Study of Transmission Line

Table of Contents

1. Introduction
2. Distributor Parameters
3. Wave Equation and Time Harmonic Equation
4. Methods and Equations
5. Lossless and Lossy Transmission Lines
6. Input Impedance
7. SWR and Impedance Matching
8. ABCD Parameters
9. Previous Year's Questions
10. Conclusion

Introduction

• What is a transmission line made of?
• A transmission line is made of both conductors and dielectrics.
• The main losses are conductor losses and dielectric losses.
• Good conductors: Copper, Brass.
• Perfect conductors: Gold, Silver.
• Main types: Parallel Plate Transmission Line, Coaxial Transmission Line, Twin Wire Transmission Line.

Distributor Parameters

• R (Resistance): Conductor loss, in series, reduces voltage in series.
• G (Conductance): Dielectric loss, in parallel, affects current.
• L (Inductance): Magnetic field storage, gives phase shift in series.
• C (Capacitance): Electric field storage, gives phase shift in parallel.

Wave Equation and Time Harmonic Equation

• Lossless Case: Value of R and G is zero, alpha = 0, beta = omega under root (L*C)
• Gamma = under root (R + j omega L) (G + j omega C)
• Beta = omega * under root (LC)

Methods and Equations

• Z0 Characteristic Impedance: v_n plus / i_n plus = v_n minus / i_n minus
• Distributed Impedance
• One Point Impedance: Without phase shift

Lossless and Lossy Transmission Lines

• Lossless: R = 0, G = 0
• Lossy: R > 0, G > 0
• In a lossless transmission line: alpha = 0, beta = omega under root (L*C)
• Lossy and distortionless: L/C = R/G
• Independent of length*

Input Impedance

• For short circuit: Z_in = j Z0 tan (βl)
• For open circuit: Z_in = -j Z0 cot (βl)
• Other cases: Z_in = Z0 (Z_L + j Z0 tan (βl)) / (Z0 + j Z_L tan(βl))

SWR and Impedance Matching

• Standing Wave Ratio (SWR): V_max / Voltage mean, current max, electric field max, magnetic field max
• Impedance matching with input impedance (series and parallel elements)
• Reflection coefficient (Gamma)

ABCD Parameters

• Admittance (Y) and Impedance (Z) parameters
• ABCD Matrix
• Transmission distance

Previous Year's Questions

• Questions extracted from various papers
• Questions involving analysis of transmission line, impedance matching, and reflection coefficient

Conclusion

• Proper analysis of the transmission line
• Comparison between different types of transmission lines
• Management and proper use of lossless and lossy transmission lines