ADAMSON UNIVERSITY
College of Engineering
Electronics and Communications Engineering Department
7
Experiment No.
Smith Chart
Monday, 7:00AM – 10:00AM
3
SCHEDULE
TRANSMISSION MEDIA AND ANTENNA SYSTEM
(LABORATORY)
Group No.
ATTENDANCE
SUBJECT
NAME
CONTRIBUTION
Conclusion & Questions
Analysis, Questions & History
Questions
Questions & Q&P
Questions
Definitions, Application &
Questions
NERIE, TRISHA CAMILLE L.
March 21, 2022
REMARKS
Compilation, Discussion &
Q&P
GIRON, GERICO G.
GUEVARRA, JOHN MICO R.
LANSANG, JOANA SONETTE B.
LORZANO, DARYL KHENT A.
LUYUN, JORGE MATTHEW V.
MADRIGAL, JOHN FRANCIS S.
D.O.P.
Grade
D.O.S.
BERNADETH B. ZARI, PECE
Instructor
April 18, 2022
SMITHS CHART
ACTIVITY 1
INTRODUCTION TO SMITH CHART
I.
DEFINITION OF SMITH CHART
For arbitrary impedance, it's a polar plot of the complex reflection
coefficient. It was created to solve complicated math problems involving
transmission lines and matching circuits, but it was replaced by computer
software. However, the Smith charts method of displaying data has maintained its
popularity over time, and it is still the preferred approach for illustrating how RF
parameters react at one or more frequencies, with tabulating the data as an option.
II.
HISTORY OF SMITH CHART
Inventor: Philip H. Smith
Date developed: January 1939
Source: http://smithchart.org/phsmith.shtml
III.
APPLICATION OF SMITH CHART

Calculations of impedance on any transmission line with any load.

Calculations of admittance on any transmission line, with any load.

Calculation of the length of a short circuited transmission line in order to achieve
the requisite capacitive or inductive reactance.

Determine VSWR

Impedance matching
SMITHS CHART
IV.
ACTIVITY 1
ATTACH COPY OF SMITH CHART
Figure 1. Smith Chart (developed by P. H. Smith, useful for transmission line analysis).
SMITHS CHART
V.
ACTIVITY 1
IDENTIFY AND DISCUSS THE PARTS OF SMITH CHART
I.
Define normalizing
Normalizing is a process of dividing impedances by the line's characteristic
impedance. It is used to plot on smith chart to find the input impedance as a
function of the length of the line. Smith charts are in what is called normalized
form, with R 5 1 at the prime center. Users customize the Smith chart for specific
applications by assigning a different value to the prime center.
II.
Write down the formula in normalizing impedance. (Define the variables
used)
𝑍𝐿
z=
Zo
Where:
z = Normalized impedance
ZL = Load impedance
Zo = Characteristic impedance
III.
Write down the formula in normalizing admittance. (Define the variables
used)
y=
𝑌𝐿
Yo
Where:
y = Normalized admittance
YL = Load admittance
Zo = Characteristic admittance
Reference: Miller, G. (Modern Electronic Communication, 9 th Edition)
SMITHS CHART
IV.
ACTIVITY 1
Normalize and plot the given load impedance.
Note: The characteristic of the line (Zo) is normally 50Ω.
