SERIES REACTANCE Xₛ
24.84 Ω
Every RF link fights the same enemy: impedance mismatch. When source and load disagree, energy bounces back as standing waves. This is a hands-on lab for the Smith chart, L / Pi / T networks, stub matching, and the Q–bandwidth tradeoff — drag, tune, and watch the physics respond.
A purely real load keeps voltage and current in phase — all power reaches the load. Add reactance and current lags voltage; the phase gap generates reflections and standing waves.
Constant-resistance circles nest toward the right; constant-reactance arcs curve into the top half (inductive, +jX) and bottom half (capacitive, −jX). The center is a perfect 50Ω match. Drag the marker — Γ, VSWR, return loss and delivered power recompute live.
BW = F / Q. A low-Q network matches over a wide band but lets harmonics through; a high-Q network is selective but touchy — component tolerance can shift the whole notch. Slide Q and watch the S11 reflection curve narrow.
Series parts slide the impedance along resistance circles; shunt parts slide it along admittance circles. More elements buy control over Q. Coil = inductor, plates = capacitor.
Series L + shunt C (low-pass) or series C + shunt L (high-pass). Lowest loss; Q is fixed by the impedances.
Shunt C — series L — shunt C. Two L networks back-to-back with a virtual R below both terminations. Q is yours to choose.
Series — shunt — series. Same Q formula as Pi; virtual R is larger than either termination.
No lumped parts at all — a line length d rotates the load to the unit conductance circle, then a shorted stub of length ℓ cancels the susceptance.
Enter a load and get the two lengths that match it: the distance d from the load where the line admittance hits Re(y)=1, and the shunt stub length ℓ whose susceptance cancels what remains. Lengths are in wavelengths (λ) on a Z₀ = 50Ω line.
Plot the load. Distance from center is your reflection; top or bottom half tells you inductive vs capacitive.
A parallel part slides you along a conductance circle onto the unit resistance circle.
A series part with equal-and-opposite reactance cancels the leftover and lands on 50Ω.
Fold the load's own parasitics into the network — fewer parts, smaller values, cheaper board.
From AN1275: match a 2.4 GHz radio whose optimum load is 23 + j11.5 Ω to a 50Ω trace at 2445 MHz, low-pass. Source conjugate is 23 − j11.5Ω; the load side is higher, so the shunt part goes toward the load.
Q gives both reactances; then resonate out the source capacitance with an extra series inductor and merge it into the final value.