Sensors & Transducers Published by IFSA Publishing, S. L.,

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1 Sensors & Transducers Publshed by IFSA Publshng, S. L., The Algorthm and Software Implementaton of the Thermal Transent Testng Technology Appled n Hgh-Power Electroncs Erpng DENG, Yaru SHEN, Zhbn ZHAO, 2 Jnyuan LI and Yongzhang HUANG North Chna Electrc Power Unversty, State Key Laboratory of Alternate Electrcal Power System wth Renewable Energy Sources, No. 2 Benong Road, Changpng Dstrct, Bejng, 02206, Chna 2 State Grd Global Energy Interconnecton Research Insttute, Future Scence and Technology Cty, Changpng Dstrct, Bejng, 02209, Chna Tel.: , fax: E-mal: dengerpnght@63.com Receved: 3 July 208 /Accepted: 28 September 208 /Publshed: 30 November 208 Abstract: Thermal transent testng technology s currently the most effectve method for obtanng thermal characterstc parameters of hgh-power electroncs and the structure functons can be used to evaluate the long lfe-tme relablty. Ths paper brefly outlnes the basc theory of the thermal transent testng technology, and then focuses on two key algorthms n the mplementaton of ths technology: deconvoluton and transformaton of thermal network model algorthms. Meanwhle, a software system of the thermal transent testng appled to power semconductor devces s establshed. Mathematcans used to solve the problem of data accuracy n network model transformaton. By comparng the commonly used deconvoluton algorthm, t s concluded that the thermal characterstc parameters of the devce calculated by Bayesan deconvoluton based on Rchardson- Lucy algorthm have better accuracy. Fnally, the measurement data of power semconductor devces tested by mature commercal thermal transent testng equpment s set as an example to verfy the accuracy and effectveness of the proposed software system. Keywords: Hgh-power electroncs, Structure functon, Thermal transent testng technology, Deconvoluton, Thermal network model transformaton.. Introducton Hgh-Power semconductor devces due to hgh voltage, hgh current, and excellent swtchng performance, have gradually been appled to hgh voltage and hgh power densty applcatons, for example, IGBT (Insulated Gate Bpolar Transstor) devces are used n the electrc tracton and hgh voltage drect current transmsson system. Thermal characterstc have always been a qute mportant concern n the applcaton of power semconductor devces. 55 % of the falure of electronc devces s caused by heat-related problems []. Therefore, t s qute mportant to accurately measure the thermal parameters of power electroncs and analyss ts thermal behavor. For hgh-power IGBT devces, juncton temperature and thermal resstance are two crtcal thermal characterstcs. Many electrcal parameters of the devce are related to the juncton temperature, 60

