Design Article
An Excelent fit, Sir!
Kendall Castor-Perry
10/5/2009 11:12 AM EDT
This is the first of two columns showing a simple technique for designing, optimizing and implementing a response-equalizing filter. The second part will look at implementing it on PSoC3; this part is about the design process. Figure 1 is the first piece of our story. It's the curve of the sensitivity of a sensor versus frequency (what kind of sensor, do you think?):
The customer wanted to equalize this so that the final sensitivity would be "independent of frequency". Now, an elementary rule of Filter Wizardry is: the frequency response of a filter doesn't stop at the edges of the graph. It's important to understand what the response should do outside this range. "Don't Care" doesn't mean "Don't Need To Care".
Now, I'll wager that the response of that sensor continues to fall off at 20dB/decade outside the graph limits. But it would be a terrible idea to boost the response with gain that continues to rise without limits. We'll want the response to flatten off or even fall back down, to avoid noise problems. For a first try, let's hold constant the response outside figure 1's frequency range, for one extra decade in each direction; figure 2:
We want to design a realizable filter with a frequency response approximating this curve to an acceptable error. The low frequencies involved indicate using a digital filter to avoid bulky external passive components. That's handy, because PSoC3 has a built-in 24bit digital filtering engine, so fast that it'll hardly have to wake up to crunch out anything I'll ask it to do here. The digital stuff is for the next column; first, let's design it in the analogue domain.
Figure 2's response is flat at one end, wavy in the middle and flat at the other end (apologies to Monty Python); that's a second order 'shelf' equalizer. The amplitude response of the general second order transfer function or 'biquad' section:
is easily computed in a spreadsheet. With ω equal to the input frequency divided by the frequency to which the transfer function is normalized, a bit of manipulation gives:
Comments
Ray Keefe
10/9/2009 6:37 PM EDT
Hi Kendall,
nice demonstration of how to go about developing a filter from a set of response criteria. I especially liked your explanation of how to get the initial coefficient guess into the right ball park on page 2.
Running a company that routinely takes on analogue design challenges including both electronics based solutions and software based equivalents on the other side of the ADC I particularly appreciate seeing examples like this.
I'm looking forward to your next column on doing the same coefficent fit and implementation in the digital domain.
As a suggestion, some of your readers might appreciate the spreadsheets being available for download. I would. No matter how many times I have solved a particular design challenge I find I can always learn something new from studying how another problem solver approaches the problem.
As for a guess at the sensor type. It is a temporal band pass response so it isn't an absolute value reading device like temperature, humidity, radiation, gas detector, accelerometer of the silicon or mechanical stain variety, accelerometer of the capacitive type, distance measurement or light metering.
Some piezo type sensors can behave like this when they aren't in a charge amplifier configuration so it could be a vibration sensor, shock sensor or an accelerometer for delta measurement only but the upper frequency rolloff seems to be at too low a frequency for this.
Siesmic detector is another guess. The roll off is at a bit too low a frequency for this so some normalisation at the upper end would be helpful.
A flow measurement device is another option. Not the spinning wheel variety but maybe a doppler shift or thermal equilibrium version. But again the time domain respose is very low for this application if it was doppler shift based.
I was project leader for the LASER based version of the VESDA Very Early Smoke Detecting Apparatus and a number of the competitor products worked on pollution measurement with time constants like this but that was on the other side of the software metrics system.
Some PIR based personal presence detection systems also have similar filters to take out the background IR and only show the changes but again that was part of the software discrimination and not necessarily the sensor itself.
Getting warm?
Thanks again for a great article on analogue design priciples and solving for a filter response requirement. Keep them coming.
Ray Keefe
http://www.successful.com.au
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bcarso
10/21/2009 1:11 PM EDT
Kendall, congrats on getting a job! Must be quite a relief.
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