What are the key characteristics and specifications that affect the choice of resistor? Factors that should be taken into consideration include initial tolerance and value selection. However, the tolerance or variation of the value of a resistor is affected by multiple parameters, as explained below.

**Temperature Coefficient**

This is a measure of the variation of the nominal value as a result of temperature changes. Generally quoted as a single value in parts per million per degree centigrade (or Kelvin), it can be positive or negative. The equation for calculating the resistance at a given temperature is:

**Rt=Ro[1+α(T-To)]**

Where **Ro** is nominal value for room temperature resistance, **To** is the temperature at which the nominal resistance is given, **T** is operating temperature and **α** is the TCR.

Put simply, a 1 MΩ resistor with a TCR of 50ppm/K will change by 50Ω per 1 degree of temperature rise or fall. This may not sound like much but consider if you were using this resistor as the gain resistor in a x10 non-inverting amplifier circuit with 0.3v on the + input. The worst-case change in output could be as much as 7.5mv which is equivalent to about 5LSBs in a 5v 12-bit ADC circuit. This kind of change can be quite noticeable in precision design. Remember also that the TCR is quoted as ±x ppm/C so it is feasible, although unlikely, that the second resistor in the circuit could change in the opposite direction hence double the possible error. Finally, it’s worth noting that some precision resistors quote variable TCRs over the temperature range the circuit is operating in, and this can complicate the design process significantly.

**Resistor Ageing or Stability**

Ageing and stability are a complex amalgam of multiple changes to the value of a resistance value over time and are the result of temperature cycling, high-temperature operation, humidity ingress and so on. Typically, the value will lead to an increase in resistance over time as conduction atoms migrate within the device.

**Thermal Resistance**

The thermal resistance is a measure of how well the resistor can dissipate power into the environment. In practice, engineers use thermal resistance to model the heat dissipation for a system – it is thought of as a set of series ‘thermal resistors’, each representing one element of the heat dissipation of the system.

This is mainly important if the design means the resistor is running at or near its maximum value and can significantly affect the long-term reliability of the system. An example of where this parameter could be used is to calculate the size of a PCB pad or ground plane requirement that would be used to keep the resistor’s value and operating temperature within acceptable limits.

**Thermal and Power Rating**

All resistors come with a maximum power rating, specified in watts. This can be anything from 1/8th watt right up to 10s of watts for power resistors. In a first pass analysis, the engineer would check that the resistor is operating within its rated value. The equation for calculating this is **P=I² R**, where **p** is the power dissipated in the resistor, **i** is the current flowing and **R** is the resistance. Sadly, things can be more complicated than this; for exact work, the engineer needs to take account of the thermal derating curve for the resistor. This specifies the amount by which the designer needs to de-rate the maximum power dissipation above a given temperature.

This might seem theoretical as often the de-rating kicks in at quite high temperatures, but a power circuit in an enclosed housing in a hot region can often exceed the cut in point and the maximum power dissipation will need to be reduced appropriately. It’s also worth noting that the maximum operating voltage of a resistor is de-rated with power dissipation.

**Resistor Noise**

Any electronic component that has flowing electrons is going to be a source of noise, and resistors are no different in this respect. In high gain amplifier systems or when dealing with very low voltage signals, it needs to be considered.

The major contributor to noise in a resistor is thermal noise caused by the random fluctuation of electrons in the resistive material. It is generally modelled as white noise (i.e. a constant RMS voltage over the frequency range) and is given by the equation **E=√4RkT∆F** where **E** is the RMS noise voltage, **R** is the resistance value, **k** is Boltzmann’s constant, **T** is the temperature and **Δf** is the bandwidth of the system.

It is possible to lessen system noise by reducing the resistance, the operating temperature or the system’s bandwidth. Additionally, there is another type of resistor noise called current noise which is a result of the electron flow in devices. It is rarely specified but can be compared if the standard numbers using IEC60195 are available from the manufacturer.

**High-Frequency Behaviour**

The final challenge to consider is the high-frequency performance of the particular resistor. In simple terms, you can model a resistor as a series inductor, feeding the resistor which has a parasitic capacitor in parallel with it.

At frequencies as low as 100Mhz (even for surface mount resistors which have lower parasitic values than through-hole parts) the parallel capacitance can start to dominate, and the impedance will drop below nominal. At a higher frequency still, the inductance may predominate, and the impedance will start to increase from its minima and may well end up above the nominal value.