Lecture 12 Smith Chart & VSWR

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

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 0 Short circuit Open circuit Im{Z}   when z = 0, -/2,… open circuit every half wavelength z 0 - In general: -j < Z(-D) < +j (can get ANY desired capacitance or inductance at a SINGLE w)

L Zo ? o z l/4 0 Examples of Z(z) transformations (cont) Example: half-wave and quarter-wave lines: Zo ZL ? z 0 Example: quarter-wave with inductive load:

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

Voltage Standing Wave Ratio (VSWR) + ZL Zo,n V(z) - z Im{} 0 toward z=-D Re{} -1 z 0 -D

Lecture 12 Smith Chart & VSWR