The document discusses cable capacitance and how it is measured. It begins by defining cable capacitance as the electrical charges stored within a cable. A cable acts as a capacitor, with the inner conductor and outer sheath acting as the conductive plates separated by insulation. Capacitance is higher for underground cables due to smaller distances between components. Capacitance affects signal transmission speed and charging current. It is measured in picofarads per foot and controlled through insulation thickness, material, and conductor size. A Schering bridge circuit is used to measure unknown cable capacitance and dissipation factor by balancing loads on the bridge's arms.

1. Capacitance and Cable Testing
Cable Electrical Characteristics :
The most important characteristics in an electronic cable are impedance, attenuation, shielding and
capacitance. In this article, we can only review these characteristics very generally, however, we will
discuss capacitance in more detail.
Impedance (Ohms) represents the total resistance that the cable presents to the electrical current
passing through it. At low frequencies the impedance is largely a function of the conductor size, but at
high frequencies, conductor size, insulation material and insulation thickness all affect the cable's
impedance. Matching impedance is very important. If the system is designed to be 100 Ohms, then the
cable should match that impedance, otherwise error-producing reflections are created at the impedance
mismatch (See related articles in this section on Return Loss ).
Attenuation is a ratio comparing power input to output. It is measured in decibels per unit length
(db/ft), and provides an indication of the signal loss through the cable. Attenuation is very dependent on
signal frequency. A cable that works very well with low frequency data may do very poorly at higher
data rates. Cables with lower attenuation are better.
Shielding is normally specified as a cable construction detail. For example, the cable may be unshielded,
contain shielded pairs, have an overall aluminum/mylar tape and drain wire or even a double shield.
Cable shields usually have two functions: the first to act as a barrier to keep external signal from getting
in and internal signals from getting out and the second to be a part of the electrical circuit. Shielding
effectiveness is very complex to measure and depends on the data frequency within the cable and the
precise shield design. A shield may be very effective in one frequency range, but a different frequency
may require a completely different design. System designers often test complete cable assemblies or
interconnected hardware for shielding effectiveness to prove their system complies with FCC
electromagnetic emission requirements.
Capacitance in cable is usually measured as picofarads per foot (pf/ft). It indicates how much charge the
cable can store within itself. If a voltage signal is being transmitted by a twisted pair or coaxial cable, the
insulation on the individual wires becomes charged by the voltage within the circuit. Since it takes a
certain amount of time for the cable to reach its charged level, this slows down and interferes with the
signal being transmitted. Digital data pulses are a string of voltage variations that can be represented by
square waves with near-vertical rise and fall transitions. A cable with a high capacitance slows down
these voltage transitions so that they come out of the cable looking more like “saw-teeth”, rather than
square waves, and the circuitry may not recognize the pulse. The lower the capacitance of the cable, the
better it performs at higher frequencies.

2. Cable Capacitance
Definition: Cable capacitance is defined as the measurement of the electrical charges
stored within it. The capacitor in the cable is constructed by two conductive material which is
separated by an insulator or dielectric. The capacitance of the cable determines the charging
current, charging KVA, and the dielectric loss.
The capacitance of an underground cable is larger than that of an overhead line of the same
length due to the following reasons.
1. The distance between the conductor is very small.
2. The distance between the core and earth sheath of the overhead line is very small.
3. The permittivity of the cable insulation is usually 3 to 5 times greater than that of the
insulation around the conductors of overhead line.
As we saw earlier in the construction of Underground cables, a cable is basically a set of one (or
three) conductors surrounded by a metallic sheath. This arrangement can be considered as a
set of two long, coaxial, cylinders, separated by insulation. The current carrying conductor
forms the inner cylinder while the metallic sheath acts as the outer cylinder. The sheath is
grounded, and hence voltage difference appears across the cylinders. The dielectric fills the
space between the charged plates (cylinders), making it a capacitor. Hence, capacitance of the
cable becomes a very important aspect, and must be calculated.
We can broadly classify cables as single-cored and three-cored. And the calculation of
capacitance is different for both.
 Capacitance Of Single Core Cable
A single core cable can be represented as shown below.
Let,
r = radius of the inner conductor and d = 2r
R = radius of the sheath and D = 2R
ε0 = permittivity of free space = 8.854 x 10-12
εr = relative permittivity of the medium
Consider a cylinder of radius x meters and axial length 1 meter. x be such
that, r < x < R.
Now, electric intensity Ex at any point P on the considered cylinder is
given as shown in the following equations.
Then, the potential difference between the conductor and sheath is V, as calculated in equations below.
After that, capacitance of the cable can be calculated as C= Q/V

