Application Note Wayne Chen AN026 – Oct 2014 DCR Temperature Compensation Abstract The DCR current sensing technique provides a good solution to get the inductor current information due to its lossless characteristic. However, the inductor DCR value may vary with the temperature, since copper is a positive temperature coefficient. Therefore, the temperature variation on the DCR value may cause the controller to sense a false current signal. To cancel the temperature effect, a DCR temperature network is usually added in the current sense loop. This application note will introduce the basic concept and the implementation methods for DCR temperature compensation. Contents 1. Why We Need a DCR Temperature Compensation Network ......................................................................2 2. Topologies of DCR Temperature Compensation ........................................................................................2 3. Derivation of DCR Temperature Compensation Network............................................................................4 4. Design Example of DCR Thermal Compensation Network .........................................................................6 5. Experiment Result.....................................................................................................................................8 6. Conclusion .............................................................................................................................................. 10 7. Reference ............................................................................................................................................... 10 Appendix I Derivation of DCR Temperature Compensation Network ............................................................ 11 AN026 © 2014 Richtek Technology Corporation 1 DCR Temperature Compensation 1. Why We Need a DCR Temperature Compensation Network Figure 1 shows the DCR current sensing network. When the time constants are equal, that is, C xRx = L / DCR, the VCX voltage can be used to obtain the inductor current signal as shown in (1). However, the DCR value will increase proportionally with the temperature, which is described in (2) where the parameter TCDCR is the temperature coefficient of the copper with a positive value. When the circuit operates in the heavy load condition, the inductor’s temperature will increase as well. That will make the regulator falsely detect the load current level and provide the inaccuracy current reporting information because the DCR value varies under different temperature conditions. Besides, the output voltage could not reach to its desired value and then violate the load-line specs while adaptive voltage position droop for Vcore applications is required. Therefore, a temperature compensation network is used to solve the problem. I L DCR(T) Vcx (1) DCR(T) DCR 1 TCDCR(T 25 ) (2) IL L DCR(T) Rx Cx VCORE + VCx ─ Figure 1. DCR current sensing network 2. Topologies of DCR Temperature Compensation The DCR temperature compensation network aims the DCR value to be invariant with the temperature, hence the V CX voltage can be only dependent on the inductor current. Since the DCR is a resistor with the positive temperature coefficient, a resistor network with the negative temperature coefficient should be inserted in the current sensing loop to compensate the DCR variations due to temperatures. When there are Y temperature points need to be compensated, the compensation network requires Y resistors and one negative temperature coefficient (NTC) thermistor to cancel out the DCR variations under these Y temperature points. However, according to the current sensing