A. 100 + j25 Ω (Giron, Gerico)
Plate 1.1. Smith Chart Plot for 𝑍𝐿 = 100 + j25 Ω
Solution:
z=
ZL 100 + j25Ω
=
= 2+j0.50 Ω
Zo
50Ω
SMITHS CHART
ACTIVITY 1
B. 50 + j75 Ω (Guevarra, John Mico)
Plate 1.2. Smith Chart Plot for 𝑍𝐿 = 50 + j75 Ω
Solution:
z=
ZL 50 + j75 Ω
=
=1+j1.5 Ω
ZO
50 Ω
SMITHS CHART
ACTIVITY 1
C. 150 + j75 Ω (Lansang, Joanna Sonette)
Plate 1.3. Smith Chart Plot for 𝑍𝐿 = 150 + j75 Ω
Solution:
z=
ZL
Zo
=
150 + j75 Ω
= 3+j1.5 Ω
50Ω
SMITHS CHART
ACTIVITY 1
D. 50- j50 Ω (Lorzano, Daryl Khent)
Plate 1.4. Smith Chart Plot for 𝑍𝐿 = 50 – j50 Ω
Solution:
z=
ZL 50-j50Ω
=
= 1-j1 Ω
Zo
50Ω
SMITHS CHART
ACTIVITY 1
E. 25 – j100 Ω (Luyun, Jorge Matthew)
Plate 1.5. Smith Chart Plot for 𝑍𝐿 = 25 – j100 Ω
Solution:
𝑍
z = 𝑍𝐿 =
𝑜
25 – j100 Ω
50
= 0.5 - j2 Ω
SMITHS CHART
ACTIVITY 1
F. 100 - j50 Ω (Madrigal, John Francis)
Plate 1.6. Smith Chart Plot for 𝑍𝐿 = 100 – j50 Ω
Solution:
z=
ZL 100 - j50Ω
=
= 2+j1 Ω
Zo
50Ω
SMITHS CHART
ACTIVITY 1
G. 75 + j100 Ω (Nerie, Trisha Camille)
Plate 1.7. Smith Chart Plot for 𝑍𝐿 = 75 + j100 Ω
Solution:
ZL 75 + j100
=
= 1.5+j2 Ω
Z0
50
SMITHS CHART
ACTIVITY 1
V. SWR DETERMINATION:
To determine the SWR draw a circle through the point and use the chart
center as the circle’s center. If the load is resistive and matched to the characteristic
impedance of the line, the standing wave ratio is 1. This is plotted as a single point
at the prime center of the Smith chart. Wherever the circle drawn through ZL for a
transmission line crosses the right hand horizontal line through the chart center,
that point is the VSWR that exists on the line. The circle drawn through a line’s
load impedance is often called its VSWR circle.
The linear scales printed at the bottom of Smith charts are used to find the
SWR, dB loss, and reflection coefficient. For example, to use the linear SWR scale,
simply draw a straight line tangent to the SWR circle and perpendicular to the
resistance line on the left side of the Smith chart.
Figure 2. Smith Chart Linear Scales (SWR)
Figure 3. Example of Smith Chart SWR determination (the SWR is 2)
SMITHS CHART
ACTIVITY 1
Determine the VSWR using Smith chart of the given load impedance above.
A. 100 + j25 Ω (Giron, Gerico)
Plate 2.1. Smith Chart Plot for 𝑍𝐿 = 100 + j25 Ω (determining the SWR)
Computation:
Γ=
ZL - Z0 (100+j25Ω)-50Ω
=
=0.3676∠0.2985
ZL+Z0 (100+j25Ω)+50Ω
SWR =
1+|Γ| 1+|0.3676|
=
= 2.1626
1-|Γ|
1-|0.3676|
SMITHS CHART
ACTIVITY 1
Measuring the VSWR in the simulation given the load impedance,
Figure 4. The measured SWR is 2.16
Table 1.1. Data obtained for the SWR measurement of the given load impedance.
Parameter
Measured
Calculated
% Difference
SWR
2.16
2.1626
0.12 %
SMITHS CHART
ACTIVITY 1
B. 50 + j75 Ω (Guevarra, John Mico)
Plate 2.2. Smith Chart Plot for 𝑍𝐿 = 50 + j75 Ω (determining the SWR)
Computation:
Γ=
ZL - Z0 (50+j75Ω)-50Ω
=
=0.6 ∠ 53.13o
ZL +Z0 (50+j75Ω)+50Ω
SWR =
1+|Γ| 1+|0.6 |
=
=4
1-|Γ|
1-|0.6 |
SMITHS CHART
ACTIVITY 1
Measuring the VSWR in the simulation given the load impedance,
Figure 5. The measured SWR is 4.00
Table 1.2. Data obtained for the SWR measurement of the given load impedance.
Parameter
Measured
Calculated
% Difference
SWR
4.00
4.00
0%
SMITHS CHART
ACTIVITY 1
C. 150 + j75 Ω (Lansang, Joanna Sonette)
Plate 2.3. Smith Chart Plot for 𝑍𝐿 = 50 + j75 Ω (determining the SWR)
Computation:
Γ=
ZL - Z0 (150+j75Ω)-50Ω
=
=0.5852 ∠ 16.3139o
(
)
ZL +Z0 150+j75Ω +50Ω
SWR =
1+|Γ| 1+|0.5852 |
=
= 3.8216
1-|Γ|
1-|0.5852 |
SMITHS CHART
ACTIVITY 1
Measuring the VSWR in the simulation given the load impedance,
Figure 6. The measured SWR is 3.82
Table 1.3. Data obtained for the SWR measurement of the given load impedance.
