# Resistor Stability and Calculating Drift

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• Resistor Stability and Calculating Drift

All resistors share one property: stresses, whether mechanical or thermal, can cause a resistor to change its electrical parameters. Temperature and power dissipation will cause this stress in circuits. When current passes through a resistor it generates heat, and the thermal reaction causes mechanical changes via expansion in the different materials. As a result, the resistance value will change, sometimes at different rates and experienced through an applied electrical load, over the duration of that load.

If such aspects as shape, length, or diameter are changed by mechanical or other means, the electrical parameters also change. The degree of change and of its predictability varies substantially with the resistor technology, i.e., the materials used to build the resistive element and the terminations.

There are also manufacturing factors that affect resistor properties. For example, in wirewound resistors, the wire is wound under tension around a core, which can elongate the wire, changing its diameter. In addition, during formation of the coil, each turn of wire has the inside surface under compression and the outside surface under tension. Over long periods, the wound element tends to change physically as the wire attempts to regain its original shape. These permanent irreversible deformations affect stability and shift the Temperature Coefficient of Resistance (TCR) from its original value.

## UNDERSTANDING RESISTOR TCR

Despite differences in designs and manufacturing processes, Temperature Coefficient of Resistance (TCR) is a commonly accepted resistor performance stability indicator. TCR is the calculation of a relative change in resistance per degree of temperature change. The common way to express the TCR is in ppm/°C, which stands for parts per million per centigrade degree.

One can easily find a calculation that will give the resistance value change based on the TCR of the resistor and amount of temperature difference. The following equation yields the temperature coefficient of resistance for the conductor material:

Where α is Temperature coefficient in ppm/°C, R is in ohms at room temperature, Rref is resistance at operating temperature in ohms, Tref is the room temperature in °C and T is the operating temperature in °C.

TCR calculation methods can vary by manufacturer, manufacturing process, materials of construction, and other aspects. To better understand TCR data as a component reliability metric, it is important to understand the method of measurement. In some cases, the TCR characteristic will be presented for a limited temperature range, while another supplier may present TCR characteristics across a wider operating range. Detailed TCR curves specific to the resistor construction and resistance value may be available to support your design.

TCR specifications can help engineers to better predict shifts in component resistance within the application, under intended operating temperatures and within the installation environment. TCR will show how resistors behave under cold operating temperatures and high operating temperatures.

## FACTORS CONTRIBUTING TO THE INSTABILITY OF RESISTORS

Stability is the change in resistance with time at a specific load, humidity level, stress, and ambient temperature. Stresses, whether mechanical or thermal, cause a resistor to change its electrical parameters.

Thermal dissipation to the leads or SMD terminals decreases the temperature at the ends. In the middle of the body there is a temperature maximum, the Hot Spot temperature. This temperature determines both the resistor stability and life. It is important that wire winding be spread uniformly over the whole free resistor length. Otherwise an intensified Hot Spot effect occurs that endangers life and stability.

Resistors are used in a wide range of applications where their stability over time is important. These include voltage divider circuits where a change in resistance directly impacts on the performance of a circuit.

There are many environmental and electrical factors that can cause the performance of a resistor to degrade over time. They include:

Heat. Resistors are specified to operate at a particular temperature. If that temperature is exceeded the resistance value will change.

Moisture. A high moisture content in the environment can degrade resistor performance.

Overload. A constant overload condition will generate excessive heat. This will degrade the resistor performance over time. Or, in extreme cases, cause resistor failure.

Mechanical damage can happen during shipping, in manufacture, or in service. Inappropriate device mounting to the system board can mechanically stress the resistor device.

Manufacturing methods do not isolate the resistive element from the various stresses arising out of handling, packaging, insertion pressures, and lead forming. Here, engineers have to take into account tension applied to axial leads on mounting and pressure on the package exerted by mechanical forces.

For most resistor types, environmental effects and load-life changes cumulatively add up to, and exceed, their initial tolerances.

## RESISTORS: KNOWING HOW THEY DRIFT AND HOW THEY AGE

If resistors age differently due to temperature differences, the scaling factor of a voltage divider, for example, will change over its service life. The normal aging trend is a steady increase in resistance at a rate influenced by various factors such as manufacturing origin, resistivity, electrical bias, and environment. The drift observed in the majority of resistors can be extrapolated to give a prediction of change over time in standard environments.

Reliability is the probability that a resistor (or any other device) will perform its desired function. There are two ways of defining reliability. One is Mean Time Between Failures (MTBF) and the other is Failure Rate per 1,000 Hours of Operation. Both of these methods of evaluating reliability must be determined using a specific group of tests and a definition of what is the end of life of a device, such as a maximum change in resistance or a catastrophic failure.

A common method to predict changes in a resistor’s ohmic value during its service life is based on load life tests and mathematical equations derived from the Arrhenius rate law. This law defines the speed of a single reaction as a function of Kelvin temperature. The Arrhenius’ law is valid for a single mechanism causing the drift while the test results on which the equation is based refer to at least two mechanisms of irreversible drift. Prediction of resistor reliability with Arrhenius plots only work when plots are linear and follow the equation. Based on this equation, the drift of a thin film resistor, for instance, doubles for every 30K temperature rise and increases with the cube root of the load duration.

## STABILITY AND LONG TERM VARIATIONS OF RESISTANCE.

Temperature drift and changes in stability occur as the component and its constituent materials undergo the normal aging process.

Initial tolerance is the variation from nominal value that can be expected when the resistor is measured before it has been used. Battery load-current sensing, for example, may need tolerance as tight as 0.1 percent or better.

Reliability is generally higher at lower power levels. If the circuit designs permit, the choice of a high ohmic value resistor or divider network will minimize the power level and improve the resistor’s performance and reliability because it is operating at lower power and electrical stress levels.

The drift characteristics (i.e., the stability of the resistance value) is up to the circuit designer. He or she may estimate the performance of the particular resistor application or set certain load and temperature limits to maintain a desired stability.

## PHYSICAL AND ELECTRICAL TESTS

MIL-STD 202 is a Department of Defense test that establishes uniform methods for testing electronic and electrical component parts, including basic environmental tests to determine resistance to the effects of natural elements and conditions.

This is an accelerated aging test at 100% rated power with a duty cycle of 75%. Operating conditions will almost certainly be easier on the component than this, which in practice means that the stress on a resistor may be lower than the given test assumption. The test is applicable for such items as capacitors, resistors, switches, relays, transformers, inductors, and others.