Abstract:
The disclosure generally relates to method and apparatus for predicting the steady state temperature of solid state devices, preferably under transient conditions. An apparatus according to one embodiment of the disclosure includes a thermocouple for detecting temperature of the solid state system; a processor in communication with the thermocouple and programmed with instructions to: construct an initial curve for the solid state system, the initial curve having a shape; obtain a plurality of theoretical temperature curves for the solid state system; select one of the plurality of theoretical temperature curves having a shape closest to the shape of the initial curve; and superimposing the selected theoretical temperature curve on the initial curve to predict the steady state temperature.

Description:
BACKGROUND 
     The amount of energy transmitted by an electronic component into a board on which the component is mounted can affect the board&#39;s and the component&#39;s performance. The energy generated by the component is a function of the construction material of the component, the material used in the board and the thermoconductivity of the component and the board. Other factors affecting the component or the board&#39;s temperature include air velocity and availability of a cooling system. Determining the amount of energy transmitted by a component into its surrounding is complex and time consuming. Such determinations are often necessary for the design of the system and require sophisticated software systems and hours of calculation. Such software typically utilize finite element analysis (FEA). 
     A typical calculation determines the component&#39;s temperature as a function of its construction material and the heat generated when the component is operating continuously at its maximum capacity. Under such conditions, the thermal profile of the component under study is typified by a curve having a rather steep initial slope which gradually approaches an asymptotic point. The temperature remains constant beyond the asymptotic point. Consequently, the asymptotic point can be viewed as the point where the device reaches its steady state temperature. That is, the point at which further rise in temperature and heat loss due to cooling reach an equilibrium. 
     Depending on the complexities of the component, the conventional models require up to several hours for determining the component&#39;s steady state temperature. If the component is operated intermittently or if the component is used at less than its maximum capacity, the conventional systems typically fail to predict a steady state temperature. Using FEA for thermal analysis of such systems can take up to several days if not weeks of calculation. Accordingly, there is a need for a method and apparatus for predicting the steady state temperature of a solid state device during transient operation. 
     SUMMARY 
     In one embodiment, the disclosure relates to an apparatus for predicting a steady state temperature of a solid state system, comprising: a thermocouple for detecting temperature of the solid state system; a processor in communication with the thermocouple and programmed with instructions to: construct an initial curve for the solid state system, the initial curve having a shape; obtain a plurality of theoretical temperature curves for the solid state system; select one of the plurality of theoretical temperature curves having a shape closest to the shape of the initial curve; and superimposing the selected theoretical temperature curve on the initial curve to predict the steady state temperature. 
     In another embodiment, the disclosure relates to a method for predicting a steady state temperature of a solid state system, the method comprising: constructing an initial curve for the solid state system, the initial curve having a shape; obtaining a plurality of theoretical temperature curves; selecting one of the plurality of theoretical temperature curves having a shape closest to the shape of the solid state system; and superimposing the selected theoretical temperature curve on the initial curve to predict the steady state temperature. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other embodiments of the disclosure will be discussed in relation to the following non-limiting and exemplary drawings, in which: 
         FIG. 1  shows the thermal response of a solid state device during a steady state operating condition; 
         FIG. 2  shows the thermal response of a solid state device during a transient operating condition; 
         FIG. 3  shows the comparative asymptotes for a solid state device operating in a transient state and a steady state; 
         FIG. 4  shows a family of non-linear curves for a solid state device; 
         FIG. 5  is an exemplary algorithm according to one embodiment of the disclosure; and 
         FIG. 6  shows an exemplary apparatus according to one embodiment of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  shows the thermal response of a solid state device during a steady state operating condition. Specifically,  FIG. 1  shows a time dependent non-linear temperature increase for a solid state device during an uninterrupted operating condition. That is, the device under study operates without an interruption or a change of its input power supply or operating conditions. At  FIG. 1  the solid state device&#39;s temperature is shown at the y-axis and the time is shown at the x-axis. For convenience, temperatures is denoted by “T” and time is denoted by “t” herein. The device under study can be a solid state device such as an electronic module, a circuit board or any other device that comprises solid state components. Moreover, the device under study can comprise a solid state unit such as a microprocessor structured within a larger unit such as a mother board. 
