Project C+ Solved （2）

Published:2011/7/27 3:02:00 Author:Amy From:SeekIC

By Prof. Martin Ohsmann

Causality

Causality states that in our physical world the flow of events is always the same: first, cause, then effect. You are aware of pain in your thumb after you hit it with a hammer and not before the unfortunate accident. If this prin­ciple is universal, is it possible in our simple circuit that a signal arrives at the output of a filter before it was applied to the input? Clearly not. To understand what really is going on in the circuit we need to take a closer look. Figure 2 shows a block diagram representing the main parts of the cir­cuit. A rectangular pulse is generated when the switch is momentarily closed at t = 0. A low-pass Filter (LPF) is used next to filter out the high frequency components and pro­duce a smoothed Gaussian impulse at B. The pulse is now introduced to the medium and recovered by the lead filter to produce the output pulse C. The recovered pulse is amplified to produce the output pulse C so that its shape is similar to the input pulse.



The circuit doubles-up the pulse shaping and lead-filter stages to optimise the effect. Additional com­ponents in the Lead Filter help reduce noise in the circuit. The more observant among you will have noticed that the output pulse rises more quickly than the input pulse. It was found to be impracti­cal to increase ’negative group delay’ effect further by adding more lead filters. So there really is noth­ing unusual about the circuit, the effect is produced using just con­ventional components. The need for 400 m of cable was also something of a red herring.

The circuit demonstrates that in this case the group velocity is not rele­vant to the (negative) time difference observed between the input and output pulses, here the front veloc­ity (the propagation speed of an abrupt change or front) of the sys­tem is more important.

The effects produced here are still the subject of hot debate on the Internet but in any case you will no doubt be pleased that causality is still intact (at least for the time being) and this experiment under­lines how careful you need to be when interpreting test results espe­cially in systems using slow pulses. A similar phenomenon to that shown here occurs with a Mach Zehnder interferometer (no, honest), where light pulses appear to arrive ‘too early’. For more information on this subject refer to 121. If you are still curious about propagation speeds and anomalous dispersion then the classic work by Jackson [3) should fill in any gaps.

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