RF & microwave

Impedance matching

Impedance matching is the art of making two parts of a circuit 'agree' on how hard to push and pull, so that energy flows from source to load instead of bouncing back. Think of pushing a child on a swing: if you shove at random moments, half your effort fights the swing; if your timing matches the swing's rhythm, almost all your push becomes motion. In RF, a 50-ohm source feeding a 50-ohm antenna delivers nearly all its power; a 50-ohm source feeding a badly mismatched 5-ohm load reflects most of it.

Engineers insert a small matching network — a few capacitors and inductors, an L-network, or a quarter-wave transmission line — between source and load to transform one impedance into the other. The goal is conjugate matching for maximum power transfer, or a match to the line's characteristic impedance to kill reflections. At microwave frequencies this is usually done on a Smith chart, sliding the impedance around until it lands on the centre (50 ohms).

Z_in = Z_0 (matched) ; Γ = (Z_L − Z_0)/(Z_L + Z_0) = 0

Maximum power transfer (conjugate match) and zero-reflection match are the same only when the source impedance is purely real and equals the line impedance — at RF the two goals can subtly differ.

Also called
matching network匹配網路