     Curve  110  of  FIG. 1  depicts the device&#39;s temperature as a function of time. Curve  110  has a varying slope between temperatures T 0  and T f . As the device temperature approaches T f , the curve flattens and curve  110  reaches its asymptote  112 . Asymptote  112  occurs at T f  and can be used to predict the steady state temperature of the device. 
       FIG. 2  shows the thermal response of a solid state device during a transient operating condition, e.g., an interrupted or changed operating condition that extends for a brief, finite time period. The transient operating condition can result from a start/stop condition or a change in the input conditions. A change in the input condition can include any change which would affect the device&#39;s processing speed or performance thereby causing an increase/decrease in the device&#39;s temperature. In  FIG. 2 , the initial (i.e., at t 0 ) device temperature is T 0 . Between times t 0  and t 1 , the solid state device is operating and its temperature rises from T 0  to T 1  as represented by curve  210  which peaks at point  212 . At t 1  the operating condition of the solid state device is interrupted, for example by cutting off power to the solid state device. 
     During the power interruption between t 1  and t 2 , the solid state device cools off at a rate represented by curve  220 . The heating and cooling processes between t 0  and t 2  represent one cycle. Cooling curve  220  is interrupted at t 2  (corresponding to point  222 ) where power is once again restored to the solid state device. Between t 2  and t 3 , the device is once again operating and generating heat. However, since the device had not reached the initial temperature T 0 , the second heating cycle  230  starts at a higher starting temperature T 2 . The heat generated during time span t 2  to t 3  is represented by curve  230 . Curve  230  is interrupted at t 3  (corresponding to point  232 ) where the solid state device&#39;s operation is interrupted. Cool down commences during time span t 3  to t 4 . The solid state device&#39;s cooling between t 3  and t 4  is represented by curve  240 . At t 4 , a second cycle is completed. 
     In  FIG. 2 , the temperature increase between the cycles is shown at ΔT H   250  which is the temperature increase between the first temperature rise  210  and the second temperature rise  230 . Similarly, the system residual cooling system ΔT C    252  shows the difference between the lowest points of cooling curves  220  and  240 . As shown in  FIG. 2 , the transient operating conditions i.e., interruptions in this example, make it nearly impossible to estimate the steady state temperature of the solid state device. The conventional modeling systems require many calculations for each heating/cooling cycle. The computation time for estimating the temperature at the end of each heating/cooling cycle can be one time unit. Consequently, the computation time for determining the steady state temperature of the entire system can be n time units, where n represents the number of transient operating cycles. It is clear then that for such systems predicting steady state temperature in a reasonable time can be virtually impossible. 
       FIG. 3  shows the comparative asymptotes for a solid state device operating in an transient and an steady states. In  FIG. 3 , curve  310  represents the temperature increase for a solid state device. At t 1 , the solid state device&#39;s temperature is T 1 . Assuming that there is a transient operating cycle e.g., an interruption at t 1 , the solid state device will cool down before heating up to T 2  and beyond. The transient operating cycles (interruptions) are not shown at  FIG. 3 . Instead, the curve  310  shows the points  320 - 380 , each of which depicts a temperature peak for solid state device at its highest point before an interruption cycle. In other words, curve  310  shows the non-linear temperature growth of the solid state device. Each of temperatures  320 - 380  can reflect the upper temperature limit of the temperature growth ΔT H  between sequential interruption operating cycles (see  FIG. 2 ). Once the upper temperature limits are plotted, curve  310  can be used to predict the steady state temperature  380  at the asymptote of curve  310 . Comparatively, asymptote  390  represents the steady state temperature of the same solid state device without interruption (steady state operation). 
       FIG. 4  shows a family of non-linear curves for a solid state device. More specifically,  FIG. 4  shows an uninterrupted or steady state temperature profile for a solid state device operating under various conditions. For example, curve  410  shows the solid state device&#39;s temperature profile where the device is operating at 25% capacity, curve  420  shows the solid state device&#39;s temperature profile where the device is operating at 50% capacity and curve  430  shows the solid state device&#39;s temperature profile where the device is operating at 100% capacity. The profile representations at the various operating capacities is exemplary and profiles at any operating capacity between 0-100% can be determined without departing from the principles of the disclosure. 
