MadSci Network: Physics

Re: Resonant Freq. of a circuit... i.e a household 10amp 240V 50HZ supply.

Date: Tue Jun 1 17:56:00 2004
Posted By: Lawrence Skarin, Rochester Museum and Science Center Technical Assistance Group
Area of science: Physics
ID: 1085738655.Ph

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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