Resistivity and Thermal Resistance

This article introduces some key electrical resistor parameters such as resistivity, thermal resistance and TCR temperature coefficient.

In practical resistor applications, these parameters resistivity, thermal resistance and TCR temperature coefficient. are not only abstract material constants but directly determine hot‑spot temperature, long‑term stability, and ultimately the reliability of the entire circuit. They also explain why different resistor technologies – wirewound, metal film, thick‑film chip, thin‑film, and foil – behave differently under load and temperature and must be selected with their thermal characteristics in mind.

Resistivity (ρ)

The resistivity, ρ, is a material constant. The higher the resistivity in the resistor material, the higher its resistance. The connection can be described as

Here
R = resistance
l = conductor length
A = conductor area.

Depending on what units we express l and A in we get different units of ρ. A common way is by expressing l in m(eter) and A in mm² , ρ then gets the unit Ω.mm²/m. If we instead choose l in m and A in m², the unit for r will be Ω.mm²/m, which usually is transformed to Ωm. That unit often is used for non-metallic materials. If we know the value of ρ expressed in Ω.mm²/m, that value has to be multiplied by the factor 10^-6 to give the value in Ωm. Thus, 10^-6 x Ω.mm²/m = 1 Ωm.

Sheet Resistivity (Ω/square)

The sheet resistivity is a measure of the resistance per surface unit of resistive films. A square surface element as shown in Figure 1. gets according to the formula [1] the resistance:

Thus, the resistance per square unit, r(sq), is independent of the surface size. It is the film thickness and its intrinsic resistivity that determine r(sq) (expressed in Ω/square).

Typical Resistive Materials and Technologies

The choice of resistive material and construction strongly influences resistivity, temperature coefficient of resistance (TCR), thermal resistance, and long‑term drift. Common resistor technologies use alloys and films that balance achievable resistance values, power capability, stability, and cost.

Technology / film type	Typical material	Approx. resistivity (Ω·mm²/m)	Typical TCR (ppm/°C)	Typical use case
Thick‑film SMD	Ru‑based cermet	High, adjustable	±100 to ±300	General purpose, high values in small chips
Metal film (leaded)	NiCr alloy	Moderate	±25 to ±100	Precision and general‑purpose leaded resistors
Wirewound	NiCr, CuNi	Moderate	±20 to ±50	High power, low noise, current sensing
Thin‑film SMD	NiCr thin film	Lower than thick‑film	±5 to ±25	Precision SMD, low noise, stable networks
Foil precision	Metal foil	Low, highly controlled	≤ ±2	Ultra‑precision, references, instrumentation

Thick‑film technologies achieve very high resistance values in compact footprints but typically exhibit higher TCR and more drift, whereas thin‑film and foil resistors use carefully engineered low‑TCR materials to provide excellent stability at the expense of higher cost and lower maximum resistance values.

Surface Temperature and HOT SPOT

The surface temperature rise of the resistor body depends on the load as shown in principle in Figure R2. As temperature rises, conduction, radiation and convection (air-cooling) from the resistor body increases which causes the temperature curve to level off.

Figure 3. shows the temperature distribution along a resistor body. Thermal dissipation to the leads or SMD terminals decreases the temperature at the ends. In the middle of the body we register a temperature maximum, the so called Hot Spot temperature. This temperature determines both the resistor stability and life.

It is important that spiraling or wire winding be spread uniformly over the whole free resistor length. Otherwise we get an intensified Hot Spot effect that endangers life and stability.

It is not only for the resistor itself the Hot Spot is of vital importance. Heat radiation may have an effect on adjacent components and circuit boards. Thus, see that there is a satisfactory distance to the resistor body from heat-sensitive adjacent components.

Internal vs Surface Hot‑Spot and Mounting Effects

The measured hot‑spot temperature on the resistor surface is usually lower than the internal hot‑spot in the resistive element itself, which experiences the highest stress. For reliable design, surface temperature is therefore treated as a conservative indicator of internal conditions, and limiting the surface hot‑spot also protects film integrity, solder joints, and nearby PCB material.

Mounting style influences thermal behaviour as well: vertical mounting of leaded resistors tends to concentrate heat near the PCB entry point, while horizontal mounting distributes heat more evenly along the body and leads. Maintaining a sufficient distance between hot resistors and heat‑sensitive components or PCB areas helps prevent local charring and unwanted thermal coupling in precision circuits.