     Each of curves  410 ,  420  and  430  reaches a steady state temperature at T 25% , T 50%  and T 100% . Also, each of curves  410 ,  420  and  430  have a unique shape and an asymptote. The steady state temperature of curves  410 ,  420  and  430  also denotes the asymptote for each respective curve. Given that each of curves  410 ,  420  and  430  shows thermal profile of an uninterrupted solid state device, a computer can readily ascertain the steady state temperature based on the curve&#39;s asymptote. The computation time for estimating the steady state temperature of each of curves  410 ,  420  and  430  can be assumed to be one time unit. 
     According to one embodiment of the disclosure, the steady state temperature of a solid state device which operates with transient operating cycles can be predicted by referencing the device&#39;s temperature profile when operating without transient operating cycles. For example, the solid state device profiled at  FIG. 3 , operates with a transient operating cycle i.e., an interruption, between temperature points  320 - 380 . To predict the device&#39;s steady state temperature reference can be made to  FIG. 4  where the same device is profiled at various operating capacities. A comparison of the shape of curve  310  ( FIG. 3 ) with one of curves  410 ,  420  and  430  ( FIG. 4 ) reveals, for example, that curve  310  and curve  410  have a similar shape. The steady state temperature of the device of  FIG. 3  can be predicted by superimposing curve  410  onto curve  310 . Alternatively, if the shape of curve  310  closely matches the shape of curve  420 , the latter can be superimposed on the former to predict the device&#39;s steady state temperature. 
       FIG. 5  is an exemplary algorithm according to one embodiment of the disclosure. At step  510  an initial curve for the solid state device under study can be constructed. Referring to  FIG. 2 , the initial curve can be constructed by plotting the temperature at points T 0 , T 1  and T 3 . A plot of these and similar points can yield an initial curve similar to curve  310  of  FIG. 3 . Next, the shape of the initial curve can be determined. The shape can be determined, for example, by finding the slope of different lines tangent to the curve at different locations along the curve. 
     In step  520  a theoretical temperature profile for the solid state device can be constructed. A theoretical temperature profile can provide the solid state device&#39;s thermal performance at various uninterrupted operating conditions. In one embodiment, the theoretical temperature profile can show the thermal performance of the solid state device at a range of 0% to 100% operating load. In other embodiments, the temperature profile can provide a thermal profile for the device under uninterrupted (steady state) operating loads of about 25%, 35%, 45%, 55%, 65%, 75%, 85%, 95%, and any other uninterrupted operating load. 
     In step  530 , the shape of the initial curve can be used to identify the theoretical temperature curve with the closest matching shape. Once the closest theoretical temperature curve is identified, the theoretical temperature curve can be superimposed (step  540 ) or fitted on to the initial curve to construct a final curve having an asymptote. Step  540  may further include adding a constant to provide a temperature shift or other conventional mathematical techniques for proper curve fitting. The asymptote of the final curve provides a basis for predicting the steady state temperature of the solid state device operating with a transient operating condition. 
       FIG. 6  shows an exemplary apparatus according to one embodiment of the disclosure. In  FIG. 6  device  610  can comprise a motherboard with processors  615 ,  617 ,  618  and  619 . In one embodiment, processor  630  can define the solid state apparatus under study. Thus, thermocouple  620  can communicate the operating temperature of device  615  to processor  630 . In an alternative embodiment, thermocouple  620  can communicate the operating temperature of device  610 . Using instantaneous temperatures, processor  630  can construct an initial curve for processor  615 . Processor  630  can comprise a computing apparatus or a firmware programmed with instructions for implementing the exemplary embodiments disclosed herein. Processor  630  can access database  640  which can include a theoretical temperature profile for a solid state device either identical or similar to processor  615 . Using the theoretical temperature profiles, processor  630  can select a theoretical temperature curve closely matching the shape of the initial curve for processor  615 . Once identified, the closely-matching theoretical temperature curve can be superimposed on the initial curve to predict an asymptote for the initial curve. The asymptote of the initial curve can be used to predict the steady state temperature of processor  615 . 
     The present disclosure may be embodied in other specific forms without departing from the spirit or essential attributes of the disclosure. Accordingly, reference should be made to the appended claims, rather than the foregoing specification, as indicating the scope of the disclosure. Although the foregoing description is directed to exemplary embodiments of the disclosure, it is noted that other variations and modification will be apparent to those skilled in the art; and may be made without departing from the spirit or scope of the disclosure.