TR NG Đ I H C BÁCH KHOA ĐÀ N NG ƯỜ Ạ Ọ Ẵ
KHOA ĐI N T - VI N THÔNG Ệ Ử Ễ

BÁO CÁO THÍ NGHIỆM
K THU T SIÊU CAO T N Ỹ Ậ Ầ
LAB 2: Basic Transmission Lines in the Frequency Domain
Student : Nguy n Th B o Trâmễ ị ả
Nguy n Văn Hi uễ ế
Group : 09A
Class : 06DT1
Đà N ng - 2010 ẵ
In this laboratory experiment, you will use SPICE to study sinusoidal waves on lossless
transmission lines. Our goal is for you to become familiar with the basic behavior of waves
reflecting from loads in transmission lines, and compare the simulations with numeric
calculations and the Smith Chart.
2.1 Basic Transmission Line Model
There is a standard lossless transmission line model T, which is specified by several
parameters. We will need to specify two of the parameters:
Z0, the characteristic impedance
TD, the time delay, which is the length of the line in time units. The
length of the line L is related to the time delay through
Lu
T
p D
(2.1)
where up is the phase velocity of waves on the transmission line.
As we saw in lecture and in our text, the phase velocity and characteristic impedance may be
derived from the “lumped element” model of the transmission line. With L’ the inductance per unit
length, and C’ the capacitance per unit length, we have
u
p
1(2.2)
L'C'
L'
Z0
2.1.1 A standard coaxial cable
C'
(2.3)
For common RG-58 coaxial cable, the characteristic impedance is Z0 = 50 and the phaseΩ
velocity up = 2/3 c. (Note: c = speed of light = 3e8 m/s)
Question 1: For such a transmission line, what are the inductance and capacitance per meter?
Answer:
- Transmission line is often schematically represented as a two-wire line, so transmission lines
(TEM wave propagation) always have at least two conductors.
i(z,t)
+
v(z,t)
-
∆z z
- Inductance per meter ( H/m ) :
+ It is the series inductance per unit length, it appears from the shape of transmission line.
Inductance per meter represents the self-inductance of the two conductors per a meter, it also
represents the stored magnetic energy per a meter of transmission line.
- Capacitance per meter ( F/m ) :
+ It is the shunt capacitance per unit length, it is due to the close proximity of the two
conductors, it also represents the stored electric energy per a meter of transmission line.
Nguy n Th B o Trâm - Nguy n Văn Hi u - 06DT1 ễ ị ả ễ ế
Page 2
The inductance and capacitance per meter are:
We have: Z
0
u
p
L'
L'. C' L'
C'
Z 050 ()
9
L'
u p
2
3
250.10
8
.3.10 (m/s)
(H/m)
250 (nH/m)
And: Z0.u p
1
L' 1 1
C' L'. C' C'
1
9
C'
Z
0
u
p
50(). 2
3
0,1.10 (F/m)
0,1 (nF/m)
.3.10
8
(m/s)
For lossless coaxial cables, the following formulas relate the differential inductance L’ and
capacitance C’ to the radius of the inner conductor a and the outer conductor b:
L'
2
b
ln
(2.4)
a
C'
2
(2.5)
b
ln
a
Question 2: For a different coaxial cable, μ = μ0 and ε = 3ε0. What is b/a if Z0 = 50 ?Ω
Answer:
We can see : L'
b b
1
2
b
ln
.ln
2ln
C'
2
a
a
2
4
a
2
b
4
2
L'
ln
b
2
L'
ln
 
 
a
C'
2..
3.
2
3
0.Z0
10
9
(F/m)
9
36
2
3.10
.50()
.50
a
2
3.10
9
7
C'
.50
04.10
7
3 5 3
.50
(H/m)
4
2.36.10
7
2.6
10
5 3
b6
60 6
So, a
e
4,235
Nguy n Th B o Trâm - Nguy n Văn Hi u - 06DT1ễ ị ả ễ ế
Page 3
Question 3: If b = 3 mm in question 2.2, what is a?
Answer: If b = 3mm in question 2.2 then:
a
b
4,235
3 (mm)
0,708 (mm)
4,235
2.2 A SPICE model of a transmission line problem.
Using SPICE, create a (matched) Thevenin source VAC with 1 Volt amplitude and 50 Ω
source impedance, leading to a transmission line model T, terminated in a 100 load. Edit the Ω
transmission line so that it has a characteristic impedance of 50 . Also, create labels Input and Ω
Load at the ends of the transmission lines, so that you can measure the voltages conveniently.
ZG
Input
50
1Vac
0Vdc VG
0 0
T1
ZL
Load
100
Z0 = 50
TD = {delay }
PARAMETERS:
delay = 5ns
0 0
Figure 1. Circuit Schematic for Part 2.2
What we would like to do is to adjust the length of the transmission line and examine the
standing wave pattern at Input over one full wavelength at a frequency of 200MHz.
Question 4: At 200 MHz, and with up = 2/3 c, what is the wavelength in the transmission line?
Answer: The wavelength in the transmission line is:
=ߣ
=
2 2
3
× .3 3 10
8
/
= (1)
=
.200 106
Question 5: What is the time delay associated with /16?λ
(Hint: Remember that TD
L
u p
L
f)
Answer: The time delay associated with /ߣ 16 is:
TD
L
u p
L

f
16
1 1
6
f
16f
16.200.10
10
3.12510 (
s)
0.3125(ns)
Hz
Use SPICE to simulate the steady state AC response of this transmission line for length 0,
/16, 2 /16, …, 15 /16, . Center your sweep on the frequency of interest and sweep linearly. λ λ λ λ