Parameter
Measured
Calculated
% Difference
SWR
3.82
3.8216
0.04 %
SMITHS CHART
ACTIVITY 1
D. 50- j50 Ω (Lorzano, Daryl Khent)
Plate 2.4. Smith Chart Plot for 𝑍𝐿 = 50 – j50 Ω (determining the SWR)
Computation:
Γ=
ZL - Z0 (50-j50Ω)-50Ω
=
=0.4472 ∠-63.43
ZL +Z0 (50-j50Ω)+50Ω
SWR =
1+|Γ| 1+|0.4472 |
=
= 2.6179
1-|Γ|
1-|0.4472 |
SMITHS CHART
ACTIVITY 1
Measuring the VSWR in the simulation given the load impedance,
Figure 7. The measured SWR is 2.62
Table 1.4. Data obtained for the SWR measurement of the given load impedance.
Parameter
Measured
Calculated
% Difference
SWR
2.62
2.6179
0.08 %
SMITHS CHART
ACTIVITY 1
E. 25 – j100 Ω (Luyun, Jorge Matthew)
Plate 2.5. Smith Chart Plot for 𝑍𝐿 = 25 – j100 Ω (determining the SWR)
Computation:
Γ=
ZL - Z0 (25-j100Ω)-50Ω
=
=0.8246 ∠ -50.9061
ZL+Z0 (25-j100Ω)+50Ω
SWR =
1+|Γ| 1+|0.8246 |
=
= 10.4025
1-|Γ|
1-|0.8246 |
SMITHS CHART
ACTIVITY 1
Measuring the VSWR in the simulation given the load impedance,
Figure 8. The measured SWR is 10.40
Table 1.5. Data obtained for the SWR measurement of the given load impedance.
Parameter
Measured
Calculated
% Difference
SWR
10.40
10.4025
0.02 %
SMITHS CHART
ACTIVITY 1
F. 100 – j50 Ω (Madrigal, John Francis)
Plate 2.6. Smith Chart Plot for 𝑍𝐿 = 100 – j50 Ω (determining the SWR)
Computation:
Γ=
ZL - Z0 (100 – j50Ω)-50Ω
=
=0.45∠-63.43
ZL +Z0 (100 – j50Ω)+50Ω
SWR =
1+|Γ| 1+|0.45 |
=
= 2.64
1-|Γ|
1-|0.45 |
SMITHS CHART
ACTIVITY 1
Measuring the VSWR given the load impedance,
𝑍𝐿 = 100 − 𝑗50 𝛺; 𝑍𝑜 = 50 𝛺
𝑍′𝐿 = 2 − 𝑗1
𝑧 = 0.4 + 𝑗0.2
𝑍𝑖𝑛 = 50(0.4 + 𝑗0.2)𝛺 = 20 + 𝑗10 𝛺
𝑽𝑺𝑾𝑹 = 𝟐. 𝟔𝟓
𝛤 = 0.45
Table 1.6. Data obtained for the SWR measurement of the given load impedance.
Parameter
Measured
Calculated
% Difference
SWR
2.65
2.64
1.55 %
SMITHS CHART
ACTIVITY 1
G. 75 + j100 Ω (Nerie, Trisha Camille)
Plate 2.7. Smith Chart Plot for 𝑍𝐿 = 75 + j100 Ω (determining the SWR)
Computation:
Γ=
ZL - Z0 (75 + j100Ω)-50Ω
=
=0.6439∠-114.6236
ZL +Z0 (75 + j100Ω)+50Ω
SWR =
1+|Γ| 1+|0.6439|
=
= 4.6164
1-|Γ|
1-|0.6439|
SMITHS CHART
ACTIVITY 1
Measuring the VSWR in the simulation given the load impedance,
Figure 9. The measured SWR is 4.62
Table 1.7. Data obtained for the SWR measurement of the given load impedance.
