General-purpose passive components
A divider of two 1 % resistors can be off by up to 50 mV on 5 V, but in 4000 simulated dividers the standard deviation is 20 mV. The worst case is safe; the statistics are realistic.
01Resistors
The ideal model of passive components was covered in passive components, in Circuit Theory I; here what matters is real components and how they are chosen. In a resistor what matters is the value, the tolerance, the temperature coefficient (TCR, in ppm/K), the power rating, the maximum voltage, the noise and the long-term stability:
| Technology | Characteristics |
|---|---|
| Carbon film | Cheap, 5 %, high and negative TCR; falling out of use |
| Metal film | 1 % or better, TCR of 15 to 100 ppm/K, low noise |
| Thick film (SMD chip) | The most widely used; 1 % to 5 %, TCR of 100 to 200 ppm/K |
| Thin film (SMD chip) | Precision of 0.1 %, TCR of 5 to 25 ppm/K |
| Wirewound | Power and precision; inductive |
| Metal foil | Maximum stability, TCR close to 1 ppm/K |
Values follow the standard series of IEC 60063, with logarithmic steps: E12 (10 %) has 12 values per decade, E24 (5 %) 24 and E96 (1 %) 96. The rated power holds up to a temperature, typically 70 °C, and above it is reduced linearly. SMD chips are designated by their size in inches: 0402, 0603, 0805, 1206.
02Capacitors
The dielectric decides almost everything in a capacitor: the capacitance per volume, the stability, the losses and the life.
| Type | Characteristics |
|---|---|
| Class 1 ceramic (C0G, NP0) | Stable: 0 ± 30 ppm/K, no voltage effect; up to tens of nF |
| Class 2 ceramic (X7R, X5R) | X7R varies ±15 % between −55 and 125 °C, and loses capacitance with the applied DC voltage |
| Y5V, Z5U ceramic | A lot of capacitance, but varies from +22 to −82 % with temperature |
| Film (polypropylene, polyester) | Low losses and self-healing; filters, audio, snubber networks |
| Aluminum electrolytic | A lot of cheap capacitance; polarized, high ESR, limited life |
| Tantalum and polymer | Compact and low ESR; tantalum ones fail short-circuited if overstressed |
The electrolyte of an aluminum capacitor slowly evaporates, and its useful life depends on temperature. As a rule of thumb, it doubles for every 10 °C below the rated temperature:
03Inductors and transformers
A commercial inductor is specified by its inductance, its DC resistance, its saturation current, where the inductance drops by a given percentage, its thermal current and its self-resonant frequency, above which it behaves like a capacitor. Core materials were covered in magnetic materials. General-purpose transformers, mains ones, are chosen for their rating in VA, their voltages, their regulation between no load and full load, their insulation class and their electrical safety.
04Tolerances: worst case and statistics
The output of a circuit depends on all of its components, and each has a tolerance and drifts with temperature. There are two ways to analyze it: the worst case, which combines all the extremes and guarantees compliance, but oversizes; and the statistical analysis or Monte Carlo, which draws thousands of circuits and estimates what fraction complies.
4000 dividers of 10 V with two 10 kΩ resistors, each drawn uniformly within its tolerance and its temperature coefficient. The histogram shows the output; the red lines, the worst case.
05In the lab
Measure fifty resistors from the same lot and plot the histogram. Does it fill the whole tolerance or is it concentrated?
Measure a 10 μF X7R capacitor with the LCR meter applying different bias voltages and compare with the manufacturer's curve.
Heat a divider with a heat gun and measure the variation of its output, with discrete resistors and with an integrated network.
06Common mistakes
- Using the nominal value of an X5R or X7R ceramic. With the applied DC voltage it can lose more than half of its capacitance.
- Forgetting power derating. A 1/4 W resistor does not dissipate 1/4 W inside a hot enclosure.
- Designing with the tolerance alone. Drift with temperature and aging add to it.
- Placing an electrolytic next to the heat sink. Every 10 °C more takes away half of its life.
07Self-assessment
How many values per decade does the E24 series have?
Twenty-four.
A 1000 h electrolytic at 105 °C operates at 65 °C. How long does it last, according to the rule of thumb?
About 16,000 hours.
What is the worst-case error of a 1:2 divider with 1 % resistors?
±1 % of the output: ±50 mV on 5 V.
What ceramic capacitor is used in a precision oscillator or filter?
A class 1 one, C0G or NP0.
08Further reading
- Charles A. Harper (ed.). Passive Electronic Component Handbook. 2nd ed., McGraw-Hill, 1997. The technology of resistors, capacitors and inductors.
- Paul Horowitz and Winfield Hill. The Art of Electronics. 3rd ed., Cambridge University Press, 2015. The opening chapter and the appendices on real components and how to choose them.
- Henry W. Ott. Electromagnetic Compatibility Engineering. Wiley, 2009. The behavior of real passives at high frequency.