topologies, the DCR temperature compensation network should be implemented in the proper place. Figure 2 and Figure 3 are respectively shown the implementation of the temperature compensation network in the sum current and differential sensing topologies. Therefore, the sum current sensing topology demonstrates the compensation network which is used to compensate three temperature points, and the differential sensing AN026 © 2014 Richtek Technology Corporation 2 DCR Temperature Compensation topology demonstrates the compensation network for two temperature points. Equations (3) and (4) are used to describe the design criterions for these two current sensing topologies. Vsum(T) I Load Rsum(T) DCR(T) Rx Rs ΔVIMON (T) I Load RIMON(T) DCR(T) RCS L1 DCR1(T) Vo PH1 Ix1 Cx1 Vcx1 n phase ILn DCRn(T) Ln PHn Rxn (4) ILoad IL1 Rx1 (3) Ixn Assume L1=…=Ln=L Cx1=…=Cxn=Cx DCR1(T)=…=DCRn(T)=DC R(T) Rx1=…=Rxn=Rx Rs1=…=Rsn=Rs Cxn Vcxn Rs1 Is1 Rsn ISUM_N ISUM_P Isn ISUM_P GM_CS IMON RIMON Isum Rsump Rsum(T) Rsums1 ISUM_OUT Rsums2 DCR Temperature Compensation Network for 3T VREF RNTC(T) Rsumout Vsum(T) Figure 2. DCR temperature compensation network in sum current sensing topology AN026 © 2014 Richtek Technology Corporation 3 DCR Temperature Compensation IL1 L1 ≈ Itotal Ix1 Rx1 Itotal ISEN1P IMON DCR1(T) ILoad VO Cx1 Vcx1 RCS1 ISEN1N Isense1 RS VIMON(T) n phase RIMON(T) Rxn RNTC(T) RP ILn Ln Ixn ISENnP DCRn(T) Cxn Vcxn RCSn ISENnN Isensen DCR Temperature Compensation Network for 2T Assume L1=…=Ln=L Cx1=…=Cxn=Cx DCR1(T)=…=DCRn(T)= DCR(T) Rx1=…=Rxn=Rx Rcs1=…=Rcsn=Rcs VREF Figure 3. DCR temperature compensation network in differential current sensing topology 3. Derivation of DCR Temperature Compensation Network In this section, the sum current sensing topology will be used as an example to derive the temperature compensation network. As shown in (3), the load current information can be correctly acquired through the Vsum voltage with a proper gain. This gain can be expressed as the ratio between Rsum and (Rx+Rs) and be shown in (5). For example, this ratio in RT8893 must set as 4 for the proper operation. Rsum k Rx Rs (5) However, in order to cancel the temperature effect on the DCR, a NTC thermistor is inserted in the R sum network to make the Vsum voltage be invariant with the temperature. The relationship between NTC and temperature is shown in (6), where β is the temperature coefficient of the NTC thermistor and is varied with different NTC thermistor. AN026 © 2014 Richtek Technology Corporation 4 DCR Temperature Compensation RNTC (T ) RNTC e 1 1 273T 27325 (6) If there are three temperature points (TL, TR, TH) need to be compensated, the Vsum voltage at these three temperature points should be set equally and the results can then be shown in (7). Rsum(T) is the equivalent resistor of the thermal compensation network with a NTC thermistor and can be obtained as (8). Rsum (T ) Rsum DCR(T ) DCR k DCR Rx Rs Rx Rs Rsum (T ) Rsums1 Rsump Rsums2 RNTC (T ) Rsump Rsums2 RNTC (T ) (7) (8) Therefore, with above equations, the parameters of the Rsum network can be accordingly found out as (9), (10), and (11). Please see Appendix I for further details. Rsump 2 k R RNTC (TR) k R RNTC (TH ) (9) Rsums2 k R Rsump (10) Rsums1 Rsum (TR) Rsump Rsums2 RNTC (TR) Rsump Rsums2 RNTC (TR) (11) 2 R (TH ) RNTC (TL) Rsum (TL) Rsum (TR) Rsum (TR) Rsum (TH ) 1 NTC where 1 2 kR RNTC (TL) RNTC (TR) RNTC (TR) RNTC (TH ) 1 2 1 After implementing the temperature compensation, the VSUM error at these three temperature points (ex: 20°C, 60°C, and 100°C) should be zero as shown in Figure 4. AN026 © 2014 Richtek Technology Corporation 5 DCR Temperature Compensation Figure 4. Vsum error after DCR temperature compensation 4. Design Example of DCR Thermal Compensation Network The following design approach will use the sum current sensing topology with RT8893 as an example, and the specifications are designed to meet the Intel VR12.5 requirements. VCORE Specification Input Voltage 10.8V to 13.2V Number of Phases 3 Vboot 1.7V VDAC(MAX) 1.8V ICCMAX 90A ICC-DY 60A ICC-TDC 55A Load Line 1.5mΩ Fast Slew Rate 12.5mV/μs Max Switching Frequency 300kHz In Shark Bay VRTB Guideline for desktop platform, the requirements of the output filter are as follows: Output Inductor: 360nH/0.72mΩ Output Bulk Capacitor: 560μF/2.5V/5mΩ(max) 4 to 5pcs Output Ceramic Capacitor: 22μF/0805 (18pcs max sites on top side) AN026 © 2014 Richtek Technology Corporation 6 DCR Temperature Compensation Step 1 : Determine the Parameters of Inductor Determine inductor value. Output inductor: 360nH/0.72mΩ Determine DCR temperature coefficient TCDCR. TCDCR = 3930ppm Therefore, the inductor DCR value with temperature effect can be calculated by using (2). The following calculation result gives an example of the DCR value at 60°C. DCR( 60 ) 0.72 103 1 3930 106 ( 60 25 ) 0.819(m) Step 2 : Determine NTC Parameter for Thermal Compensation Using NCP15WL104J03RC as a NTC thermistor, the resistance is 100kΩ and the β value is 4485. By using (6), the NTC resistance at different temperature can be calculated. When a NTC thermistor operates at 60°C, the resistance can then be calculated as follows: RNTC (60) 100 10 e 3 1 1 4485 27360 273 25 21(k) Step 3 : Design DCR Current Sensing Network and Rx, Rs and Rsum Values DCR current sensing capacitor Cx and the resistance of RX and RS can be determined from the application note of DCR Current Sensing Topology. Cx = 1μF, Rs = 3.41kΩ, and Rx = 590Ω In RT8893, the ratio between Rsum and (Rx+Rs) must set as 4 for the proper operation. Rsum = 4•(Rx+Rs) = 16kΩ Step 4 : Design Rsum Resistor Network Set three temperature points for thermal compensation. Choose (TH, TR,TL) = (100, 60, 20) For example, the Rsum value at 60°C can be obtained from (7): Rsum( 60 ) Rsum 16 103 DCR 0.72 103 14 k DCR(60) 0.819 103 Therefore, the parameters α1, α2, and KR can then be calculated as follows: AN026 © 2014 Richtek Technology Corporation 7 DCR Temperature Compensation Rsum( 20 ) Rsum( 60 ) 16 103 14 103 α1 0.02 RNTC( 20 ) RNTC( 60 ) 129 103 21 103 Rsum( 60 ) Rsum( 100 ) 14 103 12 103 α2 0.11 RNTC( 60 ) RNTC( 100 ) 21103 5 103 α2 RNTC( 100 ) RNTC( 20 ) 0.11 5 103 129 103 α1 kR 0.02 24.5 k α2 0.11 1 1 α1 0.02 Use (9), (10), and (11), the Rsump, Rsums2, and Rsums1 can be found accordingly. Rsump α2 k R RNTC( 60 ) k R RNTC( 100 ) 12 (kΩ) Rsums2 k R Rsump 12.5 (kΩ) Rsums1 Rsum( 60 ) Rsump Rsums2 RNTC (60) Rsump Rsums2 RNTC (60) 5.27 (kΩ) 5. Experiment Result Figure 5 shows the DCLL and DIMON reporting with DCR temperature compensation. From the experiment results, the DCLL and DIMON reporting are both inside the tolerance band. However, without DCR temperature compensation, the overestimated DIMON reporting result in the heavy load condition will cause DCLL to violate the load line specs as shown in Figure 6. (a) DCLL AN026 © 2014 Richtek Technology Corporation 8 DCR Temperature Compensation (b)DIMON reporting Figure 5. DCLL and DIMON reporting results with DCR temperature compensation (a) DCLL (b)DIMON reporting Figure 6. DCLL and DIMON reporting results without DCR temperature compensation AN026 © 2014 Richtek Technology Corporation 9 DCR Temperature Compensation 6. Conclusion This application note provided the implementation methods and useful design equations for DCR temperature compensation. With proper design procedure, it can effectively mitigate the temperature variation on DCR values and provide correct current information for DCR current sensing applications. 