DESIGN & PRODUCTS aNalOG DESIGN However, I must admit that the presentation isn’t perfect, and jump up by pi radians and then jump back to where it would I’ll explain what the unwrapped graph ’should’ perhaps look like have been. The trouble is, we can’t say where it would have later. been without referring to prior values on the plot. The current Now, the ‘problem’ is that pi radians represents an inver- plotting routines don’t “look back”; at the time we defined the sion of the signal passing through the filter. If you ‘take away’ plotting routines, I wasn’t sure that forcing a particular inter- the phase shift corresponding to the static time delay of (in pretation of the data was the right way to go. But I might get this case) seven samples, you’ll see that as you move into it changed in a future version. Anyway, mea culpas aside, this the stopband, the filter’s signal polarity flips abruptly between phase behaviour is sometimes pointed out in textbooks, but the non-inverting and inverting as you pass through each of the null usual line of reasoning is: Why bother about this? The signal frequencies. level is so low in the stopband that we really don’t care if that To be honest, when we plot this kind of behaviour on an un- tiny residual comes out upside down or not. wrapped presentation, we should really see the phase response But here’s the next factor to consid- Efficient POWER common box-car averaging filter, whicher: sometimes that stopband rejectionmight not be so high. Consider the SOLUTIONS rather generous to refer to those re-is nothing other than a FIR filter all ofwhose coefficients are the same. It’s from the wall to the point of load TM gions between the nulls as ‘stopbands’ at all, since they hardly ‘stop’ those frequencies, but merely hinder them a little. Figure 2 shows a response plots for a seven sample averager. Averaging filters are often used to ‘smooth’ data sets to suppress random noise and reveal underlying trends in the data. They are commonly used in the financial world, for instance. A seven sample moving averager can be 10W~400 W noise and weekly fluctuations in, say,applied to daily data to remove both a commodity price. This filter will have Digital Power Modules nulls at 0.1428 price wobbles per day Intermediate Bus l Point of Load and its multiples (in other words, once every 3.5 days, once every 1.75 days, and so on). But let’s suppose that 0.25 W~600 W Dc-Dc Converters Board Mount l Chassis Mount 1W~2400 W Fig. 2: Amplitude, phase and group delay plots for a seven sample Ac-Dc Power Supplies averager Open Frame l Chassis Mount l External With a continuous focus oneffi ciency, density, andsystem optimization, we keep our customers on theleading-edge of the power curve. Fig. 3: A six day fluctuation, and the www.cui.com/power seven day moving averager’s response 40 Electronic Engineering Times Europe October 2012 www.electronics-eetimes.com

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