Baklanov, Alexander E.

Beszédes, Bertalan

Györök, György

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Extension of Nodal Voltage Methodwith the ThermosensingGyo¨rgy Gyo¨ro¨k1, Alexander E. Baklanov2, Bertalan Besze´des11 O´buda University, Alba Regia Technical Faculty, Budai Str. 45, H-8000 Sze´kesfehe´rva´r{gyorok.gyorgy, bertalan.beszedes}@amk.uni-obuda.hu2 D. Serikbayev East Kazakhstan State Technical UniversityInstrument Engineering and Technology Automation, Protozanov Str. 69, Ust-Kamenogorsk, KazakhstanABaklanov@ektu.kzAbstract—Most of the electronic circuit simulation programcontains a components’s thermal behavior modeling. Unfortu-nately in most cases this modeling, or simulation depends onthe ambient temperature of suspected electronic devices. Thismodelings can’t use of electronic parts’s or or circuit’s selfwarming.The proposed option, methodology is particularly useful forthe simulation of high performance circuits. In this article, wesupplement this thermal simulation methods so, that it can notonly to take into account the ambient temperature, but also towarm the part itself.For the demonstration of simulation we use pSpice based MI-CROCAP software environment.I. INTRODUCTIONOn Fig. (1) is seen a typical application of a high powerswitching-mode semiconductor circuit. Fig. (2) illustrate atypical input and output signals of suspected (in this casetypical theoretical application) circuit [6] [7].Voltage generator (Ug) drives direct, with 5V, (Upp), gate(G) of Ft transistor (red color of Fig. (2). If gate-source (S)voltage (UGS) greater then threshold voltage of gate UTH , thentransistor saturate and drain (D) voltage (UD) goes down (bluecolor of Fig. (2) from power voltage (UP). Meanwhile, on RD,ID current is flowing [15] [3].RDUgFtUPUDIDτtFig. 1. Typical application of a high power switching-mode semiconductorcircuit. (UP = 12V , RD = 100Ω.) Time function of transistor’s dissipation isτt .II. THERMAL BEHAVIOR OF SELF HEATEDSEMICONDUCTORIf the Ft turned ON, it’s dissipation depends on channelresistance (RDS), and drain current (ID). So we get timefunction of dissipation power according equation (1);pFt (t) = RDS · ID(dt)2. (1)We use differential equation (2) for the description ofsemiconductor’s warming process or heat-work of suspecteddevice;Pdt = cmτ+Sατdt, (2)where c is average specific heat of semiconductor body, mis the mass of heating body, τ is temperature difference ofenvironment and semiconductor device, α is a specific heattransfer factor. We put on the value P constant. Equation (2)solve for P, result is in equation (3)P= cmdτdt+Sατ . (3)On right side of equation (2) are two components; Sατ isthe quantity which heating environment, and time function of0.00u 0.20u 0.40u 0.60u 0.80u 1.00u0.005.0010.0015.00v(2) (V)T (Secs)v(3) (V)Micro-Cap 11 Evaluation Versioncircuit_3.CIRFig. 2. Typical input and output signals of Fig. (1)’s circuit.0.00u 0.20u 0.40u 0.60u 0.80u 1.00u0.005.0010.0015.00v(2) (V)T (Secs)v(3) (V) v(4) (V)Micro-Cap 11 Evaluation Versioncircuit_3.CIR Temperature=20...100Fig. 3. Output signals of Fig. (1)’s circuit, parameterized in environmentaltemperature. ∆Tis20◦C, green lines.expression of cm dτdt gives thermal-work value what heatingsemiconductor’s body itself.If P constant, from equation 3, we get equation 4;τ(t) = τ0e−tT + τm(1− e−tT ); (4)where T = cmSα time-constant of heating, τm=PSα Is the heat-balanced overheating, τ0 = τ(t = 0) is the initial value of thefunction.III. THE USUAL TEMPERATURE SIMULATIONOn Fig. (3) is seen a environmental temperature modelingof switching mode high power transistor circuit (Fig. 2). Itfollow the well used heuristical approach, according whichUTH(∆T )≃−3mV/◦C. Exact value of course depends on realtype of a semiconductor.Is seen on Fig. (3) that output characteristics isn’t verydependent of ambient temperature, however it is change from20◦C−120◦C .It can be seen that by conventional simulation we are notreally able to model the effect of thermal changes in thesemiconductor [14]. This is especially true of the thermalprocesses on the chip and their effects [11]. If need to takeinto account the impact of the warming of its assets in othertechniques must be used.IV. EXTEND OF NODAL METHODSThe electronic circuit simulation programs use the nodalpotential method. In case of active and passive components,they also use a replacement network. Generally, one branchconsists of a voltage generator and branch resistance orimpedance (Fig. 4).We want to determine the voltage of each point (Up) of thecircuit use of equation 5:Up = Ren∑i=1In; (5)where In is the branch currents, Re is parallel sum ofbranch resistors [5] [2]. By using the Milmann rule we getthe equation 6:R1U1UPI1 R2U2R3U3RnUnI2 I3 In IkRkFig. 4. Interpretation of nodal potential in a general case.Up =n∑i=1UiRik∑i=11Ri; (6)thus, we get a direct correlation between branch voltagegenerators and branch resistors.If the temperature change is to be taken into account when de-termining the value of the nodal potential, the circuit diagramof the figure 4 is supplemented with a temperature dependentbranch. The temperature dependent solution is shown in theFig.5 [4] .RτUτUPIτR1U1R2U2RnUnI1 I2 InIkRkFig. 