Method of secondary transmission parameter determination

A wavelength shorting coefficient is often used in describing electromagnetic energy propagation in radio-frequency cables. The coefficient, ξ [ksi], characterizes diminishing of electromagnetic energy propagation velocity in cables compared with the speed of free-space propagation:

, (2.1)

where c is the light speed in free space, which is equal to 300 000 kmps;

v is a phase velocity of electromagnetic energy propagation in the coaxial pair circuit, kmps.

Every line has a particular propagation velocity of a pulse signal; it is defined by the primary transmission parameters, which depend on type of dielectric, cross-section and material of conductors.

The secondary transmission parameters of coaxial circuit a, b, Z _sim, v _ph can be expressed through the overall sizes (diameters of inner d and outer D conductors) and insulation parameters (dielectric conductivity ε, dielectric dissipation tg δ).

To estimate secondary parameters’ values the pulse method of shorting coefficient determination is often used for coaxial circuits, e.g. applying Р5-10 device or it analogue. An accuracy of the secondary parameter determination by the pulse method is mainly defined by accuracy of the shorting coefficient measurement.

To measure the shorting coefficient you need a cable sample which length is approximately equal to one fourth of the wavelength in the cable in accordance with the frequency of the measurement (e.g. if the frequency is 45 MHz then the length of the cable with solid polyethylene insulation is 1.15...1.20 m).

A determination of the transmission parameters of a coax sample at resonance frequency f _r is possible in the order given below.

Knowing the cable length you measure shorting coefficient ξ by the Р5-10 device (Appendix 9.1).

A resonance frequency f _p is determined from an equation

Hz (2.2)

Here is length of the pattern, m;

ξ is shorting coefficient.

A capacitance of the cable circuit is determined from the an expression

Fpkm (2.3)

Here – ratio of coax outer conductor’s diameter D to inner conductor’s diameter.

Knowing capacitance C or shorting coefficient ξ values a surge impedance of the circuit is evaluated as:

Ohm (2.4)

Here С is a cable capacitance, nFpkm.

An attenuation coefficient for a frequency range of (8…17)·10⁶ Hz is determined according to a formula

dBpkm, (2.5)

Here f is the calculated frequency, Hz;

D is the core diameter of the outer conductor, mm.

A phase coefficient is determined from an expression

Radian per kilometer, (2.6)

Here radian per kilometer is a cyclic frequency.

A phase velocity is determined according to a formula

kmps. (2.7)

To compare the evaluated transmission parameters obtained at temperature of t °C with norms you are to reduce | Z _sim|, aand b to their values at 20°C. The following equation is used for it

(2.8)

Here N ₂₀ is a parameter (| Z_sim|,a, b) reduced to temperature of 20°С;

N_t is the same parameter at temperature of t °С;

a _N is temperature coefficient of the corresponding transmission parameter (relative change of the value at temperature variation of 1 degree centigrade):