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ECE 391 supplemental notes - #4
72 Oregon State University ECE391– Transmission Lines Spring Term 2014
Transmission Line Circuit
Tx Rx T-Line
nonlinear source characteristic
nonlinear load characteristic
V
I
V
I
I I
V + _ V
+ _
2
73 Oregon State University ECE391– Transmission Lines Spring Term 2014
Nonlinear Terminations RS
VS
Z0, td!
NL
§ Need to consider total voltage and total current at each reflection instance
§ Use I-V characteristics of devices and transmission-line circuit
§ Graphical solution based on Bergeron method
74 Oregon State University ECE391– Transmission Lines Spring Term 2014
Review – Load-Line Method
RS
VS + _
V
I
VS
VS/RS I
V
+
_
load characteristic
source characteristic
VOP
IOP
3
75 Oregon State University ECE391– Transmission Lines Spring Term 2014
Application to TL Circuit RS
VS
Z0, td!
Load
I
V
+
_ Load
I
V
+
_
RS
+ _ VS
At times !t = td, 3td, … (2n-1)td …
At times !t = 0, 2td, … (2n-2)td, …
In+ = Vn
+
Z0In− = −Vn
−
Z0n = 1, 2, 3, …
76 Oregon State University ECE391– Transmission Lines Spring Term 2014
Understanding “Wave Load Line”
Z0
2Vinc + _
I
V
+
_ Load
I1− = −V1
− Z0
I − I1+ = −V −V1
+
Z0
I = −V − 2V1+
Z0
1st Returning Wave
slope=-1/Z0
V
I
I1+
V1+ 2V1
+
4
77 Oregon State University ECE391– Transmission Lines Spring Term 2014
Example – Resistive Termination RS
VS
Z0, td!
RL
100Ω
200Ω
50Ω
6V
ρS =13 ρL =
35
z
t/td
4
3
2
1
0
78 Oregon State University ECE391– Transmission Lines Spring Term 2014
Example (cont’d)
V
I
VS
VS/RS
I∞
source characteristic
V∞
slope=1/RL
slope=-1/RS
∞
load characteristic
5
79 Oregon State University ECE391– Transmission Lines Spring Term 2014
Near End at t = 0
V
I
VS
VS/RS source characteristic
I1+ =V1
+ Z0I =V Z0
V1+
I1+ A
∞
load characteristic
slope=1/RL
slope=-1/RS
80 Oregon State University ECE391– Transmission Lines Spring Term 2014
Far End at t = td
V
I
VS
VS/RS
load characteristic
source characteristic
I1− = −V1
− Z0
A
B ∞
I − I1+ = −V −V1
+
Z0
slope=1/RL
slope=-1/RS
I1+ + I1
−
V1+ +V1
−V+1
I+1
6
81 Oregon State University ECE391– Transmission Lines Spring Term 2014
Near End at t = 2td
V
I
VS
VS/RS
load characteristic
source characteristic
A
B ∞ C
slope=1/RL
slope=-1/RS I2+ =V2
+ Z0
I − I1+ − I1
− = V −V1+ −V1
−
Z0
I1+ + I1
−
+I2+
V1+ +V1
− +V2+
82 Oregon State University ECE391– Transmission Lines Spring Term 2014
Bergeron Method ― Linear Load
source characteristic
load characteristic
V∞
I∞
slope 1/Z0
slope -1/Z0
Vo,1
7
83 Oregon State University ECE391– Transmission Lines Spring Term 2014
Bergeron Method ― Nonlinear Load
source characteristic
load characteristic
84 Oregon State University ECE391– Transmission Lines Spring Term 2014
Example