Thermal Time Constant, τ_w

The thermal time constant, _τw, is defined as the warm-up time for the resistor surface to attain 63% or theoretically (1-1/e) of the final temperature after applied load is increased in steps, usually P_R (Figure 4). Of course, the time constant is strongly dependent on the resistor body size. It will be quicker to heat up a small body than a big one. Table 1 states standard values for some DIN classified sizes.

DIN size	0204	0207	0414
Thermal time constant, τw  (s)	2	5	20
Thermal resistance, Rth (K/W)	400	250	170

Pulse Loads and Thermal Time Constant

The thermal time constant $\tau_w$τw​ provides valuable insight into how quickly a resistor responds to step changes in load. Short pulses with a duration much shorter than $\tau_w$τw​ do not allow the body to reach its steady‑state hot‑spot temperature, while long pulses or continuous loads with duration comparable to or longer than $\tau_w$τw​ result in near steady‑state heating.

In pulse‑loaded applications, the allowable energy per pulse and repetition rate are typically specified by the manufacturer in dedicated pulse‑load or overload curves. Designers should always verify that the combination of pulse height, width, and duty cycle keeps the hot‑spot temperature below permissible limits when averaged over the thermal time constant, even if the average electrical power appears modest.

Thermal Resistance, R_th

The thermal resistance, R_th, is expressed in K/W. It describes the temperature increase of a resistor body under applied load. Since radiation causes the temperature curve to turn downwards at increasing load data about R_th concerns normalized mounting and a load of P_R. (See DIN 44 050). As shown in Figure 5. an power overload reduces the R_th.

In Equation [3] below the connection between R_th and current temperatures is described. R_th is expressed in K/W but due to the fact that the equation deals with the difference between two temperatures it doesn’t matter if we use °C or K for both values. The differences will be equally large. K₂-K₁ = [(°C₂+273) – (°C₁+273)] = °C₂-°C₁.

T_hsp = Hot Spot temp. in K or °C
T_a = ambient temp. in K or °C.
P = applied load, W.

In Table 1. there are some examples of the thermal resistance for standard DIN sizes.

Practical Use of Thermal Resistance and Derating

Thermal resistance links the applied power to the hot‑spot temperature rise according to $R_{th} = \Delta T / P$Rth​=ΔT/P. For example, a resistor with $R_{th} = 250\ \text{K/W}$Rth​=250 K/W dissipating 0.5 W will experience a temperature rise of approximately $\Delta T = 250 \times 0.5 = 125\ \text{K}$ΔT=250×0.5=125 K. At an ambient temperature of 25 °C, the hot‑spot temperature will be around 150 °C, which is close to typical maximum permissible temperatures around 155 °C. This simple calculation motivates derating the resistor and optimising heat dissipation on the PCB.

Datasheets frequently specify rated power at 70 °C ambient and use linear derating to zero power at the upper limit, for example 155 °C. A common design practice is to operate resistors at 50–70% of their nominal power rating, which significantly reduces drift and extends lifetime by keeping the hot‑spot temperature well below the maximum specified limit.

Temperature Coefficient of Resistance, TCR

The temperature coefficient of resistance, TCR, is expressed in ppm/°C.

For clarification reasons TC is often written TCR, i.e., Temperature Coefficient of Resistance.

Specification limits and actual changes may look like the ones in following figure where a family of components are shown.

Temperature coefficient of resistance is of key importance especially at high precision resistors.

Real‑World TCR Behaviour and Selection

In practice, TCR behaviour is often non‑linear over temperature, and catalogue values such as ±25 ppm/°C are usually specified over a limited interval around room temperature. At temperature extremes, especially in the negative range, many constructions show higher effective TCR and increased drift, which must be considered in precision and sensing applications.

Resistor type	Typical catalogue TCR (ppm/°C)	Typical application
Thick‑film SMD	±100 to ±300	General purpose, pull‑ups, biasing
Metal film leaded	±25 to ±100	Analogue circuits, audio, moderate precision
Thin‑film SMD	±5 to ±25	Precision SMD networks, instrumentation
Foil precision	≤ ±2	References, precision gain‑setting, metrology

Temperature‑induced resistance change can be reduced not only by choosing low‑TCR components but also by using matched networks and compensation schemes. For example, combining resistors with similar tracking TCR or opposing TCR values in gain‑setting networks can significantly reduce the effective temperature drift of the ratio even if individual components have higher absolute TCR.