Parameter
Measured
Calculated
% Difference
SWR
4.62
4.6164
0.08 %
SMITHS CHART
ACTIVITY 1
VI. REFLECTION COEFFICENT DETERMINATION
A. Discuss the determination of reflection coefficient using Smith chart
We all know that the reflection coefficient is the ratio of reflected wave to
incident wave. This value varies from -1 (for short load) to +1 (for open load), and
becomes 0 for matched impedance load. To determine this using smith chart, same
as the SWR, draw a circle plotted as a single point at the prime center of the Smith
chart. From the VSWR circle, draw a straight line tangent to the SWR circle and
perpendicular to the resistance line on the left side of the Smith chart until the line
passes the reflection coefficient linear scales.
Figure 10. Smith Chart Linear Scales (Reflection Coefficient)
Figure 11. Example of Smith Chart Reflection Coefficient determination (the Reflection
Coefficient is 0.64)
SMITHS CHART
ACTIVITY 1
B. Determine the Reflection Coefficient of the given load impedance above.
A. 100 + j25 Ω (Giron, Gerico)
Plate 3.1. Smith Chart Plot for 𝑍𝐿 = 100 + j25 Ω (determining the Reflection Coefficient)
Computation:
Γ=
(100+j25Ω) - 50Ω
ZL - Z0
=
= 0.3676∠0.2985
ZL + Z0 (100+j25Ω) + 50Ω
SMITHS CHART
ACTIVITY 1
Measuring the Reflection Coefficient in the simulation given the load impedance,
Figure 12. The measured Reflection Coefficient is 0.37
Table 2.1. Data obtained for the Reflection Coefficient measurement of the given load
impedance.
Parameter
Measured
Calculated
% Difference
Reflection
Coefficient
0.37
0.3676
0.65 %
SMITHS CHART
ACTIVITY 1
B. 50 + j75 Ω (Guevarra, John Mico)
Plate 3.2. Smith Chart Plot for 𝑍𝐿 = 50 + j75 Ω (determining the Reflection Coefficient)
Computation:
Γ=
(50+j75Ω) - 50Ω
ZL - Z0
=
= 0.6 ∠ 53.13o
ZL + Z0 (50+j75Ω) + 50Ω
SMITHS CHART
ACTIVITY 1
Measuring the Reflection Coefficient in the simulation given the load impedance,
Figure 13. The measured Reflection Coefficient is 0.60
Table 2.2. Data obtained for the Reflection Coefficient measurement of the given load
impedance.
Parameter
Measured
Calculated
% Difference
Reflection
Coefficient
0.60
0.60
0%
SMITHS CHART
ACTIVITY 1
C. 150 + j75 Ω (Lansang, Joanna Sonette)
Plate 3.3. Smith Chart Plot for 𝑍𝐿 = 150 + j75 Ω (determining the Reflection Coefficient)
Computation:
Γ=
(150+j75Ω) - 50Ω
ZL - Z0
=
= 0.5852 ∠ 16.3139o
(
)
ZL + Z0
150+j75Ω + 50Ω
SMITHS CHART
ACTIVITY 1
Measuring the Reflection Coefficient in the simulation given the load impedance,
Figure 14. The measured Reflection Coefficient is 0.59
Table 2.3. Data obtained for the Reflection Coefficient measurement of the given load
impedance.
Parameter
Measured
Calculated
% Difference
Reflection
Coefficient
0.59
0.5852
0.81 %
SMITHS CHART
ACTIVITY 1
D. 50- j50 Ω (Lorzano, Daryl Khent)
Plate 3.4. Smith Chart Plot for 𝑍𝐿 = 50 – j50 Ω (determining the Reflection Coefficient)
Computation:
Γ=
(50-j50Ω) - 50Ω
ZL - Z0
=
= 0.4472 ∠-63.43
ZL + Z0 (50-j50Ω) + 50Ω
SMITHS CHART
ACTIVITY 1
Measuring the Reflection Coefficient in the simulation given the load impedance,
Figure 15. The measured Reflection Coefficient is 0.45
Table 2.4. Data obtained for the Reflection Coefficient measurement of the given load
impedance.
