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Specialist course

The Smith Chart: Theory and Practice

Understand how the chart is constructed, use it to design impedance matches, and follow what happens as frequency changes.

Work from reflection and impedance through transmission lines, series and shunt elements, stub matching, and complete networks. Each module combines detailed explanations, interactive exploration, worked calculations, and questions with model answers.

Structure
4 in-depth modules
Approach
Derive, explore, and apply

In preparation · Purchase access for this paid course is not open yet.

A first example

A mismatch you can place on the chart.

A 100 ohm resistive load on a 50 ohm Smith chartThe matched 50 ohm load is at the center. The 100 ohm load lies one third of the chart radius to the right, on the real axis.50 Ω · match100 ΩShortOpenReal reference impedance: 50 Ω
Purely resistive loads lie on the horizontal axis. This point is a mismatch, not a loss inside the resistor.

Connect a 100 Ω resistor to a line with a real 50 Ω reference impedance. The normalized load is zL=100/50=2z_L = 100/50 = 2.

Γ=100−50100+50=13\Gamma = \frac{100-50}{100+50} = \frac{1}{3}

The reflection coefficient is positive and real, placing the load to the right of the centre. Its VSWR is 2:1; about 11.1% of the incident power is reflected at this reference plane.

Change the load in the free explorer and watch the point move. The course develops the geometry, transformations and matching decisions behind it.

Try the Smith chart explorer

Inside the deep dive

Begin with the relationship between impedance and reflection. Then use it to calculate line and component transformations, compare matching networks, and explain their frequency response.

  1. Construct and read the chart

    Turn reflected waves into a point, build the two coordinate families, and read the map you have constructed.

  2. Transform and match with lines and series elements

    Move an observation plane, add a series reactance, and calculate two complete routes to a match.

  3. Match with admittance and shunt branches

    Read the same load in admittance, add parallel components, and place and size a transmission-line stub.

  4. Choose a network and follow its frequency response

    Combine both grids, compare matching routes, and tune a reproducible two-resonator load at two target frequencies.

Before you begin

Bring basic circuit knowledge and familiarity with frequency, algebra, and complex numbers. Prior Smith chart experience is not required. These free lessons cover the foundations:

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