User Tools

Site Tools


thermal_resistance

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Previous revision
Last revision Both sides next revision
thermal_resistance [2019/06/03 18:30]
thermal_resistance [2020/07/19 01:50]
stan_zurek
Line 1: Line 1:
 +====== Thermal resistance ======
  
 +|< 100% >|
 +| //[[user/Stan Zurek]], Thermal resistance, [[http://Encyclopedia-Magnetica.com|Encyclopedia-Magnetica.com]], {accessed @YEAR@-@MONTH@-@DAY@}// |
 +
 +===== Definition =====
 +
 +**Thermal resistance** (//**R<sub>th</sub>**//) - a parameter describing steady state temperature rise versus dissipated power within a given device.
 +
 +Thermal resistance is often denoted as //**R<sub>th</sub>**// with the units of **K/W** ([[kelvin]] per [[watt]])[(Thermal_resistance>[[http://www.epcos.com/web/generator/Web/Sections/ProductCatalog/Ferrites/RMCores/PDF/PDF__Application,property=Data__en.pdf;/PDF_Application.pdf|Epcos, Ferrites and accessories, Application notes, September 2006, p. 23-29, {accessed 10 Nov 2012}]])] or **°C/W** ([[degree Celsius]] per watt).
 +
 +{{page>insert/paypal}}
 +
 +<WRAP 40% right>
 +<box 100% right #f0f0f0>
 +[[Thermal resistance of ferrite cores]] depends on their size and shape[(Thermal_resistance)]
 +[[file/thermal_resistance_of_etd_transformers_magnetica.png|{{thermal_resistance_of_etd_transformers_magnetica.png}}]]
 +{{page>insert/by_SZ}}
 +</box>
 +<box 100% right #f0f0f0>
 +Experimental measurement of thermal resistance of an [[ETD44]] transformer. The nominal power loss is applied until the transformer reaches [[thermal equilibrium]]. The [[temperature rise]] (difference between steady state and the initial temperature) divided by the applied power loss, in this case 34.4°C / 3.38 W gives the thermal resistance of 10.2°C/W for this particular prototype.
 +[[file/thermal_resistance_etd44_magnetica.png|{{thermal_resistance_etd44_magnetica.png}}]]
 +{{page>insert/by_SZ}}
 +</box>
 +</WRAP>
 +
 +Thermal resistance depends mostly on geometry and materials involved, and not on operating conditions (e.g. shape of current waveform, or [[switching frequency]]). For [[ferrite transformer|ferrite transformers]] it is found to be independent on operating frequency.[(Goldman>[[http://google.com/books?isbn=0412146614|Alex Goldman, Handbook of modern ferromagnetic materials, Kluwer Academic Publishers, 2002, ISBN 0-412-14661-4, p. 485]])]
 +
 +For example, if thermal resistance of a given device is //R<sub>th</sub>// = 8°C/W, then dissipation of 5 W will make the device to run at a temperature 8°C/W · 5W = 40°C higher than its ambient temperature.
 +
 +A similar concept is [[thermal impedance]] (//**Z<sub>th</sub>**//), which is used if the power is applied not continuously, but intermittently. The thermal impedance can be also used for defining the thermal properties under dynamic (transient) conditions. Thermal resistance applies only to the state of equilibrium (steady state).[([[http://www.infineon.com/dgdl/smdpack.PDF?folderId=db3a304412b407950112b417b3e623f4&fileId=db3a304412b407950112b417b42923f5|SMD Packages, Special Subject Book, Infineon Technologies, Jan 2000, p. 12, {accessed 16 Aug 2013}]])]
 +
 +===== Ways of deriving =====
 +
 +The value of thermal resistance for a given device depends on the ratio of its total surface area to its volume, as well as [[thermal conductivity]] of the case, access to coolant (e.g. fresh air), emissivity of the surface, etc.[(Jung-Kyun Kima, Wataru Nakayamab, Yoshimi Itoc, Sang-mo Shina, Sun-Kyu Lee, Estimation of thermal parameters of the enclosed electronic package system by using dynamic thermal response, Mechatronics, Vol. 19, Issue 6, September 2009, p. 1034–1040)] Therefore, the only certain way of deriving the value of thermal resistance is to empirically measure it under nominal operating conditions, for instance on a prototype sample.
 +
 +There are several empirical equations linking the size and shape of a given class of devices. For example for [[EE (ferrite)|EE]], [[EI (ferrite)|EI]], [[ETD (ferrite)|ETD]] and [[EC (ferrite)|EC]] ferrite transformers the following formula could be used:[([[http://google.com/books?isbn=9780123865335|Sanjaya Maniktala, Switching power supplies A-Z, 2nd edition, Newnes, 2012, ISBN 978-0-12-386533-5, p. 155]])]
 +
 +|  <html><div style="font-size: 200%;"> $R_{th} = 53 · (V_{core})^{-0.54}$ </div></html>  |  (K/W) or (°C/W)  |
 +
 +where: //V<sub>core</sub>// - core volume in cm<sup>3</sup> (i.e. this the volume of the ferrite core itself as specified by the manufacturer, and not volume of the whole transformer).
 +
 +So for instance for [[ETD44]] the core volume[[http://www.ferroxcube.com/prod/assets/etd44.pdf|Ferroxcube, Data sheet, ETD44/22/15, ETD cores and accessories, 2008, {accessed 8 Jul 2012}]] is 17.8 cm<sup>3</sup> gives a value of 11.2°C/W. And the values given in various sources of [[thermal resistance of ferrite cores]] are between 11-12°C/W, so there is a reasonably good agreement. 
 +
 +An experimental measurement for a particular winding configuration and type of [[bobbin]]) give a value of 10.2 K/W (see also the graph), which is also quite close, but shows that experimental verification on a given prototype can differ from the literature values.
 +
 +Empirical data given by [[Epcos]] also suggest that the thermal resistance is roughly proportional to the reciprocal of square root (power of -0.5) of the ferrite core volume, which is in agreement with the previous equation:[(Thermal_resistance)]
 +
 +|  <html><div style="font-size: 200%;"> $R_{th} = \frac{x}{\sqrt{V_{core}}}$ </div></html>  |  (K/W) or (°C/W)  |
 +
 +where //x// is the proportionality factor.
 +
 +===== Importance =====
 +Thermal resistance is an important parameter used for correct design of most electronic power transformers. For instance, [[enamelled wire]] has a maximum rated operating temperature, which should not be exceeded.[(http://www.hi-wire.co.uk/acatalog/technical_information.html {accessed, 9 Nov 2012}]])]
 +Depending on the cooling conditions and size, each transformer will have a specific value of thermal resistance.[(Thermal_resistance)] 
 +
 +Hence, knowing the highest expected ambient temperature (e.g. //T<sub>ambient</sub>// = 50°C), the highest allowed operating temperature (e.g. //T<sub>max</sub>// = 155°C), and the thermal resistance of transformer (e.g. 8 K/W) it is possible to calculate the maximum losses allowed in such transformer, which with the example values given above is 13.1 W. So the total loss (e.g. the sum of [[copper loss]] and [[core loss]]) must be kept below this value.
 +
 +{{page>calculator/maximum_loss_from_thermal_resistance}}
 +
 +===== See also =====
 +  *[[Thermal resistance of ferrite cores]]
 +  *[[Thermal impedance]]
 +
 +===== References =====
 +~~REFNOTES~~
 +
 +{{tag>Thermal_resistance Counter}}
thermal_resistance.txt · Last modified: 2020/07/19 01:51 by stan_zurek

Privacy and cookie policy (GDPR, etc.)