domingo, março 16, 2008

Precision Resistors

A lot of hobbyists want to make their own circuits but they face a problem: precision resistors.

There are many projects where the ratio between resistances is more important than the actual values. In these case we can measure our resistors to select the most appropriated.

Let me show an example. Suppose we have an inverter amplifier as shown in figure 1.

Figure 1 - Inverter Amplifier

Gain is determined by equation

We can see that the circuit's gain is determined by the ratio between Rf and Ri.

Suppose we want a gain of X.

If Rf = 10,000 ohms and Ri = 5,000 ohms the gain is -2.

If Rf = 20,000 ohms and Ri = 10,000 ohms the gain is -2 too.

If we use resistors with tolerance (precision) of 5% the gain could vary between -1.81and -2.21 depending on real values of resistors Rf and Ri.

If we use resistors with tolerance (precision) of 2% the gain could vary between -1.92 e -2.08 what is much better.

What if we don't have precision resistors? What can we do?

We can use our ordinary resistors (tolerance of 5%). Take a bunch of them and measure each one until you find two resistors with a resistance ratio as near as possible of the value we wish (It is 2 in our sample).

Let me illustrate with an example. Say we take a bunch of resistors of 20K and 10K ohms (nominal values) to measure.

Suppose we found some resistors of 20,900 and 10,400 ohms. So we could do Rf = 20,900 ohms and Ri = 10,400. With these values, the gain would be -2.01 that is a better result than estimated with 2% tolerance resistors.

If we found Rf = 21,000 and Ri = 10,500 than the gain would be exactly 2.

The method, presented in this post, to use ordinary resistors instead of precision resistors is suitable only in prototype development. In commercial scale it is not feasible and the use of precision resistors is mandatory.

Note: As Maurício de Oliveira wrote in his answer to the brazilian portuguese version of this article, precision resistors are manufactured in a way that they take in account changes in their resistance by changes in temperature and manufacturers to their best to minimize it.

So, there are differences between precision resistors and ordinary resistors.

In this article (that I wrote to hobbyists), I am not taken this in account because hobbyists don't design professional circuits and then it will not cause too much trouble. Then it is a valid approuch for a experimental circuit.

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