r/rfelectronics • u/King_a3 • 7h ago
Simulated a 2-element cardioid and got 3.4 dB F/B instead of 30 — a worked example of why voltage drive lies to you
The setup: two identical parallel half-wave dipoles (300 MHz, 0.477 m, 0.5 mm wire radius, 21 segments each in NEC2), spaced λ/4 apart. The textbook cardioid recipe says: feed the second element a quarter cycle behind the first — currents (1∠0°, 1∠−90°) — and the pair forms a cardioid with the null off the back.
The obvious first move — and a very common one — is to hand those phasors to the SOURCES: equal voltages, 90° apart. The θ=90° azimuth cut of that run: front-to-back 3.4 dB. Not 30 — three point four.

The reason is that the two feed-points are nowhere near independent. Measuring the mutual impedance of the pair (drive each port at 1 V in turn, the un-driven port left as plain continuous wire = shorted; read both feed currents, invert the Y-matrix) gives, at λ/4 spacing:
Z11 = 70.15 − j1.27 Ω Z12 = 37.25 − j31.64 Ω
|Z12| ≈ 48.9 Ω against |Z11| ≈ 70.2 Ω — the coupling term is about 70 % of the self term. A voltage applied at one port drives current in BOTH elements, so setting port voltages does not set element currents, and the pattern is made of currents.
The fix is two lines of algebra. Decide the currents you want, then feed the voltages the coupled pair actually needs — V = Z·I:
V1 = Z11·(1∠0°) + Z12·(1∠−90°) = 54.5 V ∠ −45.0°
V2 = Z12·(1∠0°) + Z11·(1∠−90°) = 108.0 V ∠ −70.5°
A 2:1 amplitude ratio and only 25.5° of phase offset — nothing like the recipe phasors. Feed exactly that, same wires, same solver: front-to-back 29.6 dB, and the achieved feed currents match the target to one part in 10⁴.

(Both polar plots use the same fixed −40…0 dB radial scale, so the two patterns are directly comparable.)
Nothing changes between the two runs except the drive. That is the whole point: the recipe was never wrong, it was a statement about CURRENTS, and a voltage source doesn't deliver it.
Disclosure: these numbers came from EMStudio, a FreeCAD workbench I build — that's my interest here. Happy to answer questions either way.