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Hi Bob: It's funny you used that circuit to demonstrate "Error Budget," as we recently went through this exercise with the exact same circuit as Figure 1 (see "What's All This Error Budget Stuff, Anyhow?" June 8, p. 18). Too bad it was only done after we discovered the problem while we were evaluating a production run.

(Ouch! The circuit of Figure 2 is cheap, but the first circuit is less accurate, even if you shop for 6-cent 0.1% resistors. /rap) A seasoned engineer designed in the circuit, and he should have known better. Even after having had the problem pointed out to him by a young engineer, he still stood behind the circuit, downplaying the error. (When you write down an error budget, it's kind of hard to downplay that. And if the actual output offset had a distribution that was lousy, that really confirms it. Taking out the op amp and measuring the resistors on a few bad units also will confirm the problem. /rap) This should also be a good reminder for all engineers not to become complacent with their experience and neglect "error budget" calculations.

  • Anonymous (via e-mail)
  • Pease: For sure. Thanks for the painful confirmation.

Good morning, Mr. Pease: I have a question regarding cascading first-order RC low-pass networks. If I have a one-pole lowpass RC circuit, the cutoff frequency is 1/(2PI*R*C). If I add another first-order RC low-pass to the right, in cascade, the circuit now has an FC of 1/(2PI*R*C*2.66). If I add a third RC section, FC becomes 1/(2PI*R*C*5.12), and so on. As I kept adding RC sections, the cutoff frequency was reduced more and more as more sections were added, but I was still able to gain an additional 6-dB/octave rolloff per RC section I added. This is, of course, if all R's and C's are equal and the FC's from each RC section are the same. Is there any formula for determining the cutoff frequency when the R and C values from each LP RC stage are different? For two-pole and three-pole low-pass RC circuits, all I was able to find were LC filter calculations. But I cannot take this approach since I am working with a medical device that will be in the MRI room where no L's can be used. If you don't know of any such calculations, can you recommend a way to get to them via other parameters?

  • Eduardo M. Rey (via e-mail)
  • Pease: Hello, Eduardo. Most people who have to do a lot of filtering use op amps to buffer the stages and prevent the second filter from loading the output of the first one. Also, they make Sallen-Key filters to make the rolloff more crisp. Can you use op amps? If you can't, then I can't guess how to help you. Check out NSC's Webench at, which can make good filters with two, four, six, eight, or more poles. You also can taper the filter's impedances so the second stage doesn't load the first so much. For example, the first filter might be 1k and 1 µF; the second could be 10k and 0.1; the third could be 100k and 0.01. But the impedances get pretty high. You don't have to use a factor of 10. You could use a factor of 2 or 4 or (??). Still, even if inductors aren't permitted, op amps can run on soft power supplies without causing dangerous sparks. Maybe the filter can be sealed up, as a potted module, with no chance for sparks. Do your rules have ways to permit op amps? They can run on ±2.5 V quite nicely, and I'm sure there are ways to prevent sparks. Those are the only ideas I can think of. If you just had to compute the frequency response of different networks of various R's and C's, you might use Spice. It might help for step response, too. I don't normally like to use Spice, but it might be okay for simple yet tedious cases like this. Best wishes./ rap

Hi Bob: You seem to enjoy stories of interesting uses of everyday objects. Yesterday, my 7-year-old daughter fell off a skateboard and broke her arm. I got home about the same time my wife was about to transport her to the hospital. They came out to meet me, and my poor little girl's hand was dangling from the end of her arm. Though she was trying to hold it still, it was very painful and obviously broken. It took a second, but the old Boy Scout first aid finally kicked in. "Grab a magazine for me!" I told my oldest son. He dashed off and returned with one of the May issues of Electronic Design. I wrapped the closed magazine around her arm and wrapped that with an Ace bandage. It immobilized the arm quite nicely. Even got kudos from the ER staff who said "great job—most people come in here with dangling end effectors and do no basic first aid..." Moral of the story: Magazines make great splints, and it gives you something to read while the docs are working on your baby. I encourage everyone to review basic first aid and take a CPR class. You never know who you'll help.

  • David (via e-mail)
  • Pease: Hello, David. Your quick response was quite good.

    But I usually think of a newspaper, because a newspaper is a bit softer and can be rolled longer for longer control on an adult's arm. However, for a kid, a magazine would be long enough. Thanks for the comments./ rap

Comments invited! [email protected] —or: Mail Stop D2597A, National Semiconductor P.O. Box 58090, Santa Clara, CA 95052-8090

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