An often-seen controversy in tech audio discussions is whether phase shifting a signal causes that signal to be delayed. This is important for instance in discussions about negative feedback. It makes quite a difference whether you assume that the signal that is fed back has been delayed or not. My purpose in this short essay is to argue that phase shifting a signal does not delay a signal. I have an upcoming installment (circumstances allowing) that takes the results from the present essay and applies it to the concept of negative feedback.

For this week, I want to use three different argumentative threads to prove my thesis: the first one will concern phase shifted sine waves and see if we can resolve the question. Then I will do the same with a non-sinusoidal wave. The last argument will be based on pure logic and should hopefully clinch it once and for all. So, let’s go.

Figure 1 shows a simple first-order phase lag network, through which we will pass a sine wave. Input and output are shown in Figure 2. Blue is the input signal; red is the output of the Figure 1 network. The salient points (peaks, zero crossings) occur at different points in time, and you could be excused to think that the red curve is time-delayed with respect to the blue source.

The problem with sine waves is that a delayed or phase shifted version still looks like a sine wave; there's no way to know which point on one curve correspond with the same point on the other. What if we could use some kind of marker on the source signal, and see where that marker ends up on the phase shifted output signal?

That is what Figure 3b below shows. I placed a pulse on the input signal, and we see that the pulse ends up at exactly the same time point on the phase-shifted output signal! Clearly, there is no time delay between the two signals! (The marker on the shifted wave is much lower in amplitude, and integrated; this is fully as expected when you send a pulse through a low-pass filter. But the timing is spot on).

Preliminary conclusion: phase shift does not time-delay a signal.

OK, how about non-sinusoidal waves, like a square wave? Figure 4 shows a square wave passing through the same first-order RC low pass as Figure 1. This signal has inherent markers: the rising and falling edges. As expected, the wave shape is distorted; the square wave contains a multiple of odd order harmonics at different levels, which are attenuated by the low-pass filter in different amounts (the signal is low-passed). Yet, the “markers” in the square wave (the rising and falling edges) in the output fall at exactly the same time as in the input, again proving that the signal is not delayed in time.

Last, a logical argument in the finest tradition of the ancient Greek logicians. So far, we have been looking at a phase-lag circuit. If, for some reason you still believe a phase lag delays a signal, then you must logically agree that a phase lead circuit would advance a signal. In other words, it would cause an output signal to appear before the input signal is applied. That would require a fully functioning time machine.

We’ll pick this up again next week and look at the implications of these findings for negative feedback.

Comments invited.

audioXpress visited Grimm Audio in The Netherlands to learn more about the people behind this unique company, its products, and philosophy, from source to the acoustic output. And, there's no better way to learn about product development than to visit an audio company and learn from its history and business journey. As a relatively young company, Grimm Audio has consistently put its mark on both the pro audio and hi-fi scene and Jan Didden shares what he learned about their unique in-house development philosophy. This article was originally published in audioXpress, July 2023. Read the Full Article Now Available Here

James Croft offers a very interesting analysis of David Gunness' original patent submission of his Passive Cardioid Speaker design, at the time still waiting patent prosecution. Renowned audio speaker design, David W. Gunness, now with Fulcrum Acoustic, and previously with Electro-Voice and Eastern Acoustic Works, is no stranger to this field of research where he holds numerous patents. Croft was naturally interested in providing a review of the submission, to understand what makes the “improved acoustical circuit,” which “allows improved efficiency, as well as greater flexibility with regard to the size, maximum output, and effective frequency range of the loudspeaker, as compared to prior art,” as the patent abstract claims. This is a fascinating read, especially given that Fulcrum has already proven the validity of the proposed designs in actual products. It seems clear that Gunness achieved “a very good design that should advance the art in the category of cardioid devices,” as Croft notes. This article was originally published in Voice Coil, February 2018.  Read the Full Article Now Available Here