Question

A piece of coaxial cable has 75ohms Characteristics impedance and a nominal capacitance of 69pF/m. what is its inductance per meter ? If the diameter of the inner conductor is 0.584mm, and the dielectric constant of the insulation is 2.23, what is the outer diameter of the conductor ?​

Answer 1

A) L = 0.388 μm

B) D = 3.78 mm

Step-by-step explanation:

We are given;

Characteristics impedance; Z_o = 75 ohms

Nominal capacitance; C = 69pF/m = 69 × 10^(-12) F/m

dielectric constant; k = 2.23

Inner diameter of conductor; d = 0.584 mm

A) Now formula for Characteristics impedance is given as;

Z_o = √(L/C)

Where L is the inductance per metre.

Making L the subject, we have;

L = (Z_o)²C

L = 75² × 69 × 10^(-12)

L = 0.388 × 10^(-6) m

L = 0.388 μm

B) To get the outer diameter, we will use the formula;

Z_o = (138/√k) log(D/d)

Where;

D is outer diameter.

Thus, Plugging in the relevant values;

75 = (138/√2.23) × log (D/0.584)

log (D/0.584) = 0.81158611538

(D/0.584) = 10^(0.81158611538)

D/0.584 = 6.48016576435

D = 6.48016576435 × 0.584

D = 3.78 mm