Lossless Transmission Lines (Part-V)

Ṽ_g

(i)

Z_g

(ii)

Ĩ_i

(iii)

A’

(iv)

A

(v)

Ṽ_i

(vi)

Z_in

(vii)

Generator

(viii)

d = l

(ix)

z = -l

(x)

Transmission Line

(xi)

Z0

(xii)

d = 0

(xiii)

z = 0

(xiv)

Ĩ_L

(xv)

Ṽ_L

(xvi)

Z_L

(xvii)

z = 0

(xviii)

Generator-End Equivalent Circuit

From the generator’s viewpoint, the transmission line can be replaced by its input impedance Z_in

Ṽ_i = ((Ĩ_i)(Z_in))

Input Voltage Ṽ_i: Voltage at the generator end of the line

Ṽ_i = ((Ṽ_g)(Z_in))/(Z_g + Z_in)

Voltage Divider Relation for Input Voltage: Generator-end voltage expressed using source and input impedances

Ṽ_i = (V0^+)e^(jβl) + Γe^(-jβl)

Input Voltage from Traveling-Wave Expression: Voltage at the line input using incident and reflected waves

V0^+ = (((Ṽ_g)(Z_in))/(Z_g + Z_in))(1/(e^(jβl) + Γe^(-jβl)))

Incident-Wave Amplitude (V0^+): Forward traveling-wave amplitude expressed in terms of source quantities

Incident Wave

Wave traveling from the generator toward the load

Reflected Wave

Wave traveling from the load back toward the generator.

Transmission-Line Boundary Condition at the Load

Condition relating incident and reflected waves through the load impedance

Transmission-Line Boundary Condition at the Source

Condition relating line voltage/current to the generator source and source impedance.