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Maximum power transfer theorem in antennas

Short answer

Maximum power transfer occurs when load impedance is the complex conjugate of the source impedance: Z_L=Z_A*, so R_L=R_A and X_L=−X_A. For a receiving antenna, P_max=|V_oc|²/(8R_A), with half the power lost or re-radiated in R_A. For transmitting, match the antenna to avoid reflection and mismatch loss.

State and explain the maximum power transfer theorem used in antenna, with necessary diagrams.

Maximum power transfer theorem: A source delivers maximum power to a load when the load impedance is the complex conjugate of the source impedance: Z_L = Z_S*, i.e. R_L = R_S and X_L = −X_S.

Receiving antenna

By Thevenin's theorem, the receiving antenna is a voltage source V_oc in series with its impedance Z_A = R_A + jX_A, where R_A = R_r + R_loss (radiation resistance plus loss resistance).

     Z_A = R_A + jX_A
   +----/\/\/----+
   |             |
 (~) V_oc       Z_L = R_L + jX_L   (receiver)
   |             |
   +-------------+

Maximum power reaches the receiver when Z_L = Z_A*, i.e. R_L = R_A and X_L = −X_A:

P_max = |V_oc|² / (8 R_A)      (V_oc peak value)

Under this condition an equal amount of power is dissipated or re-radiated in R_A, so at most half of the captured power reaches the receiver.

Transmitting antenna

The antenna is the load of the transmitter (through a transmission line). For maximum radiated power, the antenna input impedance must be matched to the line/transmitter: Z_A = Z_S*. If they are not matched, part of the power is reflected, giving VSWR > 1 and mismatch loss:

Mismatch efficiency = 1 − |Γ|²,  Γ = (Z_A − Z0)/(Z_A + Z0)

In practice, matching networks, baluns and stubs are used to meet this condition.

✓ Answer checked by Claude Opus 5.5 (high effort)

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