Microwave Engineering
CHO, Yong Heui
EM Wave Lab
2
Filter
Oscillator
Frequency meter
Tuned amplifier
Input impedance
Input power
Resonant frequency: Wm = We
C L j
j
Z
in
C
L j j
I I
Z VI
P
in * in 2 2
2 1 2
1 2
1
LC
1
EM Wave Lab
4
R, L, C
Input impedance
Input power
Resonant frequency
C L j
j R
Z
in
C
L j j
R I
I Z
VI
P
in * in 2 2
2 1 2
1 2
1
LC
1
Definition
3 dB bandwidth
Q in terms of R, L, C
d loss/secon Energy
stored energe
Average
Q
BW f
0Q
RC R
L P
Q W
l m
0 0
0
2 1
EM Wave Lab
6
Input impedance
R j L R j L
Z
22
2 0 2
in
R, L, C
Input admittance
Input power
Resonant frequency
C L j
j
Y R
1
in
j C
L j V R
V Y
VI
P
1
2 1 2
1 2
1
* 2 2in
* in
LC
1
EM Wave Lab
8
Q in terms of R, L, C
L RC R
P Q W
l m
0 0
0
2
Input admittance
j C
C R R j
Y 1 1 2
2 2 0 2
in
EM Wave Lab
10
Unloaded Q: resonant circuit itself
Loaded Q: External load resistor
Q Q
Q
L e1 1
1
Transmission line
Input impedance: lossy medium
) tanh(
) tan(
1
) tan(
) tanh(
tanh
0
0 in
l l
j
l j
Z l
l j
Z Z
EM Wave Lab
12
Low-loss transmission line
Phase:
l l
) tanh(
2 /
0
,
l
0 0
) tan(
)
tan(
l
Input impedance
Quality factor
jL R
j l
l Z j
j Z l
Z
2
) /
( 1
) /
(
0 0
0 0 0
in
2 2
0
R l
Q L
EM Wave Lab
14
Transmission line
Input impedance: lossy medium
) tan(
) tanh(
) tanh(
) tan(
1
coth
0
0 in
l j
l
l l
Z j
l j
Z Z
Low-loss transmission line
Phase:
l l
) tanh(
2 /
0
,
l
0 0
) tan(
)
tan(
l
EM Wave Lab
16
Input impedance
Quality factor
jC R
j l
Z j
l
l Z j
Z
2 /
1
1
) /
( )
/ (
) /
( 1
0 0
0 0 0
in
2
0
2
RC l
Q
Metallic wall
Propagation constant
Resonant condition
2 2
2
b
n a
k m
mn
mnd l
EM Wave Lab
18
Resonant wavenumber
TE101 mode and TM110 mode
Q of cavity
2 2 2
d l b
n a
k
mnlm
l e
P Q 2 W
0
Metallic wall
Propagation constant
Resonant condition
TE111 mode and TM110 mode
mnd l
EM Wave Lab
20
High Q
Fringing field
High permittivity: magnetic wall
Mechanical tuning
TE01d mode
Notation
1 /
2
L
gd
Two mirrors
High Q
Laser
Millimeter and optical applications