1. Transmission Lines Two wire open line a Strip line d w a Coaxial Cableh b

2. Transmission

3. The field distribution due to a pair of wires
Two wire open line
The field distribution due to a pair of wires

4. Two wire open line Line Behavior
When the switch is closed how long does the lamp take before it lights?
If we make it easy and let the length of the wires between battery and lamp be m, then the time between the switch closing and lamp lighting will be approximately ______s.

5. Two wire open line
Does this mean that electrons are traveling at the speed of light?
Does it mean that the mechanism relies on electromagnetic energy being transported from start to finish of the structure?
If so where is the energy stored during transit?
If it is electromagnetic energy that is stored then it has to be stored in inductance for magnetic energy and capacitance for electric energy.
This means that the transmission line has to have an inductance (per unit length) and a capacitance (per unit length).

6. Low Loss line at High Frequency
Two wire open line
Low Loss line at High Frequency
Inductance and capacitance are uniformly and continuously distributed as L (Henrys/m) and C (Farads/m) respectively.
When the switch is closed and a voltage V is applied to the line through a source impedance Zs, simple reasoning shows that the C's take a finite time to charge up through the L's; thus, the voltage propagates at a finite rate towards the load i.e. volts do not reach the load instantaneously.

7. Transmission in Capacitive Element
Let L and C be distributed inductance
and capacitance per unit length.
In time t, electric flux q = (C ·x)v (from Q = CV) is produced in time x/u sec i(amps) = q/ t = Cx• v/ t
(capacitive charging or "displacement" current)
i = Cx• v /(x/ u ) = Cvu (I)

8. Transmission in Magnetic Element
In time t, magnetic flux linkages =(L•x)i
(from = LI) ; are produced in time x/u sec
v(volts) = /t = L•x•i/t=Liu (ind Volts)…(II)
Multiplying I and II:- vi =vi CLu2
Or u = 1/  LC ms-1velocity of propagation
Dividing I by II:- i/v =vC/iL or v2/i2 =L/C
v/I = L/C……Characteristic Impedance Z0

9. Energy Transmission ; i2 L = v2C ½ Li2 = ½ Cv2
Note:- the equality of Electric and Magnetic field energy in unit length of transmission line.

10. Movement of Energy
Rate of energy input to line due to advance of wavefront, is vi watts.
resistive load, connected directly to voltage source. Rate of energy input, due to thermal dissipation in R, is vi watts (also i2R).

11. Movement of Energy
Rate of energy input = vi watts. Idea of a
'matched line': looks like an infinitely
long line.
Note: if Rg = Z0, maximum power if transferred from the generator to the line.

12. Movement of Energy
As can be seen from the intuitive picture of a transmission line, wave propagation characteristics are dependent on the inductance and capacitance of the line. Thus we need to find expressions for the L and C of typical lines.

13. Inductance in Two wire line
Assume r << S
Due to conductor A,
for 1 amp Linkages per metre, axially, L

14. Inductance in Two wire line
Due to conductor B, an identical expression is
Obtained:-

15. Mutual Inductance Between 2 Twin Lines
External field due to 1 amp in line A, at radius

16. Mutual Inductance Between 2 Twin Lines
Flux linkages per metre axially through circuit
(between conductor 1 & 2) is :-
 =
B =

17. Capacitance two wire line
Capacitance of a Twin Line (r << S)
Assign a line charge of 1 C/m to both conductors.
D at x from conductor A is;

18. Capacitance two wire line
and
Similarly for VB(=VA) 

19. R, L, C of Two wire line  Rdc= 2A2 0 d loge loge L =  a 0 C =
per unit length 
Rdc=
ohm/m
2A2 0 d
loge
loge
L =
H/m  a
0
C =
F/m
loge (d/a)

20. Characteristic Impedence
Z0Twin-wire line
Characteristic Impedence
For air, therefore Z0 = 120 loge(b/a), (approx ) 0 d
loge
L =  a
0
C =
loge (d/a)