Our original design (Figure 2) used a modulator circuit to combine a DC offset pulse and a continuous carrier wave, to create a carrier wave with a pulsed amplitude (an amplitude modulated wave). This signal was then reflected off the flat target, and the returned signal was demodulated to leave a single DC offset pulse.

The time difference between the original pulse and the returned pulse could then be used to calculate the distance from the transmitter/receiver pair to the flat target.

Unfortunately, the modulator circuit (a typical suppressed carrier modulator based around the LM1596 balanced modulator/demodulator integrated circuit from National Semiconductors (National Semiconductor Corporation, 1995)) proved to be unreliable, and the demodulator circuit (a typical SSB product detector based around the same chip) suffered from poor performance. For example, the demodulator did not return a clean pulse: much of the carrier wave was present in its output.

Another issue with this design is that the setup was very complicated, which made diagnosing problems a long and tedious process. For instance, if while tuning the equipment to increase the amplitude of the returned signal (so that it was large enough for the counter-timer to trigger), the signal suddenly died, the cause of the problem could be anything from a loose connection in one of the two circuits, to a burnt out resistor or an incorrect range setting on the sweep function generator.

Together these problems led us to abandon this particular method, and focus on more reliable alternatives. However, during this initial design stage several important points were noted.

First, with the receiver wired straight into an oscilloscope, perfect mains interference (i.e., a 50Hz sinusoidal signal) with a magnitude of 10mV could be measured. This dropped off considerably when the metal receiver stand was earthed.

Secondly, the signal reflected off the flat board dropped significantly with distance. With the two transducers touching and face to face, 100% of the signal was transmitted, but at 3.2 meters the signal drops of by a factor of 500 and by 6.8 meters the signal has reduced by a factor of 1000.

Finally, it was observed that the frequency response of the transducers had a very narrow bandwidth, peaking at 40kHz. With a difference in frequency of merely ±0.1kHz the power of the transmitted signal fell by several orders of magnitude. Thus any design must use a carrier wave of 40kHz. (This characteristic is the resonant frequency of the transducers, and is given on the data sheets as 40±1kHz.)

Our final design used the same principle, but replaced each circuit in the original idea with a 'black box' component (i.e., commercially available laboratory equipment). This resulted in a marked increase in reliability, as the component are all "industry grade".

The main chance is that instead of using a modulator circuit, we used the amplitude modulation (AM) feature of a sweep function generator. This results in a periodic 40kHz pulse, as opposed to a continuous 40kHz wave that has a periodic amplitude fluctuation. This meant that we did not need a demodulator: we could simply trigger on the first wave of the wave train. Note that the pulse needs to be wide enough to include enough frequency components so that it actually is 40kHz. If the pulse is made very short (as in the order of a few wavelengths of the 40kHz carrier wave) then the transducer would not see the signal as a 40kHz wave but as a wide spread of frequencies and it would not resonate (this would in turn mean that we would not get a signal strong enough to trigger the counter-timer).

When building this circuit, we used a "componentised" (or "object orientated") approach: each module of the circuit was built and tested separately, and was then connected to the rest using only single pieces of coaxial cable.

This minimised the diagnosing problems that were such an issue with the first design, and allowed us to focus on the goal much more (see the Acknowledgements Appendix).

The first such module is the pulse generator. This module has no external inputs, and generates a single output: a periodic, high amplitude pulse of a 40kHz, separated by no signal (0V). The period of this signal should be as long as possible, so that the pulse can travel to the target, be reflected, and trigger the counter-timer with no possibility of overlap (where the next pulse starts the counter-timer before the previous one has stopped it).

This module uses a Thurlby Thandar TG230 2MHz Sweep/Function Generator (Thurlby Thandar Instruments LTD) and a Farnell PG101 Pulse Generator (Farnell Instruments LTD). The output of the PG101 is wired into the AM/Sweep input of the TG230, and the main output of the TG230 is the output of the module.

The following settings were used.

To fine tune the output, a normal oscilloscope was not satisfactory, as the period is so long that ordinary cathode ray oscilloscopes cannot display a steady trace. We therefore used a Philips PM3302 Storage Oscilloscope. With this and the pulse generator output voltage control and the sweep function generator's amplitude modulation (AM) control, the resulting wave could be adjusted until the carrier wave was negligible in between the pulses. (This is what distinguishes this method from the carrier wave amplitude modulation method of the initial design.)

Note that by having both the pulse generator's output and the sweep function generator's output displayed on the oscilloscope at all times, this component could be easily checked whenever a problem occurred.

This module uses a Racal-Dana Universal Counter-Timer 9904M (Racal-Dana Instruments LTD, 1977), an ultrasonic transmitter transducer, and an ultrasonic receiver transducer.

The output from the pulse module is connected to the counter-timer's "start timer" input (B), and the output from the amplifier module is connected to the "stop timer" input (A). Note that the output from the receiver transducer (Rx in the diagrams) is connected to the amplifier module.

