Enter Impedance and Line Values
Use positive reactance for inductive loads. Use negative reactance for capacitive loads.
Interactive Smith Chart View
The graph uses the reflection coefficient plane. Grid curves represent common normalized resistance and reactance families.
Compact Output Table
| Metric | Value |
|---|---|
| Load impedance | 75.0000 + j25.0000 Ω |
| Normalized impedance z | 1.5000 + j0.5000 |
| Normalized admittance y | 0.6000 - j0.2000 |
| Reflection coefficient Γ(load) | 0.230769 + j0.153846 |
| |Γ| | 0.277350 |
| Angle of Γ(load) | 33.69° |
| VSWR | 1.7676 |
| Return loss | 11.1394 dB |
| Mismatch loss | 0.3476 dB |
| Wavelength | 0.197863 m |
| Electrical length βl | 1.587761 rad |
| Input impedance Zin | 29.8029 - j9.4231 Ω |
| Normalized input impedance zin | 0.5961 - j0.1885 |
| Normalized input admittance yin | 1.5252 + j0.4822 |
| Reflection coefficient Γ(input) | -0.235855 - j0.145929 |
| Angle of Γ(input) | -148.25° |
| Reflected power | 7.6923 W |
| Delivered power | 92.3077 W |
Sample Engineering Case
| R (Ω) | X (Ω) | Z0 (Ω) | f (MHz) | Length (m) | VF | |Γ| | VSWR | Input Impedance Zin |
|---|---|---|---|---|---|---|---|---|
| 75 | 25 | 50 | 1000 | 0.05 | 0.66 | 0.2774 | 1.7676 | 29.8029 - j9.4231 Ω |
| 25 | -15 | 50 | 2400 | 0.02 | 0.80 | 0.4020 | 2.3445 | 31.1810 + j16.4920 Ω |
| 50 | 0 | 50 | 900 | 0.10 | 0.66 | 0.0000 | 1.0000 | 50.0000 + j0.0000 Ω |
Core Smith Chart Equations
1. Normalized impedance: z = ZL / Z0
2. Reflection coefficient: Γ = (z - 1) / (z + 1)
3. Normalized admittance: y = 1 / z
4. VSWR: VSWR = (1 + |Γ|) / (1 - |Γ|)
5. Return loss: RL = -20 log10(|Γ|)
6. Mismatch loss: ML = -10 log10(1 - |Γ|²)
7. Wavelength: λ = c × VF / f
8. Phase constant: β = 2π / λ
9. Input impedance of a lossless line:
Zin = Z0 × (ZL + jZ0 tan(βl)) / (Z0 + jZL tan(βl))
10. Reflection coefficient rotation: Γin = ΓL × e-j2βl
Simple Workflow
- Enter the load resistance and reactance in ohms.
- Enter the transmission line characteristic impedance.
- Set the working frequency in megahertz.
- Enter the physical line length in meters.
- Provide the velocity factor for the cable.
- Optionally enter source power for reflected and delivered power values.
- Press Calculate Smith Chart Values.
- Review the result cards, output table, and chart trace.
- Download the summary using the CSV or PDF buttons.
Frequently Asked Questions
1. What does the Smith chart calculator show?
It converts load impedance into normalized impedance, reflection coefficient, admittance, VSWR, return loss, mismatch loss, and transformed input impedance. It also plots the reflection point and line rotation path on an interactive chart.
2. Why is normalization important?
Normalization divides the load impedance by the line impedance. That step makes different systems directly comparable. It also places the impedance on the standard Smith chart coordinate system.
3. What does a negative reactance mean?
Negative reactance represents capacitive behavior. Positive reactance represents inductive behavior. The sign changes the point location on the lower or upper half of the chart.
4. Why does the plotted point rotate with line length?
Moving along a lossless line changes the phase of the reflection coefficient. The magnitude stays constant, so the point rotates around the chart center instead of moving inward or outward.
5. What is a good VSWR value?
A VSWR close to 1 is best. Many RF systems target 1.5 or less. Acceptable limits depend on the application, bandwidth, power level, and component tolerance.
6. How is return loss different from mismatch loss?
Return loss describes reflected signal magnitude in decibels. Mismatch loss estimates usable power reduction caused by the reflection. Both depend on the reflection coefficient magnitude.
7. Can this tool model lossy transmission lines?
This version uses the standard lossless line impedance transformation. It is suitable for many design checks. For long or highly lossy cables, attenuation should be included separately.
8. What if the load already equals the line impedance?
Then the normalized impedance is 1 + j0. The reflection coefficient becomes zero, VSWR becomes 1, return loss approaches infinity, and the point sits at the chart center.