In-depth article with more insights can be studied here:

Understanding High-Precision Resistor Temperature Coefficient of Resistance

Temperature Rise and Heating of Resistor

Resistor is an element that converts electric energy into heat energy. It always generates heat when the electric power is consumed and the temperature rises according to the consumed power. To control the temperature rise of a resistor, the generated heat needs to be dissipated efficiently. For chip resistors, the most of the generated heat conducted from the electrode to Cu foil pattern on the PCB, and finally dissipated to the air or chassis. As the image below, expanding the pad pattern of the resistor or expanding Cu foil pattern where the resistor is connected, will lead to good heat radiation and control the temperature rise.

Temperature rise of the resistor is also controlled by improving thermal conductivity of PCB; by thick Cu foil pattern, forming solid pattern on the back side of PCB or solid pattern inside the layer if it is a multilayer substrate. Wide terminal type flat chip resistors (reversed geometry) have excellent heat radiation characteristic and perform under high power. Examples of the wide terminal flat chip resistors are shown below. Forming the electrodes on long sides of this type of resistor, shortens the distance between the heat generating point and the electrode, enables to conduct much volumes of heat to PCB by large electrodes, which leads to improve heat radiation of resistor. The rated power is much more improved than that of standard resistor in same size.

PCB Layout and Package Choices for Thermal Control

For chip resistors, most heat is conducted from the resistive element through the electrodes into the copper pads and planes, making PCB layout a primary lever for controlling temperature rise. Enlarged pads, solid copper areas, thermal vias to inner planes, and thicker copper layers all reduce effective thermal resistance and keep the resistor hot‑spot closer to ambient.

Wide‑terminal flat chip resistors, metal‑plate current‑sense resistors, and high‑power SMD packages available from multiple manufacturers are designed specifically to conduct heat efficiently into the PCB. Following the recommended land patterns and derating curves from the datasheet for each package type is essential, as assumed “standard” footprints often fail to realise the full rated power and may lead to excessive local temperature rise.

Resistor Reliability, Thermal Stress, and Lifetime

Elevated hot‑spot temperatures accelerate ageing mechanisms such as film cracking, migration, and solder joint degradation, while also stressing the surrounding PCB material. Empirically, many resistor technologies show significantly improved lifetime and reduced drift when operated well below their maximum specified temperature, often with a rule‑of‑thumb that every 10–20 °C reduction in hot‑spot temperature yields a substantial increase in expected service life.

Thermal cycling, where resistors repeatedly heat up and cool down during on‑off or pulsed operation, introduces mechanical stress due to differential expansion of the resistive element, substrate, coating, and solder joints. In power and current‑sense stages, placing resistors to avoid extreme gradients, allowing sufficient copper for heat spreading, and applying reasonable derating are key strategies for limiting drift and preventing premature failures.

Some datasheets provide long‑term stability figures, such as resistance change after 1 000 h or 10 000 h at a specified temperature and load, and these should be used together with thermal resistance and TCR data when selecting parts for precision analogue, measurement, or safety‑critical applications. Combining conservative thermal design with stable resistor technologies yields predictable behaviour over years of operation.

Conclusion

Understanding resistivity, sheet resistivity, thermal resistance, thermal time constant, and TCR is essential for specifying resistors that remain stable and reliable under real operating conditions. Proper component selection combined with good PCB thermal design—larger copper areas, optimized pad layouts, and wide‑terminal chips—allows designers to control hot‑spot temperatures, minimize drift, and avoid thermally induced failures in both the resistor and surrounding circuitry.

FAQ about Resistor Resistivity and Thermal Resistance

References

• What Is a Resistor? – introductory overview of resistor function and basic parameters.
• Understanding High‑Precision Resistor Temperature Coefficient of Resistance – detailed discussion of TCR behaviour, measurement and precision applications.
• KOA Speer Electronics – Advantages of Wide Terminal Chip Resistors (Video Resources) – application notes and videos on wide‑terminal chip resistors and thermal design.
• KOA Speer Electronics – WG73 Wide‑Terminal Surge‑Current Chip Resistors – example of wide‑terminal anti‑surge chip resistor series with enhanced heat dissipation.
• DIN 44 050 and IEC 60115 resistor standards – definitions of power rating, thermal resistance and resistor size classification (refer to official IEC / DIN publications or manufacturer technical reports that summarize these standards).