ECE 113
1s1617
Revision October 2016
Lecture 5: Network Analysis
References: Pozar, Chapter 4
Circuits at LOW frequencies
•
Circuit dimensions are small relative to wavelength (λ = c/f)
o
e.g. @ f = 100 kHz , λ
≈ 3 km
•
Treat as interconnection of lumped passive/active elements
•
Voltages and Currents defined at any point in the circuit
o
Use KCL, KVL, and Ohm’s Law to analyze these circuits
We are familiar with…
Measurement of total voltage
and/or cu
rrent is
difficult (or almost imposs
ible)
•
Circuit dimension is comparable to wavelength
o
e.g. @ f = 1 GHz , λ
≈ 30 cm
•
Measurements require clearly defined terminal
pairs
•
Complete circuit analysis requires solving
Maxwell’s Equations
For RF/Microwave Circuits…
It is more convenient to express our circuits
(networ
ks)
in terms of traveling waves (incident and
reflected waves
)
•
Recall from introduction to reflection coefficient
(last lectures of EEE 53) that
total voltage at high
frequencies can be expressed as the sum of
incident and reflected waves
OUR GOAL:
Convert representation in terms of
traveling waves to conventional low
frequency models
At high frequencies…
•
Once traveling wave voltages and currents have
been defined at various points in
an RF/Microwave
network, we a
re able to relate these
terminal
or
“port”
quantities to each other
•
This results in a matrix description of our N-port
network
•
Useful when we discuss high-frequency
representations of our active networks
N-Port Network Parameters
N-Port Network
𝑉𝑉
2
=
𝑉𝑉
2
+
+
𝑉𝑉
2
−
𝑉𝑉
1
=
𝑉𝑉
1
+
+
𝑉𝑉
1
−
𝑉𝑉
3
=
𝑉𝑉
3
+
+
𝑉𝑉
3
−
𝑉𝑉
4
=
𝑉𝑉
4
+
+
𝑉𝑉
4
−
𝑉𝑉
𝑁𝑁
=
𝑉𝑉
𝑁𝑁
+
+
𝑉𝑉
𝑁𝑁
−
