Applications of Smith Chart

Name: Applications of Smith Chart
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Calculations of transmission line parameters using Smith Chart

Created byDr. Nagnath Hulle

Last updated 2/2021

English

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What you'll learn

After completion of course students will be able to:
Convert impedance to admittance using Smith Chart
Calculate location of voltage maxima and minima on transmission line using Smith Chart
Calculate reflection coefficient using Smith Chart
Calculate input impedance of transmission line using Smith Chart
Calculate load impedance of transmission of transmission line using Smith Chart
Calculate location and length of single stub in single stub matching using Smith Chart
Calculate length of two stubs in double stub matching using Smith Chart

Course content

6 sections • 17 lectures • 1h 21m total length

Introduction to course on "Applications of Smith Chart"3:58
Explore how the Smith chart simplifies calculating transmission line and matching circuit parameters, visualize impedance, reflection coefficients, and S-parameters, and perform single and two-step matching.
Basics of Smith Chart5:18
Explore the basics of the Smith chart, including real and imaginary axes, resistance and conductance components, and the plotting of reactance and capacitance.
Plotting of impedances on Smith Chart3:24
Plot impedances on the Smith chart by normalizing to the characteristic impedance, tracing real and imaginary axes, circles, and intersections to locate impedance points.
Converting impedances to admittances and Vice Versa1:27
Convert impedances to admittances and back using the Smith chart by plotting coordinates, identifying opposite and extreme points, and performing the conversion on the chart.

Example - 1 : Calculation of transmission line parameters5:21
Calculate transmission line parameters using the smith chart, plot impedance, and determine the reflection coefficient's magnitude and angle to relate maxima and minima on the chart.
Example - 2 : Calculation of transmission line parameters3:41
Compute transmission line parameters on the Smith Chart by measuring the distance between the load and the first minimum from the normalized impedance circle, yielding 0.198 lambda with lambda-to-meter conversion.

Example - 1 : Calculation of input impedance of transmission line2:56
The lecture demonstrates calculating the input impedance of a transmission line using the Smith chart, including normalization, rotation by line length, and reading coordinates.
Example - 2 : Calculation of input impedance of parallel transmission lines9:28
Compute the input impedance of two parallel transmission lines using a Smith chart: normalize impedances, plot input points, determine total admittance, then convert back to impedance.
Example 3 - : Calculation of input impedance of transmission line2:49
Compute the input impedance of a transmission line for different lengths, using open and short circuit conditions, including λ/8, 3λ/8, and λ/2 cases.

Example - 1 : Calculation of output impedance of transmission line5:01
Calculate the output impedance of a transmission line with a Smith chart by converting distance to lambda, identifying minima and maxima, then normalize to the characteristic impedance.
Example - 2 : Calculation of output impedance of transmission line2:15
Apply the Smith Chart to calculate the output impedance of a transmission line, locating minima and maxima by tracing circle paths and converting distances to lambda.

Example-1:Solution-1: Calculation of location and length in single stub matching10:14
Explore how to use the Smith chart to perform single-stub matching, locating the stub and calculating its length to cancel reactive admittance and achieve a matched line.
Example-1:Solution-2: Calculation of location and length in single stub matching3:07
Apply Smith chart techniques to single-stub matching by plotting circles, converting impedance to admittance, and computing two feasible solutions; select the practical one based on transmission-line length.

Example - 1 : Calculation of lengths of stubs in double stub matching7:32
Compute the lengths of stubs for double stub matching on a transmission line, using a reference step two and the distance between steps.
Example - 2 : Calculation of lengths of stubs in double stub matching3:25
Apply the Smith chart to calculate lengths of stubs in double-stub matching, using lambda/8 spacing and circle intersections to locate the two stub lengths.
Example - 3 - Solution 1 : Double Stub Matching when first stub away from Load8:48
Demonstrates double-stub matching on a transmission line with the first stub away from the load, using the Smith chart loci and admittance calculations to find viable solutions.
Example - 3 - Solution 2 : Double Stub Matching when first stub away from Load3:15
Apply Smith chart methods to double stub matching with the first stub away from the load. Evaluate two possible solutions, locate stubs, and compute lambda-lengths to select the preferred configuration.

Requirements

Bacics of Neteork Theory
Basics of transmission line

Description

Calculation of transmission line matching circuit parameters using analytical approach is lengthy process, but Smith Chart provides easy solutions to such problems. It is most commonly used tool in microwave and RF engineering to visualize complex quantities.

Smith Chart is circular plot and provides graphical representation of a complex mathematical equations. It is also used to display multiple parameters simultaneously some of the parameters are impedance, admittance, reflection coefficient, scattering parameters.

Smith Chart consists of two sets of circles. First set is real circles (complete circles) whose center lie on the horizontal straight line of the Smith Chart and second set is imaginary circles (two arc circles) which lie on the either sides of the horizontal straight line. Apart from above unity real circle (complete circle) has lot of importance especially in calculation of line matching parameters.

While working matching transmission line parameters sometime it is convenient to use impedances and other time it is convenient to use admittances. Smith Chart allows use of normalized impedances for series circuits and normalized admittances for parallel circuits simultaneously.

The proposed course will cover calculation of following transmission line parameters.

1. Impedance to admittance conversion and vice versa

2. Standing wave ratio

3. Reflection coefficient

4. Location and impedance of voltage maxima and minima

5. Input impedance of transmission line

6. Output impedance of transmission line

7. Location and length of the stub in single stub matching

8. Lengths of two stubs in double stub matching

Who this course is for:

Students and researchers working in Electrical Engineering, Electronics Engineering, Microwave Engineering, Communication Engineering

Applications of Smith Chart

What you'll learn

Explore related topics

Course content

Introduction4 lectures • 14min

Calculation of transmission line parameters2 lectures • 9min

Calculation of input impedance of transmission line3 lectures • 15min

Calculation of output impedance of transmission line2 lectures • 7min

Single stub matching2 lectures • 13min

Double stub matching4 lectures • 23min

Requirements

Description

Who this course is for: