Application Note Wayne Chen AN06 Oct 04 DC Temperature Compensation Abstract The DC current sensing technique provides a good solution to get the inductor current information due to its lossless characteristic. However, the inductor DC value may vary with the temperature, since copper is a positive temperature coefficient. Therefore, the temperature variation on the DC value may cause the controller to sense a false current signal. To cancel the temperature effect, a DC temperature network is usually added in the current sense loop. This application note will introduce the basic concept and the implementation methods for DC temperature compensation. Contents. Why We Need a DC Temperature Compensation Network.... Topologies of DC Temperature Compensation.... Derivation of DC Temperature Compensation Network...4 4. Design Example of DC Thermal Compensation Network...6 5. Experiment esult...8 6. Conclusion... 0 7. eference... 0 Appendix I Derivation of DC Temperature Compensation Network... AN06 04 ichtek Technology Corporation
DC Temperature Compensation. Why We Need a DC Temperature Compensation Network Figure shows the DC current sensing network. When the time constants are equal, that is, C x x = L / DC, the V CX voltage can be used to obtain the inductor current signal as shown in (). However, the DC value will increase proportionally with the temperature, which is described in () where the parameter TC DC 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 DC 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 DC(T) () L V cx DC(T) DC TCDC(T 5) () I L L DC(T) VCOE x C x + V Cx Figure. DC current sensing network. Topologies of DC Temperature Compensation The DC temperature compensation network aims the DC value to be invariant with the temperature, hence the V CX voltage can be only dependent on the inductor current. Since the DC 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 DC 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 () thermistor to cancel out the DC variations under these Y temperature points. However, according to the current sensing topologies, the DC temperature compensation network should be implemented in the proper place. Figure and Figure are respectively shown the implementation of the temperature compensation network in the current and differential sensing topologies. Therefore, the current sensing topology demonstrates the compensation network which is used to compensate three temperature points, and the differential sensing AN06 04 ichtek Technology Corporation
DC Temperature Compensation topology demonstrates the compensation network for two temperature points. Equations () and (4) are used to describe the design criterions for these two current sensing topologies. V ΔV (T) (T) I Load DC(T) () IMON x s DC(T) (T) I Load IMON(T) (4) CS PH PHn x I x I L I Ln L C x L n V cx DC (T) n phase DC n (T) I Load Vo Ase L = =L n =L C x = =C xn =C x DC (T)= =DC n (T)=DC (T) x = = xn = x s = = sn = s xn I xn C xn V cxn s I s sn I sn ISUM_N ISUM_P ISUM_P GM_CS IMON I (T) IMON DC Temperature Compensation Network for T s s V (T) (T) out ISUM_OUT V EF Figure. DC temperature compensation network in current sensing topology AN06 04 ichtek Technology Corporation
DC Temperature Compensation L I L DC (T) I Load V O I total I total ISENP x I x C x V cx IMON ISENN CS I sense S V IMON (T) n phase L n I Ln DC n (T) IMON(T) xn I xn C xn P (T) ISENnP V cxn ISENnN CSn DC Temperature Compensation Network for T V EF I sensen Ase L = =L n =L C x = =C xn =C x DC (T)= =DC n (T)= DC(T) x = = xn = x cs = = csn = cs Figure. DC temperature compensation network in differential current sensing topology. Derivation of DC Temperature Compensation Network In this section, the current sensing topology will be used as an example to derive the temperature compensation network. As shown in (), the load current information can be correctly acquired through the V voltage with a proper gain. This gain can be expressed as the ratio between and ( x+ s) and be shown in (5). For example, this ratio in T889 must set as 4 for the proper operation. x s k (5) However, in order to cancel the temperature effect on the DC, a thermistor is inserted in the network to make the V voltage be invariant with the temperature. The relationship between and temperature is shown in (6), where β is the temperature coefficient of the thermistor and is varied with different thermistor. AN06 04 ichtek Technology Corporation 4
DC Temperature Compensation ( T) e 7 T 7 5 (6) If there are three temperature points (TL, T, TH) need to be compensated, the V voltage at these three temperature points should be set equally and the results can then be shown in (7). (T) is the equivalent resistor of the thermal compensation network with a thermistor and can be obtained as (8). ( T) DC( T) DC k DC (7) x s x s s ( T) ( T) s (8) ( T) s Therefore, with above equations, the parameters of the network can be accordingly found out as (9), (0), and (). Please see Appendix I for further details. k ( T) k ( ) TH (9) where s s k (0) s ( T) ( T) () ( T) ( T) ( T) s ( T) ( T) k After implementing the temperature compensation, the V SUM error at these three temperature points (ex: 0 C, 60 C, and 00 C) should be zero as shown in Figure 4. AN06 04 ichtek Technology Corporation 5
DC Temperature Compensation Figure 4. V error after DC temperature compensation 4. Design Example of DC Thermal Compensation Network The following design approach will use the current sensing topology with T889 as an example, and the specifications are designed to meet the Intel V.5 requirements. VCOE Specification Input Voltage 0.8V to.v Number of Phases Vboot.7V VDAC(MAX).8V ICCMAX 90A ICC-DY 60A ICC-TDC 55A Load Line.5mΩ Fast Slew ate.5mv/μs Max Switching Frequency 00kHz In Shark Bay VTB Guideline for desktop platform, the requirements of the output filter are as follows: Output Inductor: 60nH/0.7mΩ Output Bulk Capacitor: 560μF/.5V/5mΩ(max) 4 to 5pcs Output Ceramic Capacitor: μf/0805 (8pcs max sites on top side) AN06 04 ichtek Technology Corporation 6
DC Temperature Compensation Step : Determine the Parameters of Inductor Determine inductor value. Output inductor: 60nH/0.7mΩ Determine DC temperature coefficient TC DC. TC DC = 90ppm Therefore, the inductor DC value with temperature effect can be calculated by using (). The following calculation result gives an example of the DC value at 60 C. DC( 60 ) 0.70 6 900 ( 60 5) 0.89( m) Step : Determine Parameter for Thermal Compensation Using NCP5WL04J0C as a thermistor, the resistance is 00kΩ and the β value is 4485. By using (6), the resistance at different temperature can be calculated. When a thermistor operates at 60 C, the resistance can then be calculated as follows: (60) 000 e 4485 7 60 7 5 ( k) Step : Design DC Current Sensing Network and x, s and Values DC current sensing capacitor C x and the resistance of X and S can be determined from the application note of DC Current Sensing Topology. C x = μf, s =.4kΩ, and x = 590Ω In T889, the ratio between and ( x+ s) must set as 4 for the proper operation. = 4 ( x+ s) = 6kΩ Step 4 : Design esistor Network Set three temperature points for thermal compensation. Choose (TH, T,TL) = (00, 60, 0) For example, the value at 60 C can be obtained from (7): 60 ( 60 ) DC DC(60) 0.890 0.70 4 k Therefore, the parameters α, α, and K can then be calculated as follows: AN06 04 ichtek Technology Corporation 7
DC Temperature Compensation α α k ( 0 ) ( 0 ) ( 60 ) 60 40 ( 60 ) 90 0 ( 60 ) ( 60 ) ( 00 ) 40 0 ( 00 ) 0 50 α α 0.0 0. ( 00 ). ( 0 ) 0 50 90 0. 0 α 0. α 0. 0 4.5 k Use (9), (0), and (), the, s, and s can be found accordingly. k ( 60 ) k ( 00 ) ) α (kω s s k. 5 (kω) s (60) ( 60 ) 5. 7 (kω) (60) s 5. Experiment esult Figure 5 shows the DCLL and DIMON reporting with DC temperature compensation. From the experiment results, the DCLL and DIMON reporting are both inside the tolerance band. However, without DC 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 AN06 04 ichtek Technology Corporation 8
DC Temperature Compensation (b)dimon reporting Figure 5. DCLL and DIMON reporting results with DC temperature compensation (a) DCLL (b)dimon reporting Figure 6. DCLL and DIMON reporting results without DC temperature compensation AN06 04 ichtek Technology Corporation 9
DC Temperature Compensation 6. Conclusion This application note provided the implementation methods and useful design equations for DC temperature compensation. With proper design procedure, it can effectively mitigate the temperature variation on DC values and provide correct current information for DC current sensing applications. 7. eference [] ichtek, T8884B datasheet. [] ichtek, T889 datasheet. [] Intel, V.5 Pulse Width Modulation (PWM) Specification [4] ichtek, DC Current Sensing Topology Application Note. AN06 04 ichtek Technology Corporation 0
DC Temperature Compensation Appendix I Derivation of DC Temperature Compensation Network Substitute three temperature points (TL, T, TH) into (8), () to (4) can be obtained. Therefore, (5) and (6) can be respectively obtained from () () and () (4). s ( TL) s () s s ( T) ( T) s () ( T) s s ( TH) s (4) s ( T) s s s s ( T) ( T) s s ( T) s s ( T) ( T) (5) (6) Define k = + s, (5) and (6) can be further expressed as (7) and (8). ( T) s s k s s ( T) ( TL) ( T) s s ( T) k ( T) ( TL) ( T) k k ( T) k k ( T) k ( T) k ( T) s s k k ( T) ( T) k k ( T) ( T) ( T) k k ( T) ( T) ( TL) ( T) (7) ( T) AN06 04 ichtek Technology Corporation
DC Temperature Compensation ( T) s s k ( T) s ( T) s ( T) ( TH) s ( T) s ( T) k ( T) ( TH) k ( T) k k ( T) k k k ( T) ( T) s s k ( T) k k ( T) k ( T) ( T) k ( T) k ( T) ( T) ( TH) (8) ( T) Equation (9) can be derived by (8)/(7). k ( T) k k k ( T) k k ( TH) ( TL) k (9) From (8), the can be found as shown in (0). k ( T) k ( TH ) k ( T) k ( ) TH (0) Then, the s can be obtained as (). k s k () s Therefore, the s can be derived as (). AN06 04 ichtek Technology Corporation
DC Temperature Compensation ( T) ( T) s s ( T) ( T) s ( T) s ( T) () ( T) s elated Parts T8884B Multi-Phase PWM Controller for CPU Core Power Supply Datasheet Next Steps ichtek Newsletter Download Subscribe ichtek Newsletter Download PDF ichtek Technology Corporation 4F, No. 8, Tai Yuen st Street, Chupei City Hsinchu, Taiwan,.O.C. Tel: 886--556789 ichtek products are sold by description only. ichtek 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. ichtek cannot ase responsibility for use of any circuitry other than circuitry entirely embodied in a ichtek product. Information furnished by ichtek is believed to be accurate and reliable. However, no responsibility is ased by ichtek or its subsidiaries for its use; nor for any infringements of patents or other rights of third parties which may result from its use. No license is granted by implication or otherwise under any patent or patent rights of ichtek or its subsidiaries. AN06 04 ichtek Technology Corporation