How much is “a few percent over six decades”?

Question

I saw the following paragraph in a book on electronics(The Art of Electronics Third Edition):

In Chapter 2x we will examine better ways of constructing logarithmic converter circuits, along with careful methods of temperature compensation. With such methods it is possible to construct logarithmic converters accurate to a few percent over six decades or more of input current. A better understanding of diode and transistor characteristics, along with an understanding of op-amps, is necessary first. This section is meant to serve only as an introduction for things to come.

More background information:

1. In this section, authors are introducing some kinds of converters, which generate an output voltage proportional to the logarithm of a current.

2. "Methods of temperature compensation" mentioned above can make converters insensitive to changes in temperature, which is desirable.

3. This is the last paragraph of this section.

My question is: How accurate are these converters?

Answer 1

This is a technical use of the word decade, relating to logarithmic scales of measurement. The everyday usage of decade is to signify a period of 10 years. In the technical meaning we are concerned with a scale effectively working in powers of 10, so 1, 10, 100, 1000 etc. Each such step is referred to as a decade.

So in the referenced section we a dealing with measuring accurately over 6 decades of difference, that is say from 10 units (perhaps milliamps or some such) to 10,000,000 units - that is 6 factors of 10 bigger. The objective being to be accurate over that wide range. The stated accuracy being a few percent.

I read this as meaning that the measure value should be within say 3% of the actual value. Hence for

100 we should expect read between 97 and 103

10,000 between 9,700 and 10,300

10,000,000 between 9,700,000 and 1,030,000

See Wikipedia article on log scales

Answer 2

You're grouping the words wrong. Read it as: "With such methods it is possible to construct logarithmic converters accurate to a few percent; and the accuracy is maintained over six decades or more of input current. "

My dictionary says as the third meaning of decade: "A range of electrical resistances, frequencies or other quantities spanning from one to ten times a base value". So this might be a converter that measures the input current accurately to a few percent of error, for currencies from one milliampere to thousand amperes, or a similar range.

Answer 3

The meaning of the example you gave seems to be that the circuit will remain accurate within a few percent during a six decade lifetime. In other words it is telling you the accuracy will not alter over time; in this case over 60 years of constant use. "a few" usually has the meaning of from 2-4 (or so), but it is not a precise value; the author in this case is being unclear and may clarify his meaning further once past this introduction. Note that he only says that "it is possible", so how likely a circuit will be this accurate is not specified either.

One rule to follow when reading is that no matter how much meaning you want to pull out of a statement, if the writer is vague or imprecise in writing, the meaning is not there to be extracted, no matter how hard you try.