The following settings were used. (Note that the B input was used for starting the counter-timer, and the A input for stopping it.)

The A Trigger Level (sensitivity setting) had to be adjusted depending on the distance. This is due to large fall off in the signal strength with distance. (Basically, if the counter-timer does not trigger, then the sensitivity setting should be adjusted until it does.)

We originally tried using a circuit based around an operational amplifier to amplify the signal, as the signal returned from the target at a distance of around 3m and above is not enough to trigger the counter-timer. However, op. amps. saturate easily and could not provide the gain we required. We therefore used another 'black box' component, namely a High |Z| Amplifier 9432 from Ortec Brookdeal.

The settings on the amplifier were as follows.

Figure 3 shows the layout of the complete design.

This design showed vast improvements over our initial design. Firstly, the lack of any 'hand made' circuits was a great help. In this design diagnosing a problem was mainly limited to a quick check of the oscilloscope traces and a check that the transducers were pointing in the right direction.

Secondly, the use of an amplifier 'black box' instead of a 'hand made' op. amp. circuit allowed us to get a very high gain, which easily counteracted the problems with the signal loss at the distances involved.

Thirdly, the use of coaxial cable throughout resulted in considerably less mains interference than was measured when using the circuits in the initial design.

In fact, our use of proven, industrial-grade, reliable equipment throughout helped in general to get better results than a hand rolled solution could have. It also allowed settings to be customised on the fly, instead of requiring changes to the circuits (for example, changing the gain on the op. amp. circuit required a change of resistors, whereas a change of gain with the Ortec Brookdeal amplifier merely required the adjustment of a knob).

One problem with this design, although not a particularly important one, is that the sensitivity of the counter-timer needs to be continuously adjusted as the distance measured changes. This is because a low sensitivity setting will not recognise small voltages (as required with a large distance) and a high sensitivity setting will not recognise (due to clipping) the large voltages of the shorter distances.

A more serious limitation is that the range of the acoustic RADAR is only a few centimetres more than the required range of 1 to 5 metres. Similarly, only objects that have a flat surface perpendicular to the transducers can be detected. Both of these limitations are within the brief, however.

Our ultrasonic ranging system gave us the distance to the target in terms of the time between sending and receiving the pulse. To convert this into a distance, we characterised (or calibrated) the system by measuring the distance to the target and the time measured, and then plotting them (see first graph).

We measured the time taken for distances in increments of 20cm and 50cm. For each distance, we took 4 measurements, and plotted the mean. We also attempted to reduce any creeping errors by taking the measurements in a staggered fashion (1.0m, 5.0m, 2.5m, 1.5m, 3.5m, and so on).

The trend line (a linear least squares fit of these means) passes almost exactly through the origin, which indicates a low fixed error (we would expect the line to go through the origin if there was no fixed error as at 0 distance the wave should spend 0 time in travel).

The maximum spread of time measurements over distance increases by a factor of around 5 over the four meters of the range (from around 0.1% at 1m to 2% at 5m), even when taken as a fraction of the mean time (see second graph). However, up to 4.4 metres the spread stays roughly the same apart from a few outliers (between 0.1% and 0.6%).

Therefore to take accurate readings, many more readings (in the order of 40) would need to be taken for each distance, both during calibration and when taking readings for unknown distances.

The reasons why the error increases with distance include dispersion of the sound wave, false echoes, and movements in air (as the distance increases there is more air to travel through and thus the effects of air movements become more pronounced). There is also a minimum theoretical possible error, which is due to the fact that the pulse is really a wave. Since the counter-timer triggers on a positive edge (see above), if the start of the pulse is in the declining part of the sine wave, the counter will not trigger until up to half a wavelength too late. This also applies to the triggering pulse, and so the total possible error is the time for one wavelength to pass, i.e. the period. This is the inverse of 40kHz, 25 microseconds. (Note that this error does not automatically cancel itself, since the receiver does not receive the signal necessarily 'in phase' with the transmitter, due to the way it is built.)

The trend line provides us with a simple equation for converting time averages into distances:

The number in the numerator is the intercept, and the number in the denominator is the gradient. (All times are in microseconds.)

Note that to convert from the time to the distance, no use has been made of the speed of sound in air or any theories. Simply profiling the equipment as has been done gives the relationship without relying on other approximations.

At the end of the project, we were faced with a target at an unknown distance from the transmitter/receiver pair and were challenged to measure the distance using only our ultrasonic ranging system.

The four times we recorded (in microseconds) were: 19133.7, 19088.0, 19110.9, 19142.4.

Averaging these times and using the equation given above (or using the first graph), we pronounced a distance of 3.22m. The error at this distance (using the second graph) is under 1.2%. Thus the distance 3.22 ± 0.04m.