Project C+ Solved （1）

Published:2011/7/27 2:21:00 Author:Amy From:SeekIC

By Prof. Martin Ohsmann

The circuit described in the April 2004 edition of Elektor Electronics certainly gave rise to a lot of head scratching and raised eyebrows when it was shown to produce an output pulse ahead of the input pulse. Is it possible that such a simple circuit can turn the principle of causality on its head? Read on...

The idea for this article began when a student asked me if it was possible to build a filter that produced a ‘neg­ative group delay’. A quick trawl of the Internet (Google: ‘negative group delay’) soon gave some interesting hits. In particular Professor Kitano in Japan had published just such a cir­cuit that apparently exhibits a nega­tive group delay [1]. With kind per­mission from him we were able to use his ideas and circuit (slightly modified) in last month’s article. So much for the background, now on to the details...

The concept of speed

If we consider the transmission of information in a communication channel, the first characteristic we need to look at is phase velocity. With a pure sinusoidal carrier wave this is equal to the propagation speed of any point (i.e., constant phase) on this wave. Without any form of modulation it is not possible to send information, so we can see that the phase velocity has no influ­ence on the speed at which we can send information (i.e., the group velocity). Information can, for exam­ple, be transmitted on narrow-band signal pulses or envelopes and the speed of the envelope will be gov­erned by the group velocity through the medium. Now back to the origi­nal question: if a circuit possessed a negative group delay this would imply that the information acceler­ates in the medium and travels back­wards in time to arrive at the output before it was introduced at the input. This indeed is what appears to hap­pen in our circuit.

This phenomenon has apparently been observed in the field of optics where anomalous dispersion (in a narrow spectrum) has seemingly produced a negative group delay and a refractive index smaller than 1. It is often the case that these effects occur when the circuit or medium is in resonance and an equivalent elec­trical experiment is described in a paper [2] which shows an output AM envelope leading the input sig­nal thus yielding an apparent nega­tive group delay.

It is easier to observe these effects by using a filter with negative group delay at low frequencies and DC. The circuit shown in Figure 1 is a (low-pass) lead filter and produces the necessary effects. When a low frequency pulse from the generator described in the first part of this arti­cle is introduced to the lead filter, it should produce an output ’before’ the pulse is introduced.



This basic idea has been perfected by Mr. Kitano [1] in a circuit that maintains the pulse shape through the transmission medium and pro­duces a negative propagation delay. The pulse envelope travels at the group velocity and the pulse appears at the output of the filter before the input signal!

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