• Latest
  • Trending

Resistivity, Thermal Resistance and Temperature Coefficient

Würth Elektronik Launches New Line of Toggle Switches

Würth Elektronik Launches New Line of Toggle Switches

Microwave Multi Line Connectors Mounting and Handling Precautions

Microwave Multi Line Connectors Mounting and Handling Precautions

PCNS Passive Components Symposium 11-14th September 2023
Flex Suppressor Explained and its Applications

Flex Suppressor Explained and its Applications

Exploring the Benefits of High-Performance MLCC Capacitors for Aerospace and Defense

Exploring the Benefits of High-Performance MLCC Capacitors for Aerospace and Defense

Murata Establishes Joint Venture Company to Produce MLCC Raw Materials

Murata Establishes Joint Venture Company to Produce MLCC Raw Materials

Samtec New Interconnects Enhances Power and Signal Integrity

Samtec New Interconnects Enhances Power and Signal Integrity

Examining the Influence of ESR and Ripple Current on Selecting the Suitable Capacitor

Examining the Influence of ESR and Ripple Current on Selecting the Suitable Capacitor

PCB Via Design Selection; Plugging-Filling-Tenting

PCB Via Design Selection; Plugging-Filling-Tenting

SABIC Validates its 150°C Film Foil to Enable Adoption of Film Capacitors in SIC Power Modules

SABIC Validates its 150°C Film Foil to Enable Adoption of Film Capacitors in SIC Power Modules

Outlook of Passive Electronic Components Market for Oil & Gas Electronics in 2023

Outlook of Passive Electronic Components Market for Oil and Gas Electronics in 2023

  • Home
  • ABC of CLR
    • All
    • ABC of Capacitors
    • ABC of Inductors
    • ABC of Resistors
    • Mounting Guidelines

    RF Inductors and Filters

    Power transformers

    Telecom transformers

    LAN transformers

    Transformer Calculation and Applications

    Power Inductors 2 (cont.)

    Power inductors

    Current compensated chokes

    Coil with ferrite

    Trending Tags

      • ABC of Capacitors
      • ABC of Inductors
      • ABC of Resistors
      • Mounting Guidelines
    • e-Symposium
    • EPCI Membership
    • About
    No Result
    View All Result
    European Passive Components Institute
    • Home
    • ABC of CLR
      • All
      • ABC of Capacitors
      • ABC of Inductors
      • ABC of Resistors
      • Mounting Guidelines

      RF Inductors and Filters

      Power transformers

      Telecom transformers

      LAN transformers

      Transformer Calculation and Applications

      Power Inductors 2 (cont.)

      Power inductors

      Current compensated chokes

      Coil with ferrite

      Trending Tags

        • ABC of Capacitors
        • ABC of Inductors
        • ABC of Resistors
        • Mounting Guidelines
      • e-Symposium
      • EPCI Membership
      • About
      No Result
      View All Result
      European Passive Components Institute
      No Result
      View All Result
      Home ABC of CLR

      Resistivity, Thermal Resistance and Temperature Coefficient

      January 24, 2022
      Reading Time: 6 mins read
      145 9
      A A

      R1.1 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

      ………………………… [R1-1]

      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 Ωmm2/m. If we instead choose l in m and A in m2, the unit for ρ will be Ω x 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 Ωmm2/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.

      R1.2 SHEET RESISTIVITY (Ω/square)

      Figure R1-1. Surface resistivity r(sq) [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 R1-1 gets according to the formula [R1-1] the resistance:

      …………………[R1-2]

      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).

      R1.3 SURFACE TEMPERATURE and HOT SPOT

      Figure R1-2. Temperature rise versus Load. Ta = ambient temperature.

      The surface temperature rise of the resistor body depends on the load as shown in principle in Figure R1-2. As temperature rises, conduction, radiation and convection (air-cooling) from the resistor body increases which causes the temperature curve to level off.

      Figure R1-3 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.

      Figure R1-3. Temperatures:
      Thsp = Hot Spot temperature.
      Ta = ambient temperature.

      R1.4 THERMAL TIME CONSTANT, τw

      Figure R1-4. Thermal time constant,τw.

      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 PR (Figure R1-4). 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 R1-1 states standard values for some DIN classified sizes.

      Table R1-1. Examples of thermal time constants and thermal resistances.

      DIN size[1] 0204 0207 0414
      Thermal time constant, τw (s) 2 5 20
      Thermal resistance, Rth (K/W) 400 250 170

      [1] Leaded cylindrical components.

      R1.5 THERMAL RESISTANCE, Rth

      The thermal resistance, Rth, 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 Rth concerns normalized mounting and a load of PR. (See DIN 44 050). As shown in Figure R3-5 an power overload reduces the Rth.

      Figure R1-5. Thermal resistance at overload Ps and at rated power PR.

      In Equation R1-3 the connection between Rth and current temperatures is described. Rth 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.

      …………[R1-3]

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

      In Table R1-1 there are some examples of the thermal resistance for standard DIN sizes.

      R1.6 TEMPERATURE COEFFICIENT of RESISTANCE, TCR

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

      ……….[R1-4]

      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.

      Figure R1-6. Example of specified TC limits and actual records.


      ABC of CLR: Chapter R Resistors

      Resistivity, Thermal Resistance and Temperature Coefficient

      EPCI licenced content by:

      [1] EPCI European Passive Components Institute experts original articles
      [2] CLR Passive Components Handbook by P-O.Fagerholt*

      *used under EPCI copyright from CTI Corporation, USA

      Creative Commons License
      This page content is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.

      < Page 1 >

      see the next page:

      Pulse Load, Power and Voltage Derating

      Previous Post

      Derating and Category Concepts

      Next Post

      Pulse Load, Power and Voltage Derating

      Related Posts

      ABC of CLR

      RF Inductors and Filters

      850
      ABC of CLR

      Power transformers

      695
      ABC of CLR

      Telecom transformers

      541

      Discussion about this post

      Categories

      • ABC of CLR
        • ABC of Capacitors
        • ABC of Inductors
        • ABC of Resistors
        • Mounting Guidelines
      • e-Symposium
        • ESA SPCD
        • PCNS
      • EPCI news
      • news collection

      Popular Posts

      • Transformer: Parasitic parameters and equivalent circuit

        1212 shares
        Share 485 Tweet 303
      • Transformer Calculation and Applications

        662 shares
        Share 265 Tweet 166
      • Simulation with LTspice

        446 shares
        Share 178 Tweet 112
      • Introduction to Ceramic Capacitors

        443 shares
        Share 177 Tweet 111
      • Insulation Resistance, DCL Leakage Current and Voltage Breakdown

        412 shares
        Share 165 Tweet 103

      EPCI Membership

      join passive components community

      © 2023 European Passive Components Institute

      No Result
      View All Result
      • Home
      • ABC of CLR
        • ABC of Capacitors
        • ABC of Inductors
        • ABC of Resistors
        • Mounting Guidelines
      • e-Symposium
      • EPCI Membership
      • About

      Welcome Back!

      Login to your account below

      Forgotten Password?

      Retrieve your password

      Please enter your username or email address to reset your password.

      Log In
      This website uses cookies. By continuing to use this website you are giving consent to cookies being used. Visit our Privacy and Cookie Policy.