Classic Smith chart for transmission line impedance matching and RF engineering.

Free printable Smith chart PDF. Constant resistance and reactance circles for transmission line analysis and impedance matching.

Smith Chart | Free Printable RF Engineering PDF

Smith Chart

Normalise the load by dividing by the characteristic impedance (e.g., 75+j25 ohms on a 50-ohm line becomes 1.5+j0.5). Find the resistance circle (R=1.5) and reactance arc (X=+0.5) and mark their intersection. That single point captures the entire mismatch problem.

Mark the load impedance first

Moving along the transmission line away from the load corresponds to rotating clockwise on the chart. One full rotation = half a wavelength of line. Mark the wavelength scale (around the chart's outer edge) and your design length in fractions of a wavelength.

Travel toward the generator

Series elements (inductor, capacitor in series) move you along the printed constant-resistance circles. Shunt (parallel) elements move you along constant-conductance circles, which are the impedance chart rotated 180°. Either flip the chart in your head, or trace a mirror-image copy as an overlay before placing the second matching element.

Trace the admittance chart by hand for shunt elements

VSWR (voltage standing wave ratio) appears as concentric circles centred on the chart origin. Trace one VSWR circle on a transparent overlay. Moving down a transmission line keeps you on that circle, since loss-less lines don't change VSWR.

Use a transparent overlay for VSWR

Distance along a transmission line corresponds to clockwise rotation around the chart, a full revolution equals half a wavelength. Tick the outer circle in 0.05 λ increments before your first plot if you need a wavelength scale.