How much is a factor of 2?

Question

This paragraph is from The Art of Electronics third edition:

Some more home-grown philosophy: there is a tendency among beginners to want to compute resistor values and other circuit component values to many significant places, particularly with calculators and computers that readily oblige. There are two reasons you should try to avoid falling into this habit: (a) the components themselves are of finite precision (resistors typically have tolerances of ±5% or ±1%; for capacitors it’s typically ±10% or ±5%; and the parameters that characterize transistors, say, frequently are known only to a factor of 2); (b) one mark of a good circuit design is insensitivity of the finished circuit to precise values of the components (there are exceptions, of course). You’ll also learn circuit intuition more quickly if you get into the habit of doing approximate calculations in your head, rather than watching meaningless numbers pop up on a calculator display. We believe strongly that reliance on formulas and equations early in your electronic circuit education is a fine way to prevent you from understanding what’s really going on.

I can analysis the sentence "the parameters that characterize transistors, say, frequently are known only to "a factor of 2". The subject is "the parameters"(or "parameters"), the predicate is "are"(or "are known"), the object is "a factor of 2" but I don't know how much a factor of 2 is. How should I understand "a factor of 2" in here?

This is a question about English, not about electronics. The phrase here means the same thing that it does in many other contexts (admittedly, mostly technical ones). — Karl Knechtel
– Karl Knechtel, Commented 5 hours ago

Barry · Accepted Answer · 2025-12-10 23:19:08Z

A factor of 2 simply means that the actual value of the parameter in question can be as little as 1/2 the value or as much as 2 times the value. For example, if the nominal beta of a transistor is specified as 100, then its actual value for a typical transistor can range from 50 to 200.

vir · Accepted Answer · 2025-12-10 23:49:27Z

They mean that the parameters aren't tightly controlled. Look at this excerpt from a 2N2222 datasheet:

hFE is only guaranteed to be a minimum value; a typical value is only given for a single test condition and it is 3 times the minimum value, so even "worse" than a factor of 2, which would be if the typical hFE value were 200.

There's no good value proposition for tightly controlling these parameters, e.g. making hFE 300 +/-5% or whatever since techniques to minimize the effect of variations already exist and are in wide usage. E.g. for switching you drive it into saturation so even the minimum hFE gives way more current than you need or for amplification you design in more gain than you need and use a feedback network that is easy to design with tight tolerances to set the actual gain. Additionally, many parameters vary greatly with temperature (see fig. 3 on the datasheet).

Thank you for your answer. It seems your answer didn’t explain how much a factor of 2 is? — Tom
– Tom, Commented yesterday
The hFE figure of 300 for Ic = 150mA, Vce = 10V and Tj = 25°C is actually a maximum. The typical (figure 3) for hFE under those exact conditions is about 240. — Spehro 'speff' Pefhany
– Spehro 'speff' Pefhany, Commented 22 hours ago

Andy aka · Accepted Answer · 2025-12-10 23:21:24Z

A factor of two applied to a variable \$x\$ would mean a doubling or halving of \$x\$. So typically, in a bunch of transistors taken from a bag you might find that under the same test conditions and ambient temperature, the range of \$h_{FE}\$ might vary from 50 to 200. That's 100 ÷ 2 to 100 × 2.

This is one example.

sharlot vargas · Accepted Answer · 2025-12-11 16:03:04Z

In engineering, saying something changes “by a factor of 2” simply means the value is multiplied or divided by 2.

A factor of 2 increase → the value doubles (×2).
A factor of 2 decrease → the value becomes half (÷2).

So the phrase doesn’t describe an absolute amount — it describes a ratio. For example:

Going from 5V to 10V = increase by a factor of 2.
Going from 8A to 4A = decrease by a factor of 2.

It’s just a multiplicative comparison between two quantities.

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