|MadSci Network: Physics|
Hi Phill: Delighted to talk with Australians. I am a big Dr Karl Kruszelnicki fan. Electric circuits with discrete capacitance and inductance can have resonant frequencies. If there is only one inductance and one capacitance, then one resonant frequency occurs. However, the fun begins when inductance and capacitance are distributed. This turns the circuit into a "transmission line," which requires a more complicated theory. It’s called, Transmission Line Theory, if you want to look it up. Depending on what are called “terminations,” the transmission line can indeed have many resonant (and anti-resonant) frequencies. But the oscillation you are encountering is best understood from Continuous Feedback Control System Theory. There is something called the Barkhausen Criterion that says an amplifier will oscillate (make its own AC signal) if any sinewave frequency exists that gives a gain of 1 at a phase angle of 0 around a loop from an output to an input. You have encountered this when a microphone got too close to a speaker in a public address (PA) system. (However, the amplifier quickly becomes overdriven, so don’t expect the waveform to be a sinewave.) Oscillation can also occur where feedback is all electric and not acoustic. But this cannot strictly be called a resonance (although a preference for one frequency could broadly be called a resonance). Indeed, there are operational amplifier configurations called active filters that resonate at a particular frequency. And all these circuits use feedback. The 50 Hertz you have in Australia is no more prone to resonances than the 60 Hertz in North America. The inductance and capacitance needed to resonate at these low frequencies don’t exist except in power systems labs. Also, the voltage does not matter. Metals like copper have no intrinsic resonances in circuits. However, printed circuit board traces – copper, gold, silver, or any conductor, have distributed inductance (all by themselves) and distributed capacitance (relative to surrounding conductors). Therefore they are transmission lines with transmission line properties. So control and transmission line theory will give you food for thought. This reminds me of the old engineer joke that if you try to build an amplifier you get an oscillator, and vice-versa. The best to you and your wonderful country. Larry Skarin
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