The patented IDI Coax Probes are designed with a signal conductor continuously surrounded by a ground plane, very similar to a coaxial cable. The properties of the coax probes are determined using the same formulas as that of a coaxial cable at high frequencies.

Characteristic Impedance
The characteristic impedance is complex and contains both resistance and reactance and is independent of length and frequency. The characteristic impedance at high frequencies is defined by the voltage value of a single wave divided by the current value of a single wave. Since the inductance and capacitance are essentially independent of frequency in the “high” frequency range, in terms of inductance and capacitance, characteristic impedance is the square root of the inductance per unit length (L) divided by the capacitance per unit length (C).

Z₀= √ L/C
L is determined by the ratio D/d
C is determined by the ratio D/d and ε
Where: D = Inside diameter of the shielding conductor
             d = Outside diameter of the signal conductor
             ε = Dielectric constant
As the spacing between D and d increases, in general, the inductance increases while the capacitance decreases. Therefore, the characteristic impedance will decrease as the distance between the signal conductor and shielding tube decrease and increase when this distance increases.

Diameter Ratio (D/d) For a Given Dielectric Constant

Dielectric Constant
The dielectric constant (e) of a material is a measure of the relative effectiveness of that material as an insulator. For an electrical signal in a given material, the dielectric constant is approximately the inverse of the square root of the signal speed as compared to the speed of that signal in a vacuum. A vacuum is a perfect electrical insulator and has a dielectric constant of 1.00000. Air has a dielectric constant of 1.00059, virtually the same as a vacuum.



Velocity of Propagation
The velocity of propagation (VP) is the speed at which an electrical current travels through a coaxial cable or probe. Velocity of propagation is usually expressed as a percentage of the speed of light. Since the VP is inversely proportional to the square root of the dielectric constant, the lower the dielectric constant, the faster the velocity.


V = √c/ε
Where: V = Velocity of Propagation
             c = speed of light (3 x 10⁸ m/sec)
             ε = dielectric constant


Reflection
Reflection is the result of mismatched impedances in a transmission line. When the voltage hits the mismatched impedance joint, some energy is reflected. This reflection energy may interfere with the signal if it is out of phase.