S-Parameters › Smith Chart

Smith Chart — Plotter, Auto-Match & Network Calculator

Three tools in one page. ① Plotter: upload Touchstone or manually enter impedance points. ② Matching Designer: explore manually or hit Auto-Solve for instant L/pi/T component values. ③ Network Calculator: enter Z_source and Z_load, get every topology's component values immediately.

Reference Impedance
Ω
Add Impedance Point
Ω
Ω
Touchstone S11 Trace
📂
Drop .s1p / .s2p here
or click to browse
Hover / Selected Readout
Impedance
—
|Γ|
—
VSWR
—
Return Loss
—
Γ Phase
—
Plotted Points
No points plotted yet
// Smith Chart — Z₀ = 50 Ω · hover to read values
Constant R circles
Constant X arcs
Points
S11 trace
// Key Formulas
Γ = (Z−Z₀)/(Z+Z₀)  ·  Z = Z₀·(1+Γ)/(1−Γ)
VSWR = (1+|Γ|)/(1−|Γ|)  ·  RL = −20·log₁₀|Γ| dB
Upper half = Inductive (+jX)  ·  Lower half = Capacitive (−jX)
1 — Load Impedance & Frequency
Ω
2 — Current Impedance
Z (after all steps)
—
|Γ| = — · VSWR = — · RL = —
Distance to centre
|Γ| = —
3 — Add Element Manually
nH
4 — Matching Steps
No elements yet — use Auto-Solve or add manually.
Manual mode: Series L/C moves along constant-R circles. Shunt L/C moves along constant-G circles. TL section rotates Γ clockwise. Dashed preview arc shows where next element will take you.
Smith Chart Matching Designer — Z₀ = 50 Ω
Z_load
Matching path
Z_now
Target (Z₀)
Auto-solve paths
Matching Network Summary
Add elements or use Auto-Solve to see the network summary.
Smith Chart Movement Rules

Series L (+jX): UP along constant-R circle (inductive)
Series C (−jX): DOWN along constant-R circle (capacitive)
Shunt L (−jB): DOWN along constant-G circle (admittance plane)
Shunt C (+jB): UP along constant-G circle (admittance plane)
TL section: rotates Γ CLOCKWISE around centre
Target = chart centre: Z = Z₀, |Γ| = 0, VSWR = 1:1

Source & Load Impedance
Q
Ω
Impedance Ratio
L-network: exact 2-element match — Q is set by the impedance ratio (cannot be chosen freely). Works only when one impedance is larger than the other.

Pi/T network: 3-element match — Q is a free design parameter. Higher Q → narrower bandwidth but better harmonic rejection. Q must exceed Q_min = √(R_high/R_low − 1).
Enter impedances above to compute matching networks.

About the Smith Chart Tool

The Smith chart is the fundamental graphical tool of RF and microwave engineering. Invented by Philip H. Smith at Bell Labs in 1939, it maps all passive impedances onto a unit circle in the complex reflection coefficient plane (Γ-plane). Every point on the Smith chart represents an impedance Z = R + jX, and its position encodes the impedance value, the reflection coefficient magnitude and phase, the VSWR, and the return loss — all simultaneously. Understanding the Smith chart removes the need to repeatedly solve complex impedance equations by hand.

Reading the Smith Chart

The centre of the chart is the normalised impedance z = 1 + j0 — a perfect match to the reference impedance Z₀. The right edge is an open circuit (Z = ∞), the left edge is a short circuit (Z = 0). The upper half-plane is inductive (+jX), the lower half is capacitive (−jX). Constant-resistance circles run through the right edge point. Constant-reactance arcs run through the right edge point orthogonally to the resistance circles. Moving clockwise around the chart corresponds to adding electrical length toward the generator (or equivalent inductance); moving anticlockwise is toward the load.

Impedance Matching on the Smith Chart

Every impedance matching step traces a specific arc on the Smith chart. Adding a series inductor moves the point clockwise along a constant-resistance circle. Adding a series capacitor moves it anticlockwise along the same circle. Adding a shunt (parallel) inductor moves the point clockwise along a constant-conductance circle in the admittance (Y) plane. Adding a shunt capacitor moves it anticlockwise along the constant-conductance circle. A transmission line section rotates the point clockwise around the chart centre. The goal of matching is to move the load impedance point to the chart centre (Z = Z₀) through a sequence of such moves.

L, Pi and T Matching Networks

An L-network uses two reactive elements and is the simplest possible matching network. It has a fixed quality factor Q = √(R_high/R_low − 1), determined entirely by the impedance ratio. A Pi-network (two shunts flanking one series element) or T-network (two series elements flanking one shunt) uses three elements and allows the designer to choose Q freely — at the cost of one extra component. Higher Q means narrower bandwidth but better harmonic rejection. Lower Q means wideband matching with less filtering. This tool computes all valid topologies automatically.