TRANSMISSION LINES
LUMPED ELEMENTS
TYPES OF TRANSMISSION LINES
 UNBALANCED– The one wire carry signal, other one for
reference(GND)
Ex. Co-axial cable
 BALANCED– Both wires carry data One carries the signal as a
positive and other carries it as negative
 The negative signal is 180 Degree out of phase with the
positive
 Equal noise occurs on both and can cancel each other.
Ex. Unshielded Twisted Pair Cable
TRANSMISSION LINES
 TRANSIT TIME EFFECT
Signal require finite amount of time to travel along an
electric circuit which is no more comparable to the time
period of the signal
 Transmission line – Important case of EM Waves
Two conductor system
 tr = l/v (Transit Time)
 Reactive drop = Finite for any Non Zero Frequency
 l/v <<<T
(Lumped Circuit Analysis)
 Distributed Circuit Analysis
DISTRIBUTED ELEMENTS(1)
DISTRIBUTED ELEMENTS(2)
EQUATION OF VOLTAGE & CURRENT
INFINITESIMAL SECTION OF TRANSMISSION LINE
CONDUCTORS AND DIELECTRICS ARE NON IDEAL
R,L,G,C -- PRIMARY CONSTANTS OF TRANSMISSION LINE
EQUATION OF VOLTAGE & CURRENT
EQUATION OF VOLTAGE & CURRENT(2)
PROPOGATION CONST.
VOLTAGE AS A FUNCTION OF x FOR DIFF. TIME
VOLTAGE AS A FUNCTION OF x FOR DIFF. TIME
Voltage & Current ----- Wave type of solution
PHASE & ATTENUATION CONSTANT
•
•
PHASE SHIFT CONSTANT (β)
ATTENUATION CONSTANT (α )
• β λ =2π
• -20 log (e^-1)
• 1 np= 8.68 dB
--- Phase change per unit length of line(rad/m)
--- Attenuation of the wave (np/m)
EVALUATION OF ARBITARY CONSTANTS
R,L, G,C
ϒ , Z0
-- PRIMARY CONSTANTS OF TRANSMISSION LINE
-- SECONDARY CONSTANTS OF TRANSMISSION LINE
STANDING WAVES & IMPEDANCE
TRANSFORMATION
(Reflection Co efficient)
If a line is terminated in an impedance ZL the impedance seen at a distance
I from it is not ZL but is Z(l).
LOSS LESS & LOW LOSS TRANSMISSION
LINES
Loss Less
R=G=0
Low Loss
R<< wL ,G << wC
The Phase constant of the low loss line is same as loss less line.
low loss line : α <<<< β (Take α=0 in analysis)
STANDING WAVE RATIO
Substitute ϒ=jβ (Lossless Line)
Voltage or current is max. or min.--- Impedance is purely Resistive
VSWR
VSWR – Plot of |v| or |I| as a function of distance l is called the voltage or current
standing wave pattern.
-Easily measurable parameter , It does not require measurement of phase
-Range between 1 to ∞
IMPEDANCE VARIATION ON LOSSLESS LINE
Characteristics of LOSSLESS LINE
Line Characteristics repeat at every λ/2
Normalized impedance inverts every λ/4
• ZL= Zo , The impedance is same at any point on the line
• Characteristic impedance of a transmission line is 50Ω. Input
impedance of the open circuited line is Zoc=100+j150Ω. When
the transmission line is short circuited the value of the input
impedance will be
•
•
(a)50Ω
(c)7.69+j11.54Ω
(b)100+j150Ω
(d)7.69-j11.54Ω
• A lossless line in a load which reflects the part of the incident
power. If VSWR=2 The % power that reflected back is
• (a) 57.7 (b) 33.3 (c) 0.11 (d) 11.11
• A lossless line in a load which reflects the part of the incident
power. If VSWR=2 The % power that reflected back is
• (a) 57.7 (b) 33.3 (c) 0.11 (d) 11.11
• VSWR pattern in a lossless transmission line with characteristic impedance
50Ω and a resistive load is shown in figure
The reflection coefficient is given by
(a)
-0.6
(b)
-1
(e) None of these
The value of the load resistance is
(a)
50Ω
(b)
200Ω
(d)
0Ω
(e) None of these
(c)
0.6
(d)
(c)
12.5Ω
0