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Thevenin theorem for antennas

Short answer

Thevenin theorem: any linear two-terminal network equals open-circuit voltage V_th in series with impedance Z_th (sources replaced by internal impedances). For receiving antenna, induced voltage V_oc in series with antenna impedance Z_A = R_r + R_L + jX_A. Load current I = V_oc/(Z_A+Z_L); maximum power transfer with conjugate matching Z_L = Z_A*.

State the Thevenin theorem for an antenna.

Thevenin theorem: Any linear two-terminal network containing sources and impedances can be replaced by a single voltage source V_th (the open-circuit voltage at the terminals) in series with an impedance Z_th (the impedance seen into the terminals with all sources replaced by their internal impedances).

Applied to a receiving antenna

An incident wave induces an emf on the antenna. Seen from its terminals, the antenna is a voltage source V_oc (open-circuit induced voltage) in series with the antenna impedance

Z_A = (R_r + R_L) + j X_A

where R_r = radiation resistance, R_L = loss resistance, X_A = antenna reactance.

      Z_A = R_r + R_L + jX_A
   +-----/\/\/\-----+
   |                |
  (~) V_oc         [Z_L]  receiver
   |                |
   +----------------+

Current in the receiver load:

I = V_oc / (Z_A + Z_L)

With conjugate matching (Z_L = Z_A*), maximum power is delivered: P = |V_oc|²/(8 R_A) (peak V_oc).

Use: finding received power, effective aperture and mismatch loss of a receiving antenna system.

✓ Answer checked by Claude Opus 5.5 (high effort)

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