2 whch s also affected by ts thermal resstance. Thus, accurately measurng the juncton temperature and thermal resstance of hgh-power IGBT devces not only helps to optmze the heat dsspaton structure of the devce package, but also gudes users to gve full play to the devce performance and prolong ts servce lfe. Ths has become a common concern for the manufacturers and users. There are two most commonly used methods to obtan the thermal resstance or thermal behavor of power electroncs: Tradtonal steady-state method and transent thermal method [2]. Tradtonal steadystate method takes a thermocouple to get the case temperature to calculate the thermal resstance. The thermal resstance measured by ths method s the behavor of whole packagng, such as the juncton to case or heatsnk or ambent thermal resstance. It s not easy to obtan more detals wthn packagng. The transent thermal method s to get the thermal behavor of the thermal dsspaton path when the heat delvery from the chp to heatsnk and the transent thermal mpedance measure by ths method denotes the thermal resstance and capacty change along wth the heat path. Moreover, the transent thermal mpedance can be transformed by mathematcal transformatons to structure functons to get the thermal resstance and capacty of each layer accurately [3]. Thus, the thermal transent testng technology can comprehensvely analyze thermal propertes of each layer structure wthn the devce from chp to heat snk on the path of heat conducton, construct equvalent thermal model of devces, and provde relable data base for the research on thermal characterstc of the devce [4]. Hence, n order to gve full nformaton of the thermal characterstc parameters of hgh-power electroncs, a complete set of software analyss and test system s proposed n ths paper. The system can accurately measure the thermal characterstc parameters, and provde relable data foundaton for lfe expectancy, extreme operaton and overtemperature protecton [5]. The result has mportant reference value and practcal sgnfcance. 2. Methodology Fg. (a) shows a smple packagng model composed of dfferent materals. The model s placed on an deal heat snk and other surfaces are thermal adabatc. Thus, the thermal conducton s consdered as one-dmensonal. When a constant power P H s appled to the model, the model can be equvalent to the n-order RC network shown n Fg. (b). Among them, the thermal transent response functon a(t) of the model under the power P H s a( t) = P H n = R th t ( exp( )), () τ where P H s generally the unt power, R th denotes the thermal resstance of the heat transfer model equvalent to an RC network, t s the tme, τ represents the tme constant and can be calculated by thermal resstance R th and thermal capacty C th. The thermal resstance and capacty of each layer s determned by ts materal propertes and geometry [6]. Normally, the geometry of power electroncs s not so explct n applcaton that we should get the transent thermal mpedance through measurement [3]. (a) Smple one-dmensonal heat transfer model (b) The equvalent RC network Fg.. Heat transfer model and ts equvalent RC network. When the appled power step denotes as a unt power, the tme t n Formula () s logarthmc and the Formula () can be derved to obtan the convoluton formula shown n Formula (2). d dz a( = R( + n(, (2) where s the convoluton operator, the represents the constructor whch can be calculated by the followng formula = exp( z exp( ) (3) The thermal transent response functon a( n Equaton () can be obtaned by measurng the change of temperature-senstve parameters of the devce n the coolng process and combnng the relatonshp between the temperature-senstve parameters and the juncton temperature and thermal mpedance. In addton, the tme constant spectrum s clear n Formula (4) s the constructor s gven. d R( = a(, (4) dz where s the deconvoluton operator. It should be noted that the actual measured thermal transent response sgnal s usually mxed wth a 6

3 certan nose sgnal n(. These nose sgnals can affect the results of thermal transent tests that must be taken nto account when analyzng. d dz a( = R( + n( (5) The basc process of ths technology s shown n Fg. 2 below. We can see that the precondton of the thermal transent testng technology s that the transent thermal mpedance gven as shown n Formula (). Thermal transent response sgnal a(, tme constant spectrum R(, constructor and nose n( n the Formula () are all expressed as functon of logarthmc tme z. In order to get the R( from a(, the dervatve and deconvoluton should be conducted on a(. Then, splt R( nto a number of segments havng Δz wdth and compute the thermal resstance and heat capacty parameters of the Foster model. Consderng the heat capacty of Foster model wth no clear physcal meanng, hence thermal network model transformaton algorthm s used to transform the Foster model to Cauer model, whch can reflect the actual heat capacty transfer process. Fnally, the structure functon of the devce can be obtaned by accumulatng the thermal resstance and heat capacty parameters of the Cauer model n stages, or takng the dervatve after accumulatng [7]. Fg. 2. The process of the thermal transent test technology. 2.. Deconvoluton Algorthm Up to now, there are two deconvoluton algorthms that have been successfully used n the thermal transent testng technology: Fourer deconvoluton and Bayesan deconvoluton Fourer Deconvoluton The Fourer deconvoluton algorthm s based on the convoluton theorem, whch transforms the problem n the tme doman to the frequency doman for operatons. We have the equvalent formula * M ( Φ) = V ( Φ) W ( Φ) + N( Φ) = V * ( Φ) W ( Φ) (6) Thus theoretcally we can obtan the requred functon by a smple dvson as shown n Formula (7). components of the constructor are some very small tems wth a smaller magntude. After the dvson operaton, the nose sgnal wll be amplfed, resultng n many dfferences between the deconvoluton reconstructon sgnal and the orgnal sgnal, sometmes even resultng n unacceptable results. Therefore, t s necessary to properly handle the nose problem durng the applcaton process Bayesan Deconvoluton Dfferent from the Fourer deconvoluton, Bayesan deconvoluton s based on Bayes' theorem and total condtonal probablty formula. It can avod the nose problem n Fourer deconvoluton algorthm. The procedure descrbed by [8] s sutable for the tmeconstant spectrum dentfcaton has been proven. These apples the followng teratve formulas * M ( Φ) R ( = IFFT (7) W ( Φ) R da( / dz ( = R ( ( ) R ( +, (8) Because the nose corresponds to the hgh frequency component n the sgnal spectrum. Although the nose sgnal has smaller ampltude relatve to the measured sgnal, the hgh-frequency + ( da( / d R ( = R ( (9) ( R ( ) 62

