Antennas and Microwaves

Entry Page

Contents

I set up this little experiment after re-visiting the Heisenberg uncertainty principal in one of my Physics textbooks and then finding instructions for a demo here.

The screen shots in the left hand column are of an Oscilloscope displaying a sinusoidal  signal in the time domain. The upper and lower traces are timebase x50 and timebase x1 respectively, to show the detail of the signal. The images in the right hand column are of a Spectrum Analyser displaying the same signal in the frequency domain.

The first pair of images are for a continuous sine-wave at 20Mhz. The following 2 pairs of images show the effect of pulse modulating the sine-wave with increasingly narrow pulse widths.

Above we have the Oscilloscope and Spectrum Analyser (SA) plots for the 20Mhz continuous sinewave. Notice that the frequency domain plot is not a single vertical line as theory would suggest but a narrow triangle - this is the response of SA’s 100Khz resolution bandwidth filter, traced out as the spectrum analyser sweeps. However, despite this practical limitation we still get a pretty clear indication of frequency.

If we now modulate the sinewave to give short bursts of sinusoidal pulses, the frequency domain plot is immediately spread out - making it more difficult to be precise about the frequency of the sinewaves in the burst. Notice the Fourier Transform relation between the envelope of the time domain pulse and its frequency domain representation. Not dissimilar to an antenna aperture and its radiation pattern, which are also related by the Fourier Transform.

If we continue to reduce the duration of the pulse, the frequency spectrum spreads out still further. Notice that the spectrum is also reducing in overall power level, this is because there is less average power in the signal - it is spending more time flat than wiggling about. Also of interest is the envelope of the sinewave pulse, the oscillations do not start and finish instantly, they build up and then decay gradually. This is due to the finite bandwidth of the test equipment used.

Taking this to the limit, we can see that the more precisely we try to determine when our burst of sinewaves is (by reducing the pulse duration), the less precisely we know what frequency of the sinewaves is. For anyone involved with radio frequency signals this will all be quite familiar, for others, it hopefully illustrates how knowledge of one parameter can lead to ambiguity in another - the uncertainty principal.

This trade-off between related measurable parameters for the same entity crops up in all sorts of places in nature. The problem of acceptance usually occurs when the implications are counter-intuitive. For example the parameters of position and momentum for a photon are also subject to the uncertainty principal. This is difficult to imagine because our usual experience of these parameters relate to large scale objects, whose position and momentum can be measured accurately at the same time.

This modulated signal example really helped me to get a  feel for and confidence in the uncertainty principal. Once you believe in the underlying principal, it is a lot easier to accept that it may apply in other situations. Perhaps uncertainty is the natural way of things and our everyday experiences of the ‘macro world’ are simply a special case? If you want to delve deeper, there is a lot more information here.   A simulation of this experiment using the Quite Universal Simulator (QUCS) can also be downloaded.

Download QUCS model

The Uncertainty Principal

Page 1 of 1

Back to Top | Contents