signal filter math

Discussion in 'Math' started by davebee, Jan 20, 2011.

  1. davebee

    Thread Starter Well-Known Member

    Oct 22, 2008
    Is anyone here fluent in electronic signal power math?

    I'm trying to make my own 60 kHz WWVB receiver.

    I've made an active filter that works well at 60 kHz, a 3 op-amp state-variable filter where the voltage gain is equal to the Q. Measuring the voltage gain shows a gain and Q of 220.

    The WWVB radio signal marks bits by dropping power by 10 db in 0.2, 0.5 and 0.8 second pulses.

    For the 0.2 second pulse, for example, there will be 12,000 cycles of signal at the lower power.

    A power change of 10 db is also an absolute power change by a factor of 10, corresponding to a voltage change of 0.7, right? If the filter was putting out one volt at full power, then during the pulse, it would put out 0.3 volts, right?

    My question is given the Q of the filter and a power change at the input, what is the math to calculate about how much time would pass before the filter output settles to the new value?

    I'm guessing that the result will be something like a decaying exponential, so I might have to ask for something like how long (or equivalently, how many cycles) until the filter output settles to within 10 percent of the final value.

    I read that in an oscillating circuit, there will be a 2 pi times Q ratio of power loss per cycle, but can't figure out how to translate that into real numbers.