Integration w/o Smoothing; Demodulate, Integrate and then Take the Quotient
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From: Bret Cahill on 19 Feb 2010 10:59 There is no reason to smooth after demodulation in some low noise lock in amplifier situations. If you are taking the quotient of two signals that are identical except for magnitude and noise, i.e., shape, frequency and phase angle, simply low pass integrate each signal after each is multiplied by the reference. Once the S/N ratio is high enough simply take the quotient without wasting time to smooth either signal. No smoothing of either demodulated signal is necessary because the rectified humps appear in both the numerator and denominator in phase and with the same relative size as the quotient. This is important in low noise situations where there isn't time to smooth the humps. This simple filtering solution should be fairly common in electronics. Bret Cahill
From: George Herold on 19 Feb 2010 14:16 On Feb 19, 10:59 am, Bret Cahill <BretCah...(a)peoplepc.com> wrote: > There is no reason to smooth after demodulation in some low noise lock > in amplifier situations. > > If you are taking the quotient of two signals that are identical > except for magnitude and noise, i.e., shape, frequency and phase > angle, simply low pass integrate each signal after each is multiplied > by the reference. > > Once the S/N ratio is high enough simply take the quotient without > wasting time to smooth either signal. > > No smoothing of either demodulated signal is necessary because the > rectified humps appear in both the numerator and denominator in phase > and with the same relative size as the quotient. > > This is important in low noise situations where there isn't time to > smooth the humps. > > This simple filtering solution should be fairly common in electronics. > > Bret Cahill What is smoothing? "simply low pass integrate each signal after each is multiplied > by the reference." Low pass filtering is smoothing. Your low pass filter time constant sets the effective "Q" of the lockin. George H.
From: Michael A. Terrell on 19 Feb 2010 15:25 George Herold wrote: > > On Feb 19, 10:59 am, Bret Cahill <BretCah...(a)peoplepc.com> wrote: > > There is no reason to smooth after demodulation in some low noise lock > > in amplifier situations. > > > > If you are taking the quotient of two signals that are identical > > except for magnitude and noise, i.e., shape, frequency and phase > > angle, simply low pass integrate each signal after each is multiplied > > by the reference. > > > > Once the S/N ratio is high enough simply take the quotient without > > wasting time to smooth either signal. > > > > No smoothing of either demodulated signal is necessary because the > > rectified humps appear in both the numerator and denominator in phase > > and with the same relative size as the quotient. > > > > This is important in low noise situations where there isn't time to > > smooth the humps. > > > > This simple filtering solution should be fairly common in electronics. > > > > Bret Cahill > > What is smoothing? In Brett's case? Using a belt sander to remove the humps from a camel. > "simply low pass integrate each signal after each is multiplied > > by the reference." > > Low pass filtering is smoothing. Your low pass filter time constant > sets the effective "Q" of the lockin. > > George H. -- Greed is the root of all eBay.
From: Bret Cahill on 20 Feb 2010 00:02 > >There is no reason to smooth after demodulation in some low noise lock > >in amplifier situations. > > >If you are taking the quotient of two signals that are identical > >except for magnitude and noise, i.e., shape, frequency and phase > >angle, simply low pass integrate each signal after each is multiplied > >by the reference. > > >Once the S/N ratio is high enough simply take the quotient without > >wasting time to smooth either signal. > > >No smoothing of either demodulated signal is necessary because the > >rectified humps appear in both the numerator and denominator in phase > >and with the same relative size as the quotient. > > >This is important in low noise situations where there isn't time to > >smooth the humps. > > >This simple filtering solution should be fairly common in electronics. > > But it's not. Then it will make a perfect method patent. Bret Cahill
From: Bret Cahill on 20 Feb 2010 00:52
> > There is no reason to smooth after demodulation in some low noise lock > > in amplifier situations. More generally, if you are only trying to reduce the noise by a limited amount. > > If you are taking the quotient of two signals that are identical > > except for magnitude and noise, i.e., shape, frequency and phase > > angle, simply low pass integrate each signal after each is multiplied > > by the reference. > > > Once the S/N ratio is high enough simply take the quotient without > > wasting time to smooth either signal. > > > No smoothing of either demodulated signal is necessary because the > > rectified humps appear in both the numerator and denominator in phase > > and with the same relative size as the quotient. > > > This is important in low noise situations where there isn't time to > > smooth the humps. > > > This simple filtering solution should be fairly common in electronics. > > > Bret Cahill > > What is smoothing? Say a rectifier outputs a voltage proportional to |sinwt|. It's not a constant DC voltage. If you want a constant DC voltage then you must smooth somehow. > "simply low pass integrate each signal after each is multiplied > > by the reference." > Low pass filtering is smoothing. Which takes time even if the noise in an ac signal is low or non existent. If you are taking a quotient of two low noise signals as in the OP, however, then no smoothing of each (ref.) X (signal) output is necessary. You only need to integrate just long enough to reduce the noise to an acceptable level. Any voltage fluctuations due to the signals will cancel in the quotient. Bret Cahill |