Calculation of primary and secondary cable parameters

Objective

Studying the designs and characteristics of coaxial communication cables, getting acquainted with samples of cable products of various types, gaining skills in calculating primary and secondary parameters.

Calculation of primary and secondary cable parameters

Table 1 – Initial data of the coaxial cable

option number Cable type, mm Conductor material Insulation type Frequency, MHz
2.6/9.5 copper-copper Polyethylene spiral

Coaxial cables are usually used in the frequency range above 60 kHz, while the calculation of the primary parameters at these frequencies can be made using simplified formulas.

1 The active resistance of a coaxial pair consists of the resistance of the inner conductor and outer (hollow) conductor and is calculated from the expression

where f is the frequency at which the calculation is made, Hz;

mm is the radius of the inner conductor;

mm is the radius of the outer conductor.

Table 2 – Dependence of the resistance of a coaxial pair on frequency

f , MHz
R , Ohm/km 40.95384615 91.575584 129.50743 317.22713

Figure 1 – The dependence of the resistance of a coaxial pair on frequency

2 The circuit inductance L consists of the external conductor-to-conductor inductance and the internal inductance of the inner and outer conductor and is determined at frequencies > 60 kHz by the formula:

.

Table 3 – Dependence of the inductance of a coaxial pair on frequency

f , MHz
L , H/km 0.00026568 0.0002621 0.0002612 0.00026

Figure 2 – Dependence of the inductance of a coaxial pair on frequency

3 The capacitance of a coaxial pair is similar to that of a cylindrical capacitor. Its electric field is created between two cylindrical surfaces with a common axis. The capacity is determined by the formula:

where ‒ equivalent relative dielectric permittivity of the insulation.

Then at any frequency.

Figure 3 – Dependence of the capacitance of a coaxial pair on frequency

4 Insulation conductivity characterizes the energy loss in the insulation of the conductors of a coaxial pair. The conductivity of the insulation is due to the insulation resistance of the insulating material and dielectric losses. In the used frequency range (>60 kHz), the first component can be neglected. Then the insulation conductivity is determined from the expression:

,

where – the equivalent value of the dielectric loss tangent, is determined from Table 4.

Table 4 – Dependence of tgδ e on the type of cable and frequency

cable type Insulation type tgδ e . 10 -4 at frequency, MHz
2.6/9.5 Polyethylene spiral 0.4 0.4 0.5 0.6

Table 5 – Dependence of insulation conductivity on frequency

Figure 4 – The dependence of the conductivity of the insulation on the frequency

5 Wave resistance in the general case is determined by the expression

.

In the high frequency region (at f > 40 kHz), the wave impedance can be determined by the formula:

.

Table 6 – Dependence of the wave impedance modulus on frequency

f , MHz
, Ohm/km 75.05593454 74.54853547 74.42043287 74.24928562

Figure 5 – Dependence of the modulus of wave impedance on frequency

6 In the high frequency region (at f >40 kHz) , the attenuation coefficient is determined by the formula:

Table 7 – Attenuation factor versus frequency

f , MHz
, dB/km 2.373596107 5.354140207 7.596046672 18.78463224

Figure 6 – The dependence of the attenuation coefficient on frequency

7 The phase factor determines the angle of shift between current (or voltage) over one kilometer. To determine the phase coefficient in the high frequency regions (for f > 40 kHz), one can use the expression

.

Table 8 – Dependence of the phase factor on the frequency

f , MHz
, dB/km 22.240968 110.45307 220.52653 1320.1163

Figure 7 – Dependence of the phase factor on the frequency

8 The propagation coefficient modulus is determined from the formula:

.

Table 9 – Dependence of the propagation coefficient on the frequency

f , MHz
, 1/km 2.288838663 3.360771279 3.973070768 6.148495276

Figure 8 – Dependence of the modulus of propagation coefficient on frequency

9 Velocity of propagation of electromagnetic energy is a function of frequency and phase constant, which in turn depends on the primary parameters of the line. In general, it is determined by the formula:

.

Table 10 – Dependence of the phase factor on the frequency

f , MHz
, km/s 282505.03 284427.83 284917.43 285574.17

Figure 9 – Dependence of the speed of propagation of energy on frequency

Conclusion

In the course of this laboratory work, the primary and secondary parameters of a given coaxial cable were calculated.

The inner conductor of this cable is a copper wire with a diameter of 2.6 mm, on which a helix of polyethylene material is applied with different pitches, depending on the requirements for cable flexibility. The diameter of the cordel is used in such a way as to ensure that the specified electrical characteristics of the cable are obtained.

The outer conductor of the cable is made of copper wire with a diameter of 9.5 mm.

Such a cable is used for multi-channel communication and television, with an operating frequency range of up to 60 MHz.

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