Minimum phase — what a peculiar expression. I first encountered it while visiting the famous audio scientists, John Vanderkooy and Sidney Lipschitz, at their lab at Waterloo University. Audio Products was a sponsor of one of their students projects, creating a computer program to design crossovers.
John was always enthusiastic. He had taken me upstairs to one of the physics labs and dropped a coin into an unusually strong magnetic field demonstrating how eddy currents in the coin caused it to stop falling, at least not so fast.
Today, he was excited about their new piece of test equipment, a Rockwell spectrum analyzer incorporating new computer Fast Fourier Transform technology. This $50,000 behemoth would send a click through an amplifier speaker and microphone and calculate the frequency response in a few seconds, from my experience, unbelievably fast. I was used to the mechanical charts and motor driven swept sine wave that could easily take minutes for a much more primitive result.
The Rockwell analyzer had a screen that would show the probability that any particular frequency in the measurement range was directly caused by the input from the machine. John explained that when the probability was 100% the system could be characterized as minimum phase.
Other language for minimum phase is direct cause and effect. In a loudspeaker, the current from the amplifier causes the voice coil to move in its magnetic field. This is a minimum phase phenomenon. The voice coil is attached to the cone and causes the cone to push against the air, creating a sound wave. As long as the cone is moving exactly with the voice coil, this continues to be a minimum phase phenomenon. However, at higher frequencies, the cone material begins to bend when it doesn’t have enough time to keep up with the voice coil and a sound wave is transmitted through the cone material, causing vibrations within the cone material and, at some frequencies, a flapping at the outer edge of the cone.
This is not a minimum phase phenomenon. Somehow, the human hearing system is able to detect that fact. Even though the frequency response and distortion may be perfect, the cause and effect chain is imperfect. The sound quality is also imperfect.
This is why I have never been satisfied with the sound of soft dome tweeters. Even though their frequency response measurement may be perfect, at high frequencies (usually, above 10kHz) the dome is vibrating and causing sound more or less independently of the motion of the voice coil. It is analogous to the tuning fork; after being struck, the tuning fork continues to vibrate completely independent of the original force. The sound from a bowed violin string is minimum phase; the sound from a struck piano string is not.
In my opinion, one of the virtues of the inverted dome tweeter I invented to start Epicure Products is that its rigidity and hence its minimum phase characteristic extends into the top octave of human hearing. This is why I intend someday to upgrade my Silent Speaker design to incorporate an inverted dome tweeter.
The present design uses a soft dome tweeter because of financial considerations. When I designed the Silent Speaker I didn’t have the resources to make an inverted dome tweeter and no one else was doing it.