Speed of a pulse along a coaxial cable

Introduction

Flick a switch in an electric circuit and the resulting effect (for example a light coming on) seems instantaneous. Electrons drift slowly in the circuit yet the electromagnetic wave travels through the circuit at unimagininably high speed.

This simple demonstration using a PC-based oscilloscope gives a clear picture of the time taken for a pulse to travel 200 m in a coaxial cable. It also provides graphic evidence of signal attenuation.

Equipment required

• A PC with PicoScope installed
• A 200 kHz pulse generator (see below)
• 200 m of coaxial cable

Experiment setup

In view of the limited number of applications for a pulse generator in the ‘A’ level syllabus and the relatively large requirement for signal generators, suitable pulses were produced by a signal generator giving a 100 kHz square wave through an R-C pulse-shaping network. (A note is included on pulse shaping- see below)

An ADC-200/50 PC–based oscilloscope (and PicoScope software), with its timebase set to 2 µs per div, was employed.

The coaxial cable was purchased from RS components (a considerable time ago). It is much easier to use if kept on its drum!

Figure 1: circuit diagram

Carrying out the experiment

The 68 ohm resistors equal the characteristic impedance of the cable and prevent reflections.

The capacitor combines with the resistor and shapes the square wave into sharp pulses (see the note on pulse shaping).

Both ends of the outer sheath of the coax are connected to earth.

The signal generator is set at an amplitude of about 1 volt.

Channel A on the scope then shows the pulses before they enter the coax, channel B shows the corresponding pulses as they arrive after travelling 200 m in the cable a satisfying 1 µs later, equivalent to a speed of 2 x 10^8 m·s-1.

Figure 2: waveform as seen on PicoScope

Results

• 100 kHz square wave “differentiated” by RC network (see further note)
• Positive peaks represent the leading edge of the square wave
• Period (read from scope) is 10 µs (ie. 100 kHz frequency)
• BLUE trace is pulse at start of coax cable
• RED trace is pulse detected after 200 m of travel down cable
• Time delay between red and blue is 1 µs
• 200 m in 1 ms = 2 x 10^8 m·s-1.
• The Y-gain for both channels is 500 mV so that attenuation of the red pulse is nicely shown another good discussion point.

Converting the 100 kHz squarewave to pulses (PicoScope view)

• The 100 kHz square–wave (blue trace/channel A) is produced at the signal generator.
• The pulses are produced by the 68 ohm resistance and capacitance, C.
• A suitable values for C is 4700 pF a substitution box was used.
• The R-C network effectively differentiates the square-wave, a good discussion point for mathematically-inclined students (and teachers).