**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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