Smith Chart Explorer
Move between normalized impedance, admittance, and reflection-coefficient views analytically.
- Typical inputs
- Complex impedance, admittance, or Γ and an arbitrary positive real reference impedance.
- Calculated output
- Normalized z/y, Γ, VSWR, return loss, and stored comparison points.
- Model status
- Release B · documented and numerically tested
Where does this impedance map in the reflection-coefficient plane?
Analytic Smith chart
Exact inputs are authoritative; pointer movement is a convenient constrained Γ control. Stored points remain only in this bounded page session.
The point is in the inner half on the real axis. Moving the reference plane on a lossless line rotates it without changing |Γ|.
- Impedance Z
- 100.00000 + j0.00000 Ω
- Normalized z
- 2.00000 + j0.00000
- Admittance Y
- 10.00000 + j0.00000 mS
- Normalized y
- 0.50000 + j0.00000
- VSWR
- 2.00000
- Return loss
- 9.54243 dB
- Mismatch loss
- 0.51153 dB
- Reference plane
- Z₀ = 50.0000 Ω
| Point | Γ real | Γ imaginary | |Γ| | Phase |
|---|---|---|---|---|
| Current | 0.333333 | 0.000000 | 0.333333 | 0.000° |
Calculation path
- For the e^(jωt) convention, moving toward the generator rotates Γ clockwise; toward the load rotates it counter-clockwise.
What this calculator is doing
The chart is the unit-circle mapping Γ = (z−1)/(z+1). Analytic constant-resistance and constant-reactance loci accompany pointer-to-Γ conversion.
How to read the result
Read the chart as a transformation plane, not a component value. Retain the reference impedance and reference-plane location with every point.
Equations & conventions
- z = Z/Z0 is normalized impedance; y = 1/z is normalized admittance.
- The chart centre is Γ = 0 and its boundary is |Γ| = 1.
- Z0 is a positive real normalization impedance.
Independently checked example
Checked example: 100 + j0 Ω normalized to 50 Ω is z = 2 + j0 and Γ = 0.333333 + j0 at VSWR 2.
Common mistakes
- Reading an unlabelled point without knowing Z0.
- Treating chart grid lines as measured accuracy.
Assumptions, validity & omissions
- Z₀ is positive and real.
- Passive positive-resistance loads map inside the unit circle.
- Chart geometry is analytic; the grid is not measured data.
Sources & model provenance
- Keysight, S-Parameter Design Techniques (opens in a new tab) — Traveling-wave, transmission-line, and Smith-chart foundations. Accessed 2026-09-05.
- Keysight, Understanding the Fundamental Principles of Vector Network Analysis (opens in a new tab) — Reflection, S-parameters, Smith charts, and group delay. Accessed 2026-09-05.