Parameter
Measured
Calculated
% Difference
Reflection
Coefficient
0.45
0.4472
0.62%
SMITHS CHART
ACTIVITY 1
E. 25 – j100 Ω (Luyun, Jorge Matthew)
Plate 3.5. Smith Chart Plot for 𝑍𝐿 = 25 – j100 Ω (determining the Reflection Coefficient)
Computation:
Γ=
(25-j100Ω) - 50Ω
ZL - Z0
=
= 0.8246 ∠ -50.9061
ZL + Z0 (25-j100Ω) + 50Ω
SMITHS CHART
ACTIVITY 1
Measuring the Reflection Coefficient in the simulation given the load impedance,
Figure 16. The measured Reflection Coefficient is 0.82
Table 4.5. Data obtained for the Reflection Coefficient measurement of the given load
impedance.
Parameter
Measured
Calculated
% Difference
Reflection
Coefficient
0.82
0.8246
0.56 %
SMITHS CHART
ACTIVITY 1
F. 100 – j50 Ω (Madrigal, John Francis)
Plate 3.6. Smith Chart Plot for 𝑍𝐿 = 100 – j50 Ω (determining the Reflection Coefficient)
Computation:
Γ=
(100-j50Ω) - 50Ω
ZL - Z0
=
= 0.45∠-63.43
ZL + Z0 (100-j50Ω) + 50Ω
SMITHS CHART
ACTIVITY 1
Measuring the Reflection Coefficient given the load impedance,
ZL = 100 - j50 Ω; Zo = 50 Ω
Z'L = 2 - j1
z = 0.4 + j0.2
Zin = 50(0.4 + j0.2)Ω = 20 + j10 Ω
VSWR = 2.65
Γ = 0.45
Table 4.6. Data obtained for the Reflection Coefficient measurement of the given load
impedance.
Parameter
Measured
Calculated
% Difference
Reflection
Coefficient
0.45
0.45
0%
SMITHS CHART
ACTIVITY 1
G. 75 + j100 Ω (Nerie, Trisha Camille)
Plate 3.7. Smith Chart Plot for 𝑍𝐿 = 75 + j100 Ω (determining the Reflection Coefficient)
Computation:
Γ=
(75 + j100Ω) - 50Ω
ZL - Z0
=
= 0.6439∠-114.6236
ZL + Z0 (75 + j100Ω) + 50Ω
SMITHS CHART
ACTIVITY 1
Measuring the VSWR in the simulation given the load impedance,
Figure 17. The measured Reflection Coefficient is 0.64
Table 4.7. Data obtained for the SWR measurement of the given load impedance.
VI.
Parameter
Measured
Calculated
% Difference
Reflection
Coefficient
0.64
0.6439
0.61%
QUESTIONS AND PROBLEMS
Questions
1. What is the impedance chart developed by P. H. Smith, useful for transmission line
analysis?
Answer: Smith Chart
2. What is the process of dividing impedances by the line's characteristic impedance?
Answer: Normalizing
3. What do the two types of lines represent in a Smith Chart?
Answer: The first set of lines representing constant resistance are circular and are all
tangent to each other at the right-hand end of the horizontal line through the center of
the chart. Meanwhile, the second set of lines represents arcs of constant reactance.
These arcs are also tangent to one another at the right-hand side of the chart.
SMITHS CHART
ACTIVITY 1
Problems
1. A load ZL = 100 + j50 Ω is connected across a TL with Zo = 50 Ω. Find the
Normalized load impedance.
Solution:
z=
ZL 100 + j50
=
= 2+j1
Zo
50
Answer: z = 2 + j1
2. A slotted line measurement on an air-filled TEM line yields a VSWR of 1.6 at a
frequency of 1 GHz. When the load is replaced by a short, the voltage minimum moves
3 cm towards the load. Find the wavelength.
Solution:
c 3x108 m⁄s
λ= =
= 30cm
f
1x109 Hz
Answer: 30cm
3. From the problem 2, find the normalized load impedance.
Solution:
The shift in the voltage is 0.1 𝜆
Locate the voltage minimum at the impedance minimum, z min = 0.625 and move 0.1 𝜆
toward the load to a position an integral number of half-wavelengths from the load. The
impedance there, zL = 0.77 - j0.39, is the same as that of the load.
SMITHS CHART
ACTIVITY 1
Figure 18. The measured normalized load impedance
Answer: zL = 0.77 - j0.39
SMITHS CHART
VII.
