elektor electronics - 11/200576

HANDS-ON LABTALK

Karel Walraven

Prices in the supermarket are often rounded to 5 pence,but the price of cars is usually rounded to hundreds ofpounds. There is apparently a relationship between theamount to pay and the accuracy.

equal steps, were manufactured.Obviously, this range cannot bemaintained, because with lowvalues, the steps are much toolarge, and with high valuesmuch too small. The solution tothis dilemma is a better under-standing of the concept of toler-ances as follows: A 1000-Ωresistor with a ±10% tolerancecan have a value from 900 to1100 Ω. The region from 900 to1100 Ω is therefore covered.The next value has to be selectedin such a way that it neatly con-tinues the range. The value of1200 Ω is suitable, because theactual value will be between1080 and 1320 Ω. Then fol-lows 1500 Ω with a valuebetween 1350 and 1650 Ω.This is how the E12 range hascome about. For the pickyamong us: to calculate the un-rounded E12-values you need totake the twelfth root of 10, whichresults in a factor of 1.212. Sothe E12-series should actuallyhave the following values: 1.0 –1.212 – 1.468 – 1.778 –2.154 – 2.610 – 3.162 –3.831 – 4.642 – 5.623 –6.813 – 8.254. With these val-ues, the tolerance regions do notoverlap.In actual daily use we’re not thatconsistent, because with a 5%tolerance we should really beusing the E24-series. We nor-mally don’t do that, we use E12values and allow gaps betweenthe values.

(050288-1)

TolerancesHow accurate do you need to be?

are not relevant right now. Youcould say that the negative feed-back is dominant here. The char-acteristics of the negative feed-back circuit determine the mostimportant characteristics (gain,in this example) of the design.The components that are part ofthe negative feedback circuithave a much higher demandplaced on them and may nothave large tolerances. Fortu-nately, negative feedback in itssimplest form consists of notmore than two resistors andresistors are stable and easilymanufactured in just about anytolerance.

We usually use 5%-resistors (thatis, resistors with a 5% tolerance)in our designs, and occasionally1% or even less. We do that,because you will not hearwhether the volume of an ampli-fier is 5% higher or lower. If youwere to measure it (with aninstrument that has an accuracythat is better than 5%) then youcould easily measure a differ-ence between amplifiers (leftand right channel). This is alsothe reason why in your digitalvoltmeter with an accuracy of1% or better, 1% or even 0.1%resistors are used in the criticallocations.

About a century ago, somedesigners had not quite graspedthe idea of tolerances. Resistorswith values of 1000 Ω, 2000 Ω,3000 Ω, 4000 Ω, and so on in

This idea can be misleading,because we’re used to thinkingin absolute amounts. When asalesman says that a product isonly 5% more expensive andthat it doesn’t amount to much, Ialways immediately suggest thathe gives me 5% of his salary. Itis not much, is it? UnfortunatelyI have never succeeded in get-ting even a single cent this way.When you use an ordinary tran-sistor such as the BC547B, thegain can easily have a toleranceof 100%. Many electrolyticcapacitors have tolerances from–20 to +50%. With resistors, atolerance of 5% or 1% is quitenormal, but most capacitorshave a tolerance of at least10%. If you look at it that way,it is a small wonder that circuitsactually work at all! Or does itnot work that way?The designer of the electronic cir-cuit has to keep tolerances verymuch in mind. He has to designit in such a way that the properoperation of the circuit is guar-anteed under all circumstances.That is normally done be design-ing in a suitable margin, forexample, by assuming the low-est gain for all the transistors.This results in a design that hastoo much gain, which is subse-quently corrected with negativefeedback. This is a kind of trade-off, where gain is sacrificed inorder to realise a reproducibledesign. Incidentally, negativefeedback is also necessary for awhole host of other reasons that

Figure 2. Tolerance regions for the E12series. Because the values are rounded,the regions do not join exactly but overlapa little or leave a small gap.

1000

1500

2200

3300

4700

5600

1200

1800

2700

3900

1100

050288 - 12

1350

1980

2420

2970

3630

4230

6800

6120

1000010000

1000

9000

7480

5170

1650

1080

1620

1320

1980

2970

3510

4290

5040

8200

7380

9020

6160

2430

+U

050288 - 11

Figure 1. Negative feedback in its sim-plest form using Rt. We sacrifice gain andin return we obtain a fixed amplification,a stable DC adjustment and high inputresistance.