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

2. 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)

3. 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

4. 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= /  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

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