- Attenuation refers to the loss of signal strength that occurs along transmission lines and is measured in decibels per kilometer. It is influenced by factors like line construction, frequency, weather conditions, and faults. - The attenuation constant α determines the exponential decrease in amplitude per unit length of the line. The phase constant β determines the linear change in phase per unit length. - Surge impedance is the characteristic impedance of a lossless line and is a measure of the maximum power that can be delivered by the line at unity power factor, known as surge impedance loading. It can be increased by raising voltages or decreasing the surge impedance through series and shunt capacitors.

1. ATTENUATION
AND
SURGE IMPEDANCE LOADING
Presented by
ABARNA.T
11109b001

2. In general, the overall loss in carrier signal
strength incurred both at the terminal
equipment and along the line is very important
as it influences the application range of the
protection , the required transmitted power,
and the receiver sensitivities.
Attenuation(or gain) in power-line-carrier signal
is defined in terms of decibels(dB).
outputpower/received power=Po/Pi

3. Attenuation=10log10 Po/Pi dB
That is by convention a positive quantity
implying loss. Attenuation as expressed above
is a pure ratio.
LINE ATTENUATION:
The transmission efficiency of an
overhead line depends upon the line
construction and coupling phase configuration,
the operating carrier frequency, the primary
system configuration, atmospheric conditions
and the state of the line concerned…

4. i.e., whether a fault exists on it or not, thus the
loss characteristics of the overhead conductors
are less easy to specify than the terminal
equipment. It is customary, however, to
approximate by assigning a certain attenuation
for a given conductor system in terms of so
many dB/km which includes all losses.
Under normal dry weather conditions with a
clean line, the attenuation of the carrier signal
due to the transmission line itself is almost
entirely the series loss due to the

5. resistance of the conductors. Other atmospheric
conditions which effectively vary the dielectric
between the conductors such as fog and mist,
can also result in increased signal attenuation.
ATTENUATION due to LINE FAULTS;
A point of particular importance in line
faults is increase in attenuation due to the fault
depends on the distance of the fault from the
lines terminals and give rise to mismatch losses
in the form of reflections and loss of power.

6. The effect of attenuation constant(α) in the long line
can be obtained from the general expression of the
long line.
The general expression of long line is
VS= C1e^ γD + C2e^-γD
Is=1/Zo(C1e^ γD - C2e^-γD)
From the above eqn’s it is obvious that γ governs
he propagation of the component waves.
Therefore, it is called the propagation constant. γ
is given by (Z/Y)^ ½ since both Z and Y are
complex, γ is also complex and can be written as
γ=α+jβ where α and β are real and positive values.
Then,
e^γs=e^(α+jβ)

7. =e^αs. e^jβs.
e^γs is real. It increases exponentially at the rate of
e^α per unit length of the line.
Hence e^αs is called the magnitude operator,
e^jβs =cos βs + sinj βs =1at an angle of βs. Thus e^jβs
has magnitude 1 but βradians per unit while
maintaining its magnitude.
Hence it is considered as rotational operator.
Thus, we proceed from the sending end from the receiving
end, the amplitude of the voltage component
½(Vr+ZoIr) e^γs , decreases in amplitude by
e^α/unit length of

8. the line and retards in phase by β radians per unit
length. This is the characteristic of a travelling
wave and therefore this term represents a
voltage wave travelling from sending end to
receiving end of the line. Since α determines
the change in amplitude per unit length of the
line it is called the attenuation constant
expressed in meter per second and β
determines the change in phase per unit length
of the line and it is called phase constant or
wavelength constant, expressed in rad per unit
length.

9. SURGE IMPEDANCE
Surge impedance (Zc) of a line is defined as the
square root of Z/Y, where Z is the series
impedance (=R+jX) and Y is the shunt
admittance(=G+jB). Surge impedance is the
characteristic impedance of a loseless line.
For a line having negligible resistance (thus will
be the case when the conductors are of a large
cross-section) and having no shunt leakage (in
which case the value of G will be zero),
Zc=(L/C)^1/2 which is a pure resistance. It has
a value of 400 to

10. 600 ohms for an over head line and 40 to 60
ohms for an underground cable.
Zc may be measured in terms of Zoc and Zsc
where these are impedances measured at the
sending end with receiving end open-circuited
and short-circuited respectively as discussed
below:
For a transmission line
Es=AEr+BIr and
Is=CEr+DIr.
Therefore when the line at the receiving end is
open-circuited Ir=0, and

11. Es=AEr, Is=CEr
Therefore Zoc=Es/Is=A/C
Similarly when the line at the receiving is shortcircuited,
Er=0
So that Es=BIr, Is=DIr,
Zsc=Es/Is= B/D.
Multiplying Zoc.Zsc=A/C.B/D
=B/C.
(A=D for a bilateral network, which is the case
with a transmission line).

12. But from the defintion of surge impedance
Zc^2=Z/Y,
Which implies that Z/Y=B/C.
So that Zoc.Zsc=Zc^2.
Therefore surge impedance is equal to square root
of product of Zoc and Zsc.

13. It is defined as the load that can be delivered by
the line having no resistance, the load being at
unity power factor.
PR=VR^2/Zo MW ,
Where VR is the receiving end line voltage in KV
and Zo is the surge impedance of the line in
ohms. PR is known as the surge impedance
loading, also called “Natural power” of the
line.

14. For Zo=400 ohms, PR=2.5 VR^2 KW.
The above eqn gives a limit to the maximum power
that can be delivered and is useful in the design of
transmission lines. This may not be necessarily be
the maximum loading on the line. Surge
impedance loading can be used for the
comparison of loads that can be carried on the
different voltages.
Inorder to increase the power transmitted through a
long transmission line either value of receiving
end voltage is to be

15. increased or more than one transmission line can
be run in parallel. The latter method is however
very costly. Thus from the above equation , in
order to increase PR either VR is to be increased
or Zo is to be decreased.
(i)
Increase in voltage VR :
Nowadays the trend is for higher and
higher voltages so that this is the most widely
adopted method to increase the power limit for
heavily loaded long transmission lines. But
there are some

16. Practical difficulties in this method and it is
expensive .
(ii) Decrease of surge impedance Zo:
sine the spacing between the
conductors cannot be decreased much, it being
dependent in the line voltages and corona etc.,
the value of Zo cannot be varied as such. But
some are artificial means are employed to
decrease Zo. For a loseless transmission
Zo=(L/C)^1/2 and γ=jω(LC)1/2=jβ. We know
that γ is the propagation constant and β is the
phase

17. Shift. The latter determines the torque angle,
between Vs and Vr and hence system stability.
To decrease Zo either l is decreased using series
capacitor or C is increased using shunt
capacitance.