7. Reference [1] Richtek, RT8884B datasheet. [2] Richtek, RT8893 datasheet. [3] Intel, VR12.5 Pulse Width Modulation (PWM) Specification [4] Richtek, DCR Current Sensing Topology Application Note. AN026 © 2014 Richtek Technology Corporation 10 DCR Temperature Compensation Appendix I Derivation of DCR Temperature Compensation Network Substitute three temperature points (TL, TR, TH) into (8), (12) to (14) can be obtained. Therefore, (15) and (16) can be respectively obtained from (12)–(13) and (13)–(14). Rsum (TL) Rsums1 Rsump Rsums2 RNTC (TL) (12) Rsump Rsums2 RNTC (TL) Rsump Rsums2 RNTC (TR) Rsum (TR) Rsums1 (13) Rsump Rsums2 RNTC (TR) Rsum (TH ) Rsums1 Rsump Rsums2 RNTC (TH ) (14) Rsump Rsums2 RNTC (TH ) Rsump Rsums2 RNTC (TL) Rsump Rsums2 RNTC (TL) Rsump Rsums2 RNTC (TR) Rsump Rsums2 RNTC (TR) Rsump Rsums2 RNTC (TR) Rsump Rsums2 RNTC (TR) Rsum (TL) Rsum (TR) Rsump Rsums2 RNTC (TH ) Rsump Rsums2 RNTC (TH ) Rsum (TR) Rsum (TH ) (15) (16) Define kR=Rsump+Rsums2, (15) and (16) can be further expressed as (17) and (18). Rsump Rsums2 RNTC (TL) Rsump Rsums2 RNTC (TL) Rsump Rsums2 RNTC (TR) Rsump Rsums2 RNTC (TR) Rsum (TL) Rsum (TR) Rsums2 RNTC (TL) Rsums2 RNTC (TR) Rsump Rsum (TL) Rsum (TR) Rsump Rsums2 RNTC (TL) Rsump Rsums2 RNTC (TR) k R Rsump RNTC (TL) k R Rsump RNTC (TR) Rsump Rsum (TL) Rsum (TR) k R RNTC (TL) k R RNTC (TR) k R Rsump RNTC (TL) k R RNTC (TR) k R Rsump RNTC (TR) k R RNTC (TL) Rsump Rsum (TL) Rsum (TR) k R RNTC (TL) k R RNTC (TR) 2 Rsump RNTC (TL) RNTC (TR) R (TL) Rsum (TR) k R RNTC (TL) k R RNTC (TR) sum 1 AN026 2 Rsump k R RNTC (TL) k R RNTC (TR) Rsum (TL) Rsum (TR) RNTC (TL) RNTC (TR) © 2014 Richtek Technology Corporation (17) 11 DCR Temperature Compensation Rsump Rsums2 RNTC (TR) Rsump Rsums2 RNTC (TR) Rsump Rsums2 RNTC (TH ) Rsump Rsums2 RNTC (TH ) Rsum (TR) Rsum (TH ) Rsums2 RNTC (TR) Rsums2 RNTC (TH ) Rsump Rsum (TR) Rsum (TH ) Rsump Rsums2 RNTC (TR) Rsump Rsums2 RNTC (TH ) k R Rsump RNTC (TR) k R Rsump RNTC (TH ) Rsump Rsum (TR) Rsum (TH ) k R RNTC (TR) k R RNTC (TH ) k R Rsump RNTC (TR) k R RNTC (TH ) k R Rsump RNTC (TH ) k R RNTC (TR) Rsump Rsum (TR) Rsum (TH ) k R RNTC (TR) k R RNTC (TH ) 2 Rsump 2 RNTC (TR) RNTC (TH ) R (TR) Rsum (TH ) k R RNTC (TR) k R RNTC (TH ) sum 2 Rsump k R RNTC (TR) k R RNTC (TH ) Rsum (TR) Rsum (TH ) RNTC (TR) RNTC (TH ) (18) Equation (19) can be derived by (18)/(17). 2 Rsump 2 k R RNTC (TR) k R RNTC (TH ) k R RNTC (TL) 2 Rsump 1 k R RNTC (TH ) k R RNTC (TL) k R RNTC (TR) 2 R (TH ) RNTC (TL) 1 NTC kR 1 2 1 (19) From (18), the Rsump can be found as shown in (20). 2 Rsump 2 k R RNTC (TR ) k R RNTC (TH ) Rsump 2 k R RNTC (TR) k R RNTC (TH ) (20) Then, the Rsums2 can be obtained as (21). Rsump Rsums2 k R Rsums2 k R Rsump (21) Therefore, the Rsums1 can be derived as (22). AN026 © 2014 Richtek Technology Corporation 12 DCR Temperature Compensation Rsum (TR) Rsum (TR) Rsums1 Rsum (TR) Rsump Rsums2 RNTC (TR) Rsump Rsums2 RNTC (TR) Rsump Rsums2 RNTC (TR) Rsump Rsums2 RNTC (TR) (22) Related Parts RT8884B Multi-Phase PWM Controller for CPU Core Power Supply Datasheet Next Steps Richtek Newsletter Subscribe Richtek Newsletter Download Download PDF Richtek Technology Corporation 14F, No. 8, Tai Yuen 1st Street, Chupei City Hsinchu, Taiwan, R.O.C. Tel: 886-3-5526789 Richtek products are sold by description only. Richtek reserves the right to change the circuitry and/or specifications without notice at any time. Customers should obtain the latest relevant information and data sheets before placing orders and should verify that such information is current and complete. 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