Transmission Lines and Equivalent

Circuits

By

Maryam Liaqat

Federal University of Pernambuc(UFPE), Recife, Brazil

Contornos Elemento Teoria do Circuito Regra Kirchoff Circuito Equivalente para linhas de trasmissão Análisa linhas de Transmissão Linhas de transmissão sem perdas plano paralales Reflxão sobre a perda menos linhas encerrada Casos especiais denúncia

Elementos Agrupados Resistancia

Capacitor

Indutor

Elemento Teoria do Circuito

• Electric effect happens instantaniously throughout the Circuit

• Net Charge of Circuit is null

• Megnatic Coupling among lumped components is negligible

Kirchhoff’s Rule Kirchhoff’s Voltage Rule

Kirchhoff’s Current Rule

Equivalent Circuit for Transmission Lines

The lumped circuit elements are much

smaller than the characteristic

wavelength . Transmission circuit

has greater transportation of

voltage and current than

wavelength.

R and G are dissipative loss.

L and C are Stored Energy. Transmission Lines

Electrical circuit Federal University of Pernambuc(UFPE), Recife, Brazil

Analysis of Transmission lines Segments by Kirchhoff’s Rules

From Voltage Rule

From Current Rule

Lossless Plane-Parallel Transmission Line

Inductance per unit length can be calculated by Faraday’s Law and current through a conductor plate can be calculated by Maxwell-Ampere’s Law

Reflection on Lossless Terminated Line

ZL is the load impedance across the line conductors

At Z=0,

Transmission line impedance Zline (-d) with line terminated by load ZL≠Z0.

Special Termination Cases

Shorted Transmission Line ( ZL=0)

Open Circuit Transmission Line (Zl= infinit)

Line Impedance at d=-lamb/2

Line Impedance at d=lamb./4

Shorted Transmission Line ( ZL=0)

At ZL=0 , the reflection coefficient is unity therefore the Zline is dependent only on the distance and characteristic impedance. The Current is maximum in this case but voltage is nullify.

Open Circuit Transmission Line (Zl= infinit)

In open circuit the load is completely removed and therefore reflection coefficient is -1 and the Zline is exactly opposite to the shorted terminated lines. Voltage is maximum at the point of load and current is null

Line Impedance at d=lamb/2 and at d=lamb./4 At half-wave point, Zline is equal to ZL and independent of transmission line

characteristics

Quarter-wave transformation can be used for the length of the line ( lamb/4) with impedance Z1 (quarter-wave transformer) to match the input transmission line of Impedance Z0 to the given load ZL. Here reflaction co-efficient is zero therefore

Thanks for Attention