Preferred Value Numbering System

The basic idea of this is that for a given range, values are spaced logarithmically to cover an entire number lines. Standard sets are called “E-series; all values have the same tolerance within the series. Below is an E12 series with 10% tolerance:

For example, if I needed a 26 ohm resistor, I can look at this and see that there is no 26 ohm resistor available with 10% tolerance, but we do have a 27 ohm. Either I can just use the 27 ohm or I pay more money for more steps on the scale to get something closer to 26.

Example

Given $V_{in}=5\text{V}$, $R_1=100\text{k}\Omega$, choose the closest E24 value for $R_2$ so that $V_{out}=3.3\text{V}$. What size SMD (surface mount device) resistors will you need? Assume we are working with a voltage divider circuit.

E24 values (5% tolerance): 1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1

We have:

$$\begin{array}{rl}{V}_{out}& =V_{in}\left(\frac{R_2}{R_1+R_2}\right)\\ 3.3& =5\left(\frac{R_2}{10+R_2}\right)\\ R_2& =19.4k\Omega \end{array}$$

From the values above, we see that there is no 19.4 resistor, only 18 and 20 (the provided E24 values need to be multiplied by 10).

• We could choose the 20 kOhm resistor because it is the closest, and thus would minimize error.
• We could choose the 18 kOhm resistor as the 20 kOhm would exceed the 3.3V output.

Let’s say we choose $R_2=20\text{k}\Omega$, we would have:

$$V_{out}=3.333\text{ V}$$

We also need to consider the size of the resistor; they need to dissipate heat, and a small resistor might not be able to handle it and melt off the board.

$$P_{R_2}=\frac{V^2}{R}=\frac{3.333^2}{20K}=544\mu W$$