Passive Components, Part 1: Resistors

Undoubtedly, rx the basic building block of any circuit is the lowly resistor. The apparent simplicity of this device often allows designers to overlook some non-ideal properties that cause to performance degradation in high-performance circuits. Here, approved
I will try to go over some of these properties of resistors so as to help others avoid common pit-falls.

The popular designs of through-hole resistors falls into several categories: wire wound, for sale carbon composite, carbon film and metal film. The wire wound resistors, as the name implies, get their precise characteristics from lengths of wire wrapped around a core in either an inductive or non-inductive manner. The carbon composite resistor is a cylinder composed of a mixture of black carbon and an insulator to give the required characteristics. The film resistors fall into two categories, those whose film composition is varied to give appropriate resistance or those where the film is uniform and the path from one terminal to the other is laser trimmed for a fixed resistance. SMT resistors can also be obtained in the previous designs, however, film resistors are by far the most popular. One can see from the start that the inherent series inductance of various resistor designs can contribute a significant impedance at high frequencies. Furthermore, there can be non-negligible capacitance between “traces” on film resistors and the wire loops on wire wound resistors. Now the simple resistor model becomes a ideal resistance in parallel with a capacitance and in series with an inductance, so, if care is not taken, one can design a resistor bridge that can cause ringing at circuit operating frequencies. Inductive wire wound resistors suffer the poorest frequency response with possible inductances on the order of 10uH and shunt capacitance of 5pF for a resistance of about 10kOhm.

Another important characteristic of a resistor is its temperature coefficient (TC). This is the value (usually in ppm/C) which describes the change in resistance per degree celsius. So the resistor specifies a nominal resistance value, say 10kOhm, with a tolerance of 1%, so it is actually 10kOhm +/- 100Ohm. Assuming that this is a precision resistor, it can have a respectable TC of 10ppm/C, so if your circuit is exposed to 100C temperature ranges, then that gives you 1000ppm variation, or 1/1000 of the 10kOhm. This may not seem significant, but if the resistor involved is used to somehow interface a ADC, the best resolution over the temperature range is 10bit (1/1024 of full swing) due to the resistor TC alone. Having noted that, 10ppm/C is very, very good. The TC for copper PCB traces is often on the order of 3000-4000ppm/C, so if the resistor is very small, the copper TC will have a significant contribution to errors. Further problems arise when there are networks of resistors that dissipate power. Resistors have a specified thermal dissipation coefficients so the temperature change of a resistor due to power dissipation can be calculated. If a pair of resistors are nominally matched, once they dissipate different power, they can become unmatched due to different temperatures. Furthermore, the values of resistors can change with applied voltage on the order of 1-200ppm/V (for high MOhm resistors) and with age, on the order of 10-100ppm/year.

Finally, there are thermocouple effects. Whenever dis-similar materials are joined that are at different temperatures, they develop a voltage drop across the interface. Schematically, most resistors have at least two of these: one from metal terminal to resistor material and one from resistor material to the other terminal. If the whole resistor is at a uniform temperature then these two cancel each other out, otherwise, the resistor can develop an additional voltage drop that is not really there. For this reason, it is suggested that resistors are mounted so that their terminal-terminal axis is perpendicular to the thermal gradient (meaning, the whole resistor is at a constant temperature).
There are also some interesting noise properties of resistors, but I will write about that later.

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