Measuring Pulse Speed in RG-58A/U Cable

Nov 02, 2012

This note describes using the Analog Discovery design kit along with the Waveforms software to measure the speed of electrical pulse propogation in coaxial cable. A short electrical pulse is launched down a length of coaxial cable and the reflected pulse and its delay are observed under various cable termination conditions.

The Setup:

The simple configuration is shown below. A short electrical pulse (~ 1ns) generated with a simple avalanche transistor circuit, is coupled to a length of cable. The Waveforms oscilloscope Ch1 is connected at the input to the coaxial line as shown and monitors the pulse launched into the cable. The narrow electrical pulse propogates down the coaxial cable transmission line, is reflected at the far end and returns to the input end where the return pulse is also observed. The length of the cable and the delay time of the pulse enable the propogation velocity (essentially the "speed of light" in the cable) to be determined. The delayed pulse is observed with the far end (a) open circuited (b) shorted and (c) terminated with a 50Ω connector:


The RG-58A/U cable consisted of a few cables connected using BNC unions. The total length, including the unions was 232". Therefore, the pulse delay pathlength is twice this or 464" (1178.6 cm). The scope traces below show the input pulse with the coax cable disconnected, the input and reflected pulse with open end, shorted end and 50Ω terminated end:

With the cable open at the far end, the reflected pulse is the same sign as the input pulse since the reflection coefficient with an open (~ infinite load) is 1.0. The pulse delay is 59.6nsec. With the cable shorted at the far end, the reflected pulse is inverted as expected since the reflection coefficient with a short (~ 0 impedance load) is -1.0. The pulse delay is the same at 59.6ns. Finally, with the cable terminated at the far end with a 50ohm connector, the reflected pulse is absent, consistent with a reflection coefficient of zero for a coaxial cable characteristic impedance Zo equal to the termination load. The secondary oscillations observed are probably due to seconday reflections at the connectors and reflections from the primary pulse at the circuit input.

The pulse propogation velocity is easily calculated as:
Vp = 11.79 m / 59.6e-9 sec = 1.98e8 m/sec. = 0.66C
where C is the speed of light in vacuum or 3.00e8 m/sec. This velocity value agrees with the velocity factor of 0.66 for this type of coaxial cable.

The total capacitance of the cable was measured using a multimeter at 596 pF or 31 pF/' or 102 pF/m, again in agreement with the cable specifications. The phase velocity (approximately the pulse or "group" velocity here) neglecting cable losses is given by:

where Cc and Lc are the capacitance and inductance per unit length of the cable. Using the measured values of Vp and Cc, the inductance of the cable is determined to be 250 nH/m or 76 nH/'.
Finally, the characteristic impedance of the cable, neglecting cable losses, is:

and a value of Zo = 49.5Ω is calculated in agreement with the nominal 50Ω value for this type of cable.