a cell phone system, as an example where antenna path loss calculation is of high importance when calculating needed number of base stations and where to place them.

active devices like amplifiers are rarely reciprocal,

That is true, but as these are very seldom found between antenna ports, is it no need to include these when calculating path loss between two antenna ports and it would anyway be a bad idea with active circuits placed between antennas as there is no power supply in free space.
If such amplifiers or any else non-reciprocal element had been normal occurring in free space had Friis equation added a note about that: "look out for amplifiers between the both antenna ports".
Friis equation is very clear at that point. It is a measurement from port to port and not even antenna transmission losses, reflections, diffraction or indirect scattering are included, neither any non reciprocal amplifiers.
It is a real world measurement from antenna port to antenna port just as you can simulate S21 in CST or similar software between two antennas.
Revers same measurement in CST and tell if S12 not have same value.

It is a useful value to calculate as later  selecting of needed Tx power, possible bandwidth and modulation type can be critical depending on if satisfying coverage will be reached with proposed antennas.

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See bottom attached image.

This is an example where path loss is calculated and needed to be known before hardware is constructed and sent away.
It is very big differences between earth an mars parabolic antennas gain and it is almost 20 dB difference in receiver sensitivity for Orbiter and earth equipment but S12 antenna path loss value is equal to S21.

Please define if you is adding statement about how path loss and Friis equation is defined and eventual flaws with its calculation or if you describe something completely else, such as a malfunctioning overpowered transmitter and its poor designed power handling in its non reciprocal components.

We ALL know that such problems exist and most of us do even know that amplifiers seldom are reciprocal between its ports (S12 differ from S21)
 but it is NOT a part of antenna path calculation and is not even distant covered by Friis equation as opposite is clearly declared.

Try to understands some of the text written here: https://resources.system-analysis.cadence.com/blog/msa2021-understanding-the-circuit-and-antenna-reciprocity-theorem

For me are these calculation real world, normal thing to calculate and of practical use. Faulty designed transceivers with corona discharges and saturated transformer cores not so much. It is probably more a thing for a repair shop.

[T3sl4co1l]

That is true, but as these are very seldom found between antenna ports, is it no need to include these when calculating path loss between two antenna ports and it would anyway be a bad idea with active circuits placed between antennas as there is no power supply in free space.

For example, pumped laser media has an amplifying effect; but as far as I know, it's reciprocal, acting on whatever wave you give it -- so you still need iso/circulators to do that anyway.  The fields equivalent of a tunnel diode of matched (negative) impedance, it just sits there doing its thing.

Tim