5. The temperature dependent solution. Temperature-sensing supplementbranch in red dashed box.Thus, the equation can be supplemented with the equationof the heat sensor branch [9]. So we get equation 7:Up = Ren∑i=1In+ReIτ ; (7)where τ is the the temperature-sensing current component.From 7 and 6 we get equation 8:Up =n∑i=1UiRi+UτRτk∑i=11Ri; (8)The element of the branch is the voltage generator andthe resistor, each of which can be defined as temperaturedependent electronic part [8].V. CONTROLLED VOLTAGE GENERATORBy using the equations 4, complete with heuristic results, wecan write the voltage generator transfer characteristic equation(9).Uτ = f(τ(t)dt,h); (9)where; τ(t) time function of semiconductor heating fromequation 4, h is a heuristical constant from earlier experiments,measures.The physical content of the proposed solution is thermalcoupling of a thermal sensor (Uτ ) with the tested semicon-ductor whose output voltage is temperature dependent (Fig.V).RDUgFtUPUDIDUττtFig. 6. Thermocouple of a high power transistor (Ft ) and a thermos drivenvoltage generator (Uτ ).Such a temperature sensor voltage generator may be aspecial thermocouple or a semiconductor circuit designed forthis purpose (AD22100, Analog Devices [1]). The latter isan forward-mode current generator drive silicon diode, asdescribed in the equation 10:ID = I0(T )((eUDnUT −1); (10)where; I0 is the maximal reverse current, T is temperature,n is the emission coefficient; 1 ≤ n < 2, UT thermic voltage(equation 11):UT (T ) =kTq; (11)where; q is the elementary charge, k is Boltzmann-constant.The equations 10, 11 gives the practical used result equation12∂UD∂T∣∣∣ID=constant=UD−UG−3UTT; (12)where; UG is band gap voltage.For ∆UD in practice and from equation 12 is −1,7mV/◦Clargeness change.[12] [13]As a voltage generator of the Fig. , a current generatordriven a forward mode silicon diode is used (Fig. ). Withits output voltage, connect in serial the UGS voltage of thetransistor.RDUgFtUPUDIDτtIgFig. 7. Thermocouple of a high power transistor (Ft ) and a silicon diode.Thus, we get the dependent output characteristic of semi-conductor own heat (Fig. ). In the figure, green lines indicatethe temperature change.If we enlarge the important part of the Fig. (8), is seen thedifferent values of the saturation voltage (Fig. 9).It can be seen that the model works, the output characteristicof the transistor is temperature dependent.VI. USE OF HEAT SENSITIVE RESISTORIf a constant-voltage generator is used, we assume thatresistor is temperature dependent. In this case, the resistor (Rτ )itself is thermal coupled with the power transistor (Fig. 10).In the case of thermistors, we are approaching the change ofresistance with the usual formulas, equation 13:R(T ) = R∞eBT ; (13)where B is thermal sensing index in equation 140.00u 0.20u 0.40u 0.60u 0.80u 1.00u0.005.0010.0015.00v(2) (V)T (Secs)v(3) (V) v(4) (V)Micro-Cap 11 Evaluation Versioncircuit_3.CIR Temperature=20...300Fig. 8. Output characteristics with modified UTH voltage parameters.0.00n 32.00n 64.00n 96.00n 128.00n 160.00n0.001.002.00v(2) (V)T (Secs)v(3) (V) v(4) (V)Micro-Cap 11 Evaluation Versioncircuit_3.CIR Temperature=20...300Fig. 9. The relevant enlarged part of turn ON curve of Fig. (8).B=T2T1T2−T1 lnR1R2; (14)where R∞ is in equation 15R∞ = R1eBT1 ; (15)where R1 = RT=20◦C and R2 = RT=100◦C [10].We can proceed similarly to the use of thermistor as inFig. by diode. Of course, we can choose another mode tochange the transistor driven by changing the resistance of thethermistor. In this case we need to build different of Ug andUτ and this driven to transistor’s UGS voltage; UGS =Ug−Uτ .RDUgFtUPUDIDRττtUτR1Fig. 10. Thermistor as a heating sensor.VII. CONCLUSIONSPresent article is part of a lengthens future work in whichwe intend to supervise high-reliability electronic circuits witha microcontroller. To do this, we perform a modeling processin which a circuit simulation method compares the test circuitto some of its voltages, theoretically calculated. To do this,thermal modeling is very useful, and through some simpleexamples we can prove that the procedure works, it can beused.REFERENCES[1] Analog Devices. AD22100 voltage output temperature sensor with signalconditioning. http://www.datasheetcatalog.com/datasheets.pdf/A/D/2/2/AD22100.shtml, 6(1):151–160, 2009.[2] Gy. Gyo¨ro¨k, M. Mako´, J. Lakner. Combinatorics at electronic circuitrealization in FPAA. Acta Polytechnica Hungarica, Journal of AppliedSciences, 6(1):151–160, 2009.[3] Gyo¨ro¨k Gyo¨rgy. Programozhato´ analo´g a´ramko¨ro¨k mikroveze´rlo¨ko¨rnyezetben. O´budai Egyetem, ISBN 978 615 5018 97 8, Budapest,2013.[4] Gyo¨ro¨k Gyo¨rgy. Sza´mı´to´ge´p perife´ria´k I. O´budai Egyetem, OE AREK8003 ISBN 978 615 5018 57 2, Budapest, 2013.[5] Gy. Gyo¨ro¨k. Self configuration analog circuit by FPAA. 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Extension of Nodal Voltage Method with the Thermosensing

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