GW Instek GRF-3300 Series Student Manual - Manual (Page 4)

GRF-3300 Manual
3 312
z
O
z
O
e I e I z I
J J     
) ( (16-2)
the complex propagation constant as:
) )( ( C j G L j R j
Z Z E D J   
(16-3)
The characteristic impedance Zo can be defined as:




Io
Vo
Io
Vo
Zo
C j G
L j R jL R
Y
Z
J 
 
(16-4)
From the electromagnetic theory, we know:
PH
X
U
1
dt
dz
(16-5)
where
P is the permeability and H is permittivity of the medium. In free space, we
have sec / 10 998 . 2 / 1 8 m c
O O
u H P X
U
, which is the speed of light..
For the transmission line, the phase velocity is
r O O
H H P X
U
/ 1 , (16-6)
r
H
is the relative permittivity, also known as dielectric constant of the medium
(substrate of the PCB).
We can find the wavelength as:
f
U
X
O
(16-7)
and the wave number:
O
E
f
=2S/E (16-8)
where
D is the attenuation constant, and E is the wave number.