4 The deconvoluton algorthm usng the teratve formula shown n Equaton (8) s called Rchardson- Lucy algorthms, and shown n Equaton (9) s the Postve teratve deconvoluton. Whether Formula (8) or Formula (9), the ampltude of the reconstructed sgnal wll be amplfed durng each teraton. In order to make the reconstructed sgnal as close as possble to the orgnal nput sgnal, the correcton I needs to be ntroduced to mprove the formula. R da( / dz ( = R ( ( )* I R ( +, (0) + ( da( / d R ( = R ( * I () ( R ( ) 2.2. Network Model Transformaton Algorthm Because the Foster network model descrbes the node-to-node thermal capacty wthout explct physcal meanng, the Foster network model needs to be converted nto a Cauer network model that descrbes the thermal capacty between the nodes and reference nodes. The exstng network model transformaton algorthm has been relatvely mature, and the detaled converson process s gven n [7]. However, due to the lmtaton of software accuracy, truncaton error and operaton error occur when the network model converson operaton s performed. The obtaned structure functon s nconsstent wth realty. Therefore, approprate calculaton software should be selected durng processng to avod ths stuaton. The method that have been publshed and used to solve the data accuracy problem of the network model converson process n the thermal transent testng technology s the GMP (GNU MP Bgnum Lbrary) open source math lbrary mentoned n the JESD 5-4 standard. However, GMP lbrary functons are wrtten n C language. When callng n nterpretve language programmng software, you need to wrte a specal nterface functon, or drectly use t n the C language-based software. No matter whch way the use should have the basc knowledge of programmng. The smulaton verfed that usng Mathematca, a mult-precson calculaton software, not only can acheve the same accuracy as GMP, but also s smpler and easer to operate than GMP. Ths greatly reduces the dffculty of algorthm mplementaton. Based on the above theory, ths paper establshes a software system of thermal transent testng technology as shown n Fg. 3, whch s used to measure the thermal characterstc parameters of power electroncs. Pretreatment Fg. 3. The Thermal transent testng software system. 3. Case Study Takng the thermal transent response sgnal of power electroncs measured by commercal thermal transent tester as an example, and the tme constant spectrum calculated by the equpment as a reference value. Ths artcle compares two knds of common deconvoluton algorthms. Meanwhle, the thermal transent testng software system establshed n ths paper s used for smulaton analyss to verfy the valdty and accuracy of the system. In order to make the results comparable, the smulaton parameters are set wth the testng equpment parameters. 3.. Deconvoluton Algorthms Comparson In order to compare the accuracy of thermal transent test results when dfferent deconvoluton algorthms are appled, ths paper uses dfferent deconvoluton algorthms to deal wth the same measurement data. The tme constant spectrum 63

5 devaton Δ s defned as the crteron for measurng the accuracy of the algorthm. The smulaton results are shown n Table and Fg. 4. Δ = [ X ( R( ] n 2 (2) Table. The devaton of tme constant spectral calculated by dfferent deconvoluton methods. Devaton Fourer deconvoluton Bayesan deconvoluton Rchardson- Postve Lucy teratve algorthm deconvoluton Δ nsulaton durng the transent thermal mpedance measurement [9]. And then, the measured thermal mpedance s used to obtan the structure functon curves whch s shown n Fg. 5 and Fg 仿仿结仿 基基值 Fg. 5. Cumulatve structure functon 仿仿结仿基基值 Fg. 4. The structure functon of dfferent deconvoluton algorthms. Table shows that the result of Rchardson-Lucy algorthm s closer to the reference value. The devaton of Rchardson-Lucy algorthm s , whch s far less than the Fourer deconvoluton, and less than the postve teratve deconvoluton. The result also shows that compared wth the Fourer deconvoluton algorthm and the Bayesan deconvoluton based on the Postve teratve deconvoluton, the structure functon usng the Bayesan deconvoluton based on the Rchardson- Lucy algorthm s most consstent wth the reference value The Smulaton Verfcaton of Software System Takng the measurement data of a hgh-power semconductor devce as an example, the thermal transent testng software system establshed n ths paper s used for smulaton calculaton. The devce under test s a sngle IGBT chp submodule from press pack IGBT. The collector sde of the submodule s cooled by heatsnk and emtter sde s thermal Fg. 6. Dfferental structure functon. Choosng the structure functon curve obtaned from the thermal transent testng equpment as a reference, t can be seen that the smulaton results through the software system mentoned above are n good agreement wth the reference values. The error between them s very small. Therefore, the software system establshed n ths paper can obtan the thermal parameters of the devce accurately and effectvely. Furthermore, the nternal structure of the devce can be dentfed by combnng two structure functons. Each layer structure s marked wth dfferent colors respectvely. The software establshed n ths paper contans fve man parts as shown n Fg. 7 below. Frstly, the transent thermal mpedance should be loaded n the program and then make a dervaton on t. After that the deconvoluton s used to get tme constant spectra and then transform to Foster thermal network model by dscretzaton. Fnally, we should transform the Foster thermal model to Cauer thermal model to get the cumulatve and dfferental structure functons. 64

6 Fg. 7. The proposed software to realze the transent thermal technology. 4. Conclusons A complete set of software system of the thermal transent testng appled to hgh-power semconductor devces s establshed n ths paper based on the research status of thermal transent testng technology at home and abroad. Amng at the problem of deconvoluton algorthm, ths paper compares the commonly used deconvoluton algorthm to get the concluson that the Bayesan deconvoluton algorthm based on Rchardson-Lucy algorthm obtans the most accurate structure functon. In response to another key ssue: data accuracy n the process of network model converson, t s proposed to reduce the dffculty of mplementng the algorthm by usng Mathematca to acheve the same effect as GMP. Fnally, takng the actual measured data measured by a mature commercal thermal transent test equpment for power semconductor devces as an example, the valdty and accuracy of the system establshed n ths paper are verfed. Acknowledgements Ths work s supported by the Scence and Technology Project of State Grd (SGRI-GB and SGRI-GB ) and the State Key Laboratory of Alternate Electrcal Power System wth Renewable Energy Source, North Chna Electrcal Power Unversty (Grant No. LAPS7003). References []. MIL-A-87244A.Avoncs/Elecsoncntergrty program requrements. [2]. Deng E., Zhao Z., Zhang P., et al., Study on the methods to measure the juncton-to-case thermal resstance of IGBT modules and press pack IGBTs, Mcroelectroncs Relablty, 207. [3]. Deng E., Zhao Z., Zhang P., et al., Study on the Method to Measure the Thermal Contact Resstance wthn Press pack IGBTs, IEEE Transactons on Power Electroncs, 208 (n prnt). [4]. B. Smth, T. Brunschwler, B. Mchel, Comparson of transent and statc test methods for chp-to-snk thermal nterface characterzaton, Mcroelectroncs Journal, Vol. 40, Issue 9, 2009, pp [5]. Székely V., Identfcaton of RC networks by deconvoluton: chances and lmts, IEEE Transactons on Crcuts & Systems I: Fundamental Theory & Applcatons, Vol. 45, Issue 3, 998, pp [6]. L J., Deng E., Zhao Z., Zhang P., et al., Modellng the Cauer Thermal Network for Press Pack IGBTs, n Proceedngs of the Asa-Pacfc Electromagnetc Week Conference on Electromagnetc Compatblty (AP-EMC 207), X an, Chna, 6-9 October 207. [7]. JESD 5-4. Transent Dual Interface Test Method for the Measurement of the Thermal Resstance Juncton to Case of Semconductor Devces wth Heat Flow Trough a Sngle Path. [8]. Pruksch M., Fleschmann F., Postve Iteratve Deconvoluton n Comparson to Rchardson-Lucy Lke Algorthms, Astronomcal Data Analyss Software and Systems VII, A.S.P. Conference Seres, Vol. 45, 998, p

7 [9]. Deng E., Zhao Z., Zhang P., et al., Study on the Method to Measure the Juncton-to-Case Thermal Resstance of Press-Pack IGBTs, IEEE Transactons on Power Electroncs, Vol. 33, Issue 5, 208, pp Publshed by Internatonal Frequency Sensor Assocaton (IFSA) Publshng, S. L., 208 ( 66