Lecture 12 Smith Chart & VSWR 6.013 ELECTROMAGNETICS AND APPLICATIONS Luca Daniel Lecture 12 Smith Chart & VSWR

Examples of Z(z) transformations Example: Open Circuit Load, ZL = : capacitor Co 0 when z = -/4, -3/4,… z short circuit every half wavelength z =-D Open circuit Short circuit Im{Z}   when z = 0, -/2,… open circuit every half wavelength z - In general: -j < Z(-D) < +j (can get ANY desired capacitance or inductance at a SINGLE w)

Examples of Z(z) transformations (cont) Example: half-wave and quarter-wave lines: Zo ? ZL z Example: quarter-wave with inductive load: Zo z l/4 ? L o

Alternative approach to finding Z(z) I(z) (1) Normalize Load: + V(z) Zo,n ZL - (2) z Compute reflection coef: z = - D Z(z) or “find” it on the  plane (Smith Chart) (3) “Rotate” reflection coef. Im{} (toward generator clockwise)  = j Im{Zn}=+j inductor (D= /2  full rotation) Re{Zn}=3 Re{Zn} = 0 Re{Zn}=1 Im{Zn}=0 resistor (4) Compute Normalized Line Impedance  = 1  = -1 Re{}  = 0 Zn = 0 short Zn = 1 Z =Z0 Zn =  open or “read” it from Smith Chart Im{Zn} = -j capacitor (5) “Un-Normalize” Line Impedance toward z=-D  = -j

Voltage Standing Wave Ratio (VSWR) + V(z) Zo,n ZL - z Im{} toward z=-D Re{} -1 z -D