TRƯỜNG ĐẠI HỌC BÁCH KHOA ĐÀ NẴNG
KHOA ĐIỆN TỬ - VIỄN THÔNG

BÁO CÁO THÍ NGHIỆM
KỸ THUẬT SIÊU CAO TẦN
LAB 2: Basic Transmission Lines in the Frequency Domain
Student : Nguyễn Thị Bảo Trâm
Nguyễn Văn Hiếu
Group : 09A
Class : 06DT1

class="bi x8 ya w0 h0"
Đà Nẵng - 2010
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:
 Z
0
, the characteristic impedance
 T
D
, 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

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.
Nguyễn Thị Bảo Trâm - Nguyễn Văn Hiếu - 06DT1
Page 2
The inductance and capacitance per meter are:
We have:
Z 0
u p
L'

L'. C'  L'
C'
Z 0 50 ()
9
L'




0
,
1
.
1
0

(
F
/
m
)



0
,
1

(
n
F
/
m
)

.
3

0Answer:
We can see :
L'

 b  b
1

2
 b

ln
.ln
 
2 ln
 
C'
2
 a

 a

2
4

 a

2
 b
4
2


.50

a

 
2
3.10
9
7
C'
.50


0 4.10
7
3 5 3
.50

(H/m)
4
2.36.10
7
2.6
10
5 3
b 6
60 6
So,
a

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 u
p
= 2/3 c, what is the wavelength in the transmission
line? Answer: The wavelength in the transmission line is:
ߣ
ݑ
ݑ
ݑ =
2 2
3
ݑ
3×3.10
8
= 1(ݑ)
=
200.10
=

1
1
  
6

f
16f
16.200.10
10


3
.
1
2
5

1
0

(
s
)



0
.
3
1

Nguyễn Thị Bảo Trâm - Nguyễn Văn Hiếu - 06DT1
Page 5
Using Excel, make a table of the voltage magnitudes and current magnitudes at
nodes Input and Load for each length.
Line Time Input Input Load Load Input
No. Length Delay Voltage Current Voltage Voltage Impedance
(m) (ns) (mV) (mA) (mV) (mA) (Ω)
0 0.0000 0.0000 666.667 6.667 666.667 6.667 100.00 + j00.000
1 0.0625 0.3125 628.990 7.998 666.667 6.667 69.476 - j 36.845
2 0.1250 0.6250 527.046 10.541 666.667 6.667 40.000 - j 30.000
3 0.1875 0.9375 399.908 12.580 666.667 6.667 28.085 - j 14.894
4 0.2500 1.2500 333.333 13.333 666.667 6.667 25.000 - j 00.000
5 0.3125 1.5625 399.908 12.580 666.667 6.667 28.085 + j14.894
6 0.3750 1.8750 527.046 10.541 666.667 6.667 4.000+ j 03.000
7 0.4375 2.1875 628.990 7.998 666.667 6.667 69.476 + j36.845
8 0.5000 2.5000 666.667 6.667 666.667 6.667 100.00 + j00.000
9 0.5625 2.8125 628.990 7.998 666.667 6.667 69.476 - j 36.845
10 0.6250 3.1250 527.046 10.541 666.667 6.667 40.000 - j 30.000
11 0.6875 3.4375 399.908 12.580 666.667 6.667 28.085 - j 14.894
12 0.7500 3.7500 333.333 13.333 666.667 6.667 25.000 - j 00.000
13 0.8125 4.0625 399.908 12.580 666.667 6.667 28.085 + j14.894
14
0.8750
4.3750
527.046
10.541 666.667
6.667
4.000 + j 03.000
15 0.9375 4.6875
628.990

r
m
i
n
e

t
h
e

V
S
W
R
,

a
n
d

f
r
o
m

t
h
e

V

the
change of input voltage as a function of Time Delay.
We can simulate the input voltage as a function of Time Delay because Time Delay and Length
of transmission line relate together from
the formular :
TD
L
 . With u
p
is a constant, L
u p
increases n-fold as well as T
D
increases n-fold. So, examining the change of the input voltage as
a function of T
D
is like doing this with L (length of transmission line).
- With L = λ, we have :
T
L
u p

L
.f

1 1
9




0
.
1
0

So, we can establish a parameter in pspice with 0 at start value and 5ns at end
value. In
addition, we examine L at the points which are λ/16-equidistant together.
Therefore, increment in parametric sweep is 0,3125ns like above value (question 5).
- Use PSPICE to plot the magnitude of the voltage at Input as a function of length:
720mV
(2.5000n,666.667m)
600mV
(1.25
00
n,333.333m)
400mV
Length
0m
0.5m
300mV
0
0.5n 1.0n 1.5n
2.0n 2.5n 3.0n
3.5n
M(V(INPUT
))
delay
- From the Voltage Values on the
plot and the relationship:

.
3
3
3
m
V
1m
4.0n 4.5n5.0n
V max
, determine the
V min
Nguyễn Thị Bảo Trâm - Nguyễn Văn Hiếu - 06DT1
Page 7
ݑݑݑݑ =
ݑݑݑ
ݑ
ݑݑݑݑ
666.667
ݑݑ
3
3
3
.
3
3
3
ݑݑ
=

2

0 0.5n 1.0n 1.5n 2.0n 2.5n 3.0n 3.5n 4.0n 4.5n 5.0n
I(ZG)
delay
- From the Current Values on the plot, determine the VSWR, and from the VSWR
calculate
||:
I
max
= 13.3333mA
I
min
= 6.6667mA
VSWR =
I
max
I
min
1
3
.
3
3
3
3
m
A

=
6.6667mA = 2
Γ

60
40
Length
0m
0.5m
1m
20
0 0.5n 1.0n 1.5n 2.0n 2.5n 3.0n 3.5n 4.0n 4.5n5.0n
R(V(INPUT)/I(ZG))
delay
Nguyễn Thị Bảo Trâm - Nguyễn Văn Hiếu - 06DT1
Page 9
- Plot the
Imaginary
Part of the
Impedance
using
PSPICE:
40
20
0
-20
Length
0m 0.5m
1m
-40
0 0.5n 1.0n 1.5n 2.0n 2.5n 3.0n 3.5n 4.0n 4.5n5.0n
IMG(V(INPUT)/I(ZG))
delay
Question 9: Using the scales at the bottom of the Smith Chart, find the VSWR and |