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Antenna #18. Reciprocity Theorem Explained: When Can You Swap Transmit (Tx) & Receive (Rx) Antennas?

You’ve just built an antenna that meets your gain, bandwidth, and impedance requirements. Now, you’re considering using it for both receiving & transmitting signals. Will these parameters: gain, bandwidth, and impedance remain the same in both modes (Tx & Rx) of operation?

The answer lies in a fundamental property of most antennas: reciprocity. Thanks to antenna reciprocity, key characteristics such as impedance, gain, radiation pattern, bandwidth and resonant frequencies remain identical whether the antenna is transmitting or receiving signals. This principle was mathematically established by Lorentz through the reciprocity theorem.

If a voltage is applied to the terminals of an antenna A and the current measured at the terminals of another antenna B,
then an equal current will be obtained at the terminals of antenna A if the same voltage is applied to the terminals of antenna B.
A consequence of this theorem is that the antenna gain must be the same whether used for receiving or transmitting.

Two antennas, whose input impedances are Z1 and Z2, are separated by a linear and isotropic (but not necessarily homogeneous) medium, as shown. One antenna (#1) is used as a transmitter and the other (#2) as a receiver.

The equivalent network of each antenna is shown below. The internal impedance of the generator Zg is assumed to be the conjugate of the impedance of antenna #1 〖(𝑍〗_𝑔= 𝑍_1^∗=𝑅_1−〖𝑗𝑋〗_1) while the load impedance ZL is equal to the conjugate of the impedance of antenna #2 (𝑍_𝐿= 𝑍_2^∗=𝑅_2−〖𝑗𝑋〗_2).

Transmit-Receive (Tx-Rx) antenna interchangeability refers to the ability to use the same antenna for both transmitting and receiving signals, either simultaneously or alternately. This is possible under certain conditions, primarily determined by the antenna's design, operating frequency, and system requirements. Here are the key scenarios when Tx-Rx interchangeability is feasible:
1. Reciprocity Principle
Antennas are generally reciprocal devices, meaning their radiation and reception patterns (gain, directivity, impedance, etc.) are identical regardless of whether they are used for Tx or Rx.
When Interchangeable: If an antenna is linear and passive (no active components like amplifiers), it can typically be used for both Tx and Rx at the same frequency.

2. Frequency Compatibility
Same Frequency:
If the system operates in half-duplex (Tx and Rx at different times, like in radar or walkie-talkies), the same antenna can be switched between modes.
For full-duplex (simultaneous Tx/Rx at the same frequency), special designs like circulators or diplexers are needed to isolate Tx and Rx signals (e.g., in radar or some communication systems).
Different Frequencies (FDD Systems):
In Frequency Division Duplex (FDD) systems (e.g., cellular base stations), antennas must support both Tx and Rx bands but may require duplexers to separate the frequencies.

3. Power Handling
Tx antennas must handle high power without damage (e.g., heating or arcing), while Rx antennas deal with weak signals.
When Interchangeable: If the antenna's power rating is sufficient for Tx, it can often be used for Rx (but not always vice versa).

4. Polarization and Radiation Pattern
The antenna's polarization (linear, circular) and radiation pattern must match for both Tx and Rx.
Example: A circularly polarized antenna for satellite comms must maintain the same polarization for Tx/Rx to avoid signal loss.

5. System Architecture
Radar Systems: Often use the same antenna with a transmit / receive (T/R) switch.
MIMO/Phased Arrays: Antennas in these systems are typically shared for Tx/Rx but require careful calibration.

6. Time Division Duplex (TDD) Systems
In TDD (e.g., Wi-Fi, 5G NR), the same frequency is used for Tx and Rx at different times, so antennas are inherently interchangeable.

When Interchangeability is Not Possible:
Active Antennas: If the antenna has integrated amplifiers or filters optimized for only Tx or Rx.
Asymmetric Designs: Some antennas (e.g., high-gain Tx antennas for uplink vs. broad-beam Rx antennas) are purpose-built for one direction.
Isolation Requirements: In high-power systems (e.g., broadcast Tx), Rx antennas may need physical separation to avoid overload.