How it works
The Smith Chart maps the complex normalised impedance z = r + jx onto the reflection coefficient plane Γ = (z−1)/(z+1). Circles of constant normalised resistance r are centred on the real axis; arcs of constant normalised reactance x are circles centred on the vertical line Re(Γ) = 1. Moving clockwise on the chart corresponds to moving away from the load toward the generator; one full revolution = λ/2 movement along the line. VSWR = (1+|Γ|)/(1−|Γ|) is read directly from the circle passing through the load point and the real axis. The centre of the chart is z = 1+j0, the perfect match point where |Γ| = 0.
Key points to remember
VSWR of 1 means perfect matching; VSWR of 2 corresponds to |Γ| = 1/3 and represents a 10% power reflection. The purely real impedance points lie on the horizontal axis; the short-circuit point (z=0) is the leftmost point and the open-circuit point (z=∞) is the rightmost. A λ/4 transformer maps the load impedance to its reciprocal in normalised form, equivalent to rotating 180° on the Smith Chart. Single-stub matching places a short-circuited stub at a specific distance from the load to cancel the imaginary part of the input admittance; double-stub matching allows the stub positions to be fixed — a practical advantage in hardware implementation.
Exam tip
Every Anna University and GATE ECE paper has a Smith Chart problem where you must find the VSWR and the distance to the first voltage maximum from a given complex load — always normalise the impedance first, then plot the point, draw the |Γ| circle, and read VSWR from where the circle crosses the right-hand real axis.