ACTIVITY 1
ANALYSIS
In this activity, the group were able to compute the parameters and plot it in the
Smith Chart. Each member of the group is given a respective letter which contains the
value of load impedance needed to determine the Normalized Impedance using the formula
𝑍
Zn = 𝑍𝑜𝐿 where ZL is the load impedance and ZO is the characteristic Impedance, the
Voltage Standing Wave Ratio using the formula, VSWR =
1 + |Γ|
1 − |Γ|
coefficient and the Reflection Coefficient can be obtained by Γ =
where Γ is the reflection
𝑍𝐿 − 𝑍𝑂
𝑍𝐿 + 𝑍𝑂
. The given values
of load impedance are a)100 + j25 Ω, b)50 + j75 Ω, c)150 + j75 Ω, d)50 - j50 Ω, e)25 j100 Ω, and f)100 - j50 Ω.
The output of the parameters mentioned are individually represented by circles,
arcs, and lines, which position and size is in accordance to its computed value. By marking
the line that represents the resistance depending on the value of the first digit of the result
of computed normalized impedance, tracing the impedance grid from the marked point in
the Smith Chart will form a circle. The second digit of the normalized impedance then
determined the reactance. If imaginary number “j” is negative, reactance is capacitive, the
arc that will form is in the lower side of the resistance line and if positive then the reactance
is inductive, the arc that will form is in the upper side of the resistance line. The normalized
impedance computed in a is 2 + j0.5 Ω, in b is 1 + j1.5 Ω, 3 + j.15 Ω in letter c, 1 – j1 Ω in
letter d, 0.5 – j2 Ω in letter e, and 2 – j1 Ω in letter f.
To identify the VSWR and Reflection Coefficient, other circle is formed where its
center is the center of the line and it must reach the intersection of the resistance and
reactance. From the left side of newly drawn circle, a line is drawn down to the radially
scaled parameters. The computed VSWR and Reflection Coefficient are compared to its
measured value which yielded 0% to approximately 0% differences.
SMITHS CHART
ACTIVITY 1
VIII. CONCLUSION
In conclusion of this experiment, the group was able to learn, understand, and
demonstrate the useful applications of Smith Chart and the basic principles behind it. The
Smith Chart was found to be a very useful tool in solving complicated math problems
involving transmission lines and matching circuits with arbitrary impedances known.
Given for any transmission line with any load, it is possible to calculate for impedances,
admittances, and the length of a short circuited line, the requisite capacitive or inductive
reactance, the VSWR, or impedance matching. The use of the chart involves a series of
plotting methods by taking given known values and plotting it on the Smith Chart following
a strict procedure to acquire the corresponding value required to be calculated. In most
cases, normalizing the given impedances or admittances would be the first step. Doing so,
allows the user to plot the normalized value on the chart. From there, a circle tangent to the
intersection of the components of the normalized value, with its center on the center of the
chart, can be used as reference to determine the calculated values from the scale below the
chart. By drawing a vertical line downwards, tangent to the left-most side of this reference
circle, this line matches to a specific corresponding value on the scale below to determine
the VSWR and reflection coefficient as well. Moreover, users can customize the Smith
Chart for specific applications by assigning a different value to this reference circle or to
the prime center. By following these steps, it was proven to be a much easier method of
solving complex calculations involving transmission line parameters that are found crucial
to various applications of transmission lines. Overall, the experiment was found and proven
to be a success as most students acquire a significantly zero value for percent difference of
theoretical and actual values of VSWR and Reflection Coefficient for each respective given
complex load impedances.
SMITHS CHART
ACTIVITY 1
BIBLIOGRAPHY
Miller G. (2014). The Smith Chart. Modern Electronic Communication (Ninth Edition). pp. 534
Frenzel L. (2016). The Smith Chart. Principles of Electronic Communication Systems (Fourth
Edition). pp. 490
Smithchart Amateur Radio Society (n.d.). P.H.Smith and the Smith Chart. Retrieved from URL:
http://smithchart.org/phsmith.shtml
Odunlade E. (2019). Basics of Smith Charts and how to use it for Impedance Matching. Retrieved
from URL: https://circuitdigest.com/article/basics-of-smith-chart-and-how-to-use-if-forimpedance-matching
Microwaves
101
(n.d.).
Smith
Chart
Tool.
Retrieved
https://www.microwaves101.com/smith-chart/smith-chart-tool-v1
from
URL: