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an10384 triacs: how to calculate power and predict tjmax rev. 01 ? 10 august 2005 application note document information info content keywords triac, silicon controlled rectifier, power, thermal resistance, heatsink, t j max, knee voltage, slope resistance abstract this application note describes how to calculate the power dissipation for triacs and silicon controlled rectifiers. thermal calculations are also included to help the circuit designer to predict the maximum junction temperature or calculate the required heatsink t hermal resistance. four worked examples ensure that all t he power and thermal questions that arise during the design process are covered.
philips semiconductors an10384 triac power and thermal calculations ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 2 of 16 contact information for additional information, please visit: http://www.semiconductors.philips.com for sales office addresses, please send an email to: sales.addresses@ www.semiconductors.philips.com revision history rev date description 01 20050810 first revision
philips semiconductors an10384 triac power and thermal calculations 1. introduction triacs are used to control ac mains loads. in the majority of applications, the triac will dissipate sufficient power to make thermal considerations necessary. the size of heatsink must be calculated and the maximum junction temperature must be predicted. such thermal design procedures must be followed if long-term reliability of the application is to be assured. thermal design and analysis form an essential part of the design and development process. the thermal design requires several stages of calculation involving power, thermal resistance and temperature rise. this app lication note introduces those calculations. worked examples are included, the data fo r which is derived from the customer?s application or the triac?s data sheet. 2. calculating triac power triac power dissipation is influenced by the load current. full sine wave current (full wave conduction) is assumed, since it presents the worst-case condition of maximum triac power dissipation. it also makes for the easiest calculations. if calculations are required for half wave conduction (e.g. for an scr), plea se refer to the following subsection: ?how to calculate i t(rms) and i t(ave) for half wave conduction?. (1) 2 )( )( rmstsaveto irivp += p ? triac power dissipation (w). v o ? triac knee voltage (v). this value is given in philips data sheets on the i t / v t curve. if the value is not available, it can be obtained from the i t / v t curve as described in the following subsection: ?how to calculate v o and r s ?. i t(ave) ? average load current (a). this value is calculated from the application?s rms load current using equation 2. (this assumes full wave conduction and sinusoidal load current, which will give wors t-case power dissipation.) (2) )( )( 22 rmst avet i i = r s ? triac slope resistance ( ). this value is given in philips data sheets on the i t / v t curve. if the value is not available separately, it can be obtained from the i t / v t curve as described in the following subsection: ?how to calculate v o and r s ?. i t(rms) ? rms load current (a). this value is measured in the application. ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 3 of 16
philips semiconductors an10384 triac power and thermal calculations 2.1 how to calculate i t(rms) and i t(ave) for half wave conduction fig 1. half wave conduction ? e.g. scr at full power on ac mains. pk pk avet i t ti i = = 2 2 )( (3) ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 4 of 16 422 2 2 2 )( pk pk rmst i t ti i = = (4) (5) 2 )( pk rmst i i =
philips semiconductors an10384 triac power and thermal calculations 2.2 how to calculate v o and r s if values for v o and r s are not given in the data sheet , you will have to generate the data yourself. this is easy to do. 1. make an enlarged photocopy of the i t / v t curve. 2. draw a tangent to the max v t @ t j max curve at the rated current of the triac. 3. the point where the tangent crosses the v t axis gives you v o . 4. the slope of the tangent v t / i t gives you r s . fig 2. using the tangent method to calculate v o and r s . (note: for worst-case conditions and a hot triac, always use the ?max v t @ t j max? curve.) ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 5 of 16
philips semiconductors an10384 triac power and thermal calculations 3. calculating t j max t j max is influenced by ambient temperature, triac power dissipation and the thermal resistance between junction and ambient. for th is application note, only the steady state condition will be considered. [in the short-te rm transient condition, transient thermal impedance (z th ) applies. this will always be lower than the steady-state thermal resistance (r th ). the transient condition is a lot more complicated and beyond the scope of this guide.] (6) athj aj rptt ? += t j ? junction temperature ( c). t a ? ambient temperature ( c). p ? triac power dissipation (w). r th j-a ? junction-to-ambient thermal resistance ( c/w). 3.1 analysis of r th j-a thermal resistance is similar to electrical resistance in that the total resistance can be broken down into several smaller resistances in series. for the most popular package (to220), r th j-a is composed of the following resistances: (7) athhshsthmb mbthjathj rrrr ? ? ? ? ++= figure 3 shows thermal resistance broken down in pictorial form. ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 6 of 16
philips semiconductors an10384 triac power and thermal calculations fig 3. composition of thermal resistance for the to220 package. r th j-mb ? junction-to-mounting base thermal resistance ( c/w). this is fixed and governed by the device as it is influenced by die size . refer to the relevant data sheet for the exact value. r th mb-hs ? mounting base-to-heatsink thermal resistance ( c/w). this is controlled by the equipment manufacturer because it is governe d by the mounting method ? e.g. with or without thermal grease, screw or clip mounted, insulating pad material, etc. r th hs-a ? heatsink-to-ambient thermal resistance ( c/w). this is governed by the application and is under the sole control of the equipment manufacturer. ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 7 of 16
philips semiconductors an10384 triac power and thermal calculations ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 8 of 16 please note that there are some important ca veats in the way the thermal resistance is specified because it depends on the package type and the practicality of isolating a metallic thermal reference point. 1. for plastic packages without a metal mounting base, r th j-mb + r th mb-hs is replaced by a single spec of r th j-hs , since the heatsink is t he nearest metallic reference point. 2. for low power plastic packages where a heatsink would not be used, only r th j-lead is specified, since the leads are the nearest metallic reference point. most of the heat would be conducted through the leads to the pcb, with a little radiated directly from the package to ambient. for these packages we would specify a total r th j-a with certain assumptions about how the device is mounted on the pcb, which represent typical use. 3. for some surface mount packages without a mounting base but a solder point instead, r th j-mb is replaced by r th j-sp . for these packages we would specify a total r th j-a when the device is mounted onto a pcb with a specified area of copper. table 1 lists the philips triac packages a nd the means of specifying their thermal resistance. thermal resistance values are gi ven wherever they ar e fixed by the package type or mounting method. if the thermal resist ance is influenced by the triac die, the correct value can be obtained from the data sheet. table 1: philips triac packages and their thermal resistance specs. package type thermal resistance spec value ( c/w) sot54 (to92) r th j-lead r th j-a (pcb mounted, lead length = 4 mm) 60 150 sot78 (to220) r th j-mb r th mb-hs (clip, with grease, no insulator) r th mb-hs (screw, with grease, no insulator) r th mb-hs (clip, no grease, no insulator) r th mb-hs (screw, no grease, no insulator) r th mb-hs (clip, with grease, 0.1 mm mica insulator) r th mb-hs (clip, with grease, 0.25 mm alumina insulator) r th mb-hs (screw, with grease, 0.05 mm mica insulator) r th mb-hs (screw, no grease, 0.05 mm mica insulator) r th j-a (free air without heatsink) see data sheet 0.3 0.5 1.4 1.4 2.2 0.8 1.6 4.5 60 sot82 r th j-mb r th mb-hs (clip, with grease, no insulator) r th mb-hs (clip, no grease, no insulator) r th mb-hs (clip, with grease, 0.1 mm mica insulator) r th mb-hs (clip, no grease, 0.1 mm mica insulator) r th j-a (free air without heatsink) see data sheet 0.4 2.0 2.0 5.0 100 sot186a (plastic to220) r th j-hs (with grease) r th j-hs (no grease) r th j-a (free air without heatsink) see data sheet see data sheet 55 sot223 r th j-sp r th j-a (free air, minimum pad area, fr4 pcb) see data sheet 150 typ. sot404 (d 2 pak) r th j-mb r th j-a (free air, minimum pad area, fr4 pcb) see data sheet 55 typ. sot428 (dpak) r th j-mb r th j-a (free air, minimum pad area, fr4 pcb) see data sheet 75 typ.
philips semiconductors an10384 triac power and thermal calculations 4. worked examples 4.1 vacuum cleaner a triac is used in a phase control circuit to control the speed of a vacuum cleaner motor. confirm by calculating for worst-ca se conditions that the triac?s t j max of 125 c will not be exceeded. application information: motor power = 1.2 kw max. mains supply = 230 v rms. a v p i rmst 22.5 230 1200 )( === the triac is clamped to the die-cast metal hous ing of the turbine, without thermal grease, for heatsinking purposes. therefore an insulated triac package is required. maximum heatsink temperature is 80 c. calculations: a 12 a hi-com triac is recommended to cope wi th the inrush current, which can be very high in this application. the suggested triac is bta212x-600b, which uses the isolated sot186a package, suitable for heatsinking di rectly to the turbine housing. its i gt of 50 ma is well matched to the drive circuit. using equation 2, a i i rmst avet 70.4 22.522 22 )( )( = = = from the data sheet, v o = 1.175 v and r s = 0.0316 . using equation 1, w irivp rmstsaveto 38.622.50316.070.4175.1 2 2 )( )( =+= += using equation 7, athhshsthmb mbthjathj rrrr ? ? ? ? ++= from the data sheet, r th j-hs = 5.5 c/w without heatsink compound. r th hs-a can be regarded as zero, since the turbine housing acts as an infinite heatsink with a maximum temperature fixed at 80 c under worst-case airflow conditions. therefore rth j-a is 5.5 c/w. using equation 6, c rptt athj aj =+=+= ? 1155.538.680 this is below t j max of 125 c, therefore acceptable. ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 9 of 16
philips semiconductors an10384 triac power and thermal calculations 4.2 refrigerator compressor a triac is used in an electronic thermostat that controls the on-off switching of a refrigerator compressor. what maximum heatsi nk thermal resistance is allowed to keep the triac?s junction temperature within its t j max of 125 c? application information: steady state motor current = 1.4 a rms. maximum inrush current = 17 a peak in the first half cycle. mains supply = 230 v rms. a surface mounted triac is required for direct soldering to the controller pcb. maximum ambient temperature is 40 c. the triac gate is triggered from a microcontroller with 20 ma current sink capability. calculations: an 8 a hi-com triac is recommended to cope with the inrush current. the suggested triac is bta208s-600e, which uses the sot428 (dpak) package. its i gt of 10 ma is well matched to the drive capability of the microcontroller. using equation 2, a i i rmst avet 26.1 4.122 22 )( )( = = = from the data sheet, v o = 1.264 v and r s = 0.0378 . using equation 1, w irivp rmstsaveto 67.14.10378.026.1264.1 2 2 )( )( =+= += using equation 6, athj aj rptt ? += we already know that t a = 40 c and p = 1.67 w, and in this case, t j = t j max = 125 c. rearranging the equation gives wc p tt r aj athj /51 67.1 40125 = ? = ? = ? ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 10 of 16
philips semiconductors an10384 triac power and thermal calculations using equation 7, athhshsthmb mbthjathj rrrr ? ? ? ? ++= from the data sheet, r th j-mb = 2 c/w. we need to find r th mb-a . rearranging the equation gives wc rrr mbthjathjathmb /49251 = ? = ?= ?? ? this is effectively the ?heatsink? thermal resist ance, since the pcb is our heatsink in this case. as an approximate guide, this thermal resistance can be obtained with a copper pad area of 500 mm 2 (refer to philips application note ?s urface mounted triacs and thyristors?, document order number 9397 750 02622). please note that the actual thermal resist ance will be reduced by other, non-dissipating components in close proximity to the triac, while it will be increased by any components that dissipate power in the presence of the tr iac. it is essential therefore to measure the prototype to discover the true thermal performance. ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 11 of 16
philips semiconductors an10384 triac power and thermal calculations 4.3 top-loading (vertical axis) washing machine the machine uses a reversing induction motor that?s contro lled by two triacs. will the triacs? t j max of 125 c be exceeded if they are operated without a heatsink? application information: full load motor power = 300 w. mains supply = 230 v rms. a v p i rmst 3.1 230 300 )( === isolated triac package is required. maximum ambient temperature is 40 c. calculations: this application requires 1000 v triacs to withstand the high ac mains voltage that the motor imposes across them. a three-quadrant design is mandatory for maximum immunity to false triggering. the bta208x-1000c or bta208b-1000c is recommended. these are 8 a, 1000 v, hi-com triacs with i gt of 35 ma. they use the sot186a all- plastic insulated package and sot404 (d 2 pak) surface mount package respectively. using equation 2, a i i rmst avet 17.1 3.122 22 )( )( = = = from the data sheet, v o = 1.216 v and r s = 0.0416 . using equation 1, w irivp rmstsaveto 49.13.10416.017.1216.1 2 2 )( )( =+= += using equation 6, athj aj rptt ? += we already know that t a = 40 c and p = 1.49 w. from the data sheet, r th j-a for the sot186a package in free air is 55 c/w. c t j =+= 1225549.140 this is below the t j max of 125 c. therefore the triacs can be operated without heatsinks. ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 12 of 16
philips semiconductors an10384 triac power and thermal calculations 4.4 power tool a heavy-duty electric drill uses a universal (b rush) motor whose speed is controlled by a half-wave phase control circuit. calculate the maximum power dissipation in the silicon controlled rectifier and calculate the heatsink thermal resistance required to maintain the junction temperature below t j max. application information: maximum peak value of motor current = 5 a. a surface mounted triac is required for mounting within the trigger switch. maximum ambient temperature is 50 c. the scr is air-cooled from the motor cooling fan. calculations: the bth151s-650r is recommended. its 12 a rms rating and ruggedised internal construction provide a high repetitive surge gu arantee for the best reliability in repetitive overload situations. it uses the sot428 (dpak) package. using equation 3, a i i pk avet 59.1 5 )( === using equation 5, a i i pk rmst 5.2 2 5 2 )( === from the data sheet, v o = 1.06v and r s = 0.0304 . using equation 1, w irivp rmstsaveto 88.15.20304.059.106.1 2 2 )( )( =+= += using equation 6, athj aj rptt ? + = we already know that t a = 50 c and p = 1.88w, and in this case, t j = t j max = 125 c. rearranging the equation gives wc p tt r aj athj /9.39 88.1 50125 = ? = ? = ? ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 13 of 16
philips semiconductors an10384 triac power and thermal calculations using equation 7, athhshsthmb mbthjathj rrrr ? ? ? ? ++= from the data sheet, r th j-mb = 1.8 c/w. we need to find r th mb-a . rearranging the equation gives wc rrr mbthjathjathmb /1.388.19.39 = ? = ?= ? ? ? this ?heatsink? thermal resistance covers the steady-state condition and is easily achievable with a small degree of airflow through the switch module. ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 14 of 16
philips semiconductors an10384 triac power and thermal calculations ? koninklijke philips electronics n.v. 2005. all rights reserved. application note rev. 01 ? 10 august 2005 15 of 16 5. disclaimers life support ? these products are not designed for use in life support appliances, devices, or systems where malfunction of these products can reasonably be expected to result in personal injury. philips semiconductors customers using or selling these products for use in such applications do so at their own risk and agree to fully indemnify philips semiconductors for any damages resulting from such application. right to make changes ? philips semiconductors reserves the right to make changes in the products - including circuits, standard cells, and/or software - described or contained herein in order to improve design and/or performance. when the product is in fu ll production (status ?production?), relevant changes will be communica ted via a customer product/process change notification (cpcn). philips semiconductors assumes no responsibility or liability for the use of any of these products, conveys no licence or title under any patent, copyright, or mask work right to these products, and makes no representations or warranties that these products are free from patent, copyright, or mask work right infringement, unless otherwise specified. application information ? applications that are described herein for any of these products are for illustrative purposes only. philips semiconductors make no representation or warranty that such applications will be suitable for the specified use without further testing or modification.
philips semiconductors an10384 triac power and thermal calculations ? koninklijke philips electronics n.v. 2005 all rights are reserved. reproduction in whole or in part is prohibited without the prior written consent of the copyright owner. the information presented in this document does not form part of any quotation or contract, is believed to be accurate and reliable and may be changed without notice. no liability will be accepted by the publisher for any consequence of its use. publication thereof does not convey nor imply any license under patent- or other industrial or intellectual property rights. date of release:10 august 2005 published in the netherlands 6. contents 1. introduction .........................................................3 2. calculating triac power .......................................3 2.1 how to calculate i t(rms) and i t(ave) for half wave conduction ..........................................................................4 2.2 how to calculate v o and r s .................................5 3. calculating t j max ................................................6 3.1 analysis of r th j-a ..................................................6 4. worked examples ................................................9 4.1 vacuum cleaner ..................................................9 4.2 refrigerator compressor ...................................10 4.3 top-loading (vertical axis) washing machine ...12 4.4 power tool .........................................................13 5. disclaimers ........................................................15 6. contents .............................................................16

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