3. When the capacitance of a cable is known, then its capacitive reactance is given by Xc = 1/(2πfC) Ω.
Then the charging current of the cable can be given as,
Ic= Vph / Xc A
 Capacitance Of Three Core Cable
Consider a three cored symmetric underground cable as shown in the following figure
(i). Let Cs be the capacitance between any core and the sheath and Cc be the core to
core capacitance (i.e. capacitance between any two conductors).
In the above figure (ii), the three Cc (core to core capacitance) are delta connected and the core to
sheath capacitance Cs are star connected due to the sheath forming a single point N. The circuit in figure
(ii) can be simplified as shown in figure (iii). Outer points A, B and C represent cable cores and the point
N represents the sheath (shown at the middle for simplification of the circuit).
Therefore, the whole three core cable is equivalent to three star connected capacitors each of
capacitance Cs + 3Cc as shown in fig. (iii).
The charging current can be given as, Ic = 2πf(Cs+3Cc)Vph A

4.  Effects Of Capacitance In Underground Cables
We know that capacitance is inversely proportional to separation between plates. Hence, if the
separation between the plates is large, capacitance will be less. This is the case in Overhead
Lines where two conductors are separated by several meters. The converse, of course, is also
true. If the separation is small, the capacitance is more. In Underground cables, obviously, the
separation is relatively smaller. Hence capacitance of underground cables is much more than
that of Overhead lines.
The most important factor that is affected by this is the Ferranti effect. It is more pronounced in
cables than in lines. This induces several limitations.
Also, with increased capacitance, the charging current drawn is also increased.
Underground cables have 20 to 75 times the line charging current compared to Overhead lines.
Due to these two conditions, the length of Underground cables is limited.
 Controlling Cable Capacitance :
Since cable capacitance is so important, a lot of analysis goes into minimizing it. This can be
accomplished by:
1. Increasing the insulation wall thickness
2. Decreasing the conductor diameter
3. Using an insulation with a lower dielectric constant.
The size of the conductor is usually determined by the electrical requirements of the circuit that
the cable interconnects. If the circuit has been designed to require a 22 AWG wire, you cannot
reduce it to 28 AWG just to reduce the capacitance. Also, the insulation wall thickness cannot
be increased beyond reason since this increases the diameter of the cable, increasing costs and
affecting terminations. Thus, the insulation chosen for the cable often becomes the critical
variable.
All dielectric constants are compared to air or vacuum, which is given a value of 1.0. A poor
quality PVC insulation may have a dielectric constant of 5.0 to 6.0 or higher. Polyethylene has a
much better dielectric constant of approximately 2.0. Foamed polypropylene or polyethylene
insulations have constants as low as 1.6.
By balancing conductor size, insulation material and insulation wall thickness, the cable
designer can produce electronic cables that are tailor made to transmit high frequency digital
data pulses over a maximum distance. The signal output from these cables maintains the
required wave form definition and minimizes possible data errors.

5.  Measuring Cable Capacitance
A Schering Bridge is a bridge circuit used for measuring an unknown electrical capacitance and
its dissipation factor.
Definition :
A Schering Bridge is a bridge circuit used for
measuring an unknown electrical capacitance
and its dissipation factor. The dissipation factor
of a capacitor is the the ratio of its resistance to
its capacitive reactance. The Schering Bridge
is basically a four-arm alternating-current (AC)
bridge circuit whose measurement depends on
balancing the loads on its arms.
Explanation :
In the Schering Bridge above, the resistance values of resistors R1 and R2 are known, while the
resistance value of resistor R3 is unknown.
The capacitance values of C1 and C2 are also known, while the capacitance of C3 is the value
being measured.
To measure R3 and C3, the values of C2 and R2 are fixed, while the values of R1 and C1 are
adjusted until the current through the ammeter between points A and B becomes zero.
This happens when the voltages at points A and B are equal, in which case the bridge is said to
be 'balanced'.
When the bridge is balanced, Z1/C2 = R2/Z3, where Z1 is the impedance of R1 in parallel with
C1 and Z3 is the impedance of R3 in series with C3.
In an AC circuit that has a capacitor, the capacitor contributes a capacitive reactance to the
impedance.

6. When the bridge is balanced, the negative and positive reactive components are equal and
cancel out, so
Similarly, when the bridge is balanced, the purely resistive components are equal,
so C2/C3 = R2/R1 or C3 = R1C2 / R2.
The dissipation factor is given by:
D = tan(ẟ) = wR1C1 = wR3C3
Advantages of Schering Bridge :
1. Balance equation is independent of frequency
2. Used for measuring the insulating properties of electrical cables and equipments
loss angle
ẟ