scispace - formally typeset
Search or ask a question

Showing papers on "Junction temperature published in 2004"


Journal ArticleDOI
TL;DR: In this paper, the degradation rate of white LEDs was investigated and it was shown that the degradation process depends on both the junction temperature and the amplitude of short-wavelength radiation.

595 citations


Journal ArticleDOI
TL;DR: In this paper, a theoretical model for the dependence of the diode forward voltage (Vf) on junction temperature (Tj) was developed, and an expression for dVf∕dT was derived that took into account all relevant contributions to the temperature dependence of Vf including the intrinsic carrier concentration, the band-gap energy, and the effective density of states.
Abstract: A theoretical model for the dependence of the diode forward voltage (Vf) on junction temperature (Tj) is developed. An expression for dVf∕dT is derived that takes into account all relevant contributions to the temperature dependence of the forward voltage including the intrinsic carrier concentration, the band-gap energy, and the effective density of states. Experimental results on the junction temperature of GaN ultraviolet light-emitting diodes are presented. Excellent agreement between the theoretical and experimental temperature coefficient of the forward voltage (dVf∕dT) is found. A linear relation between the junction temperature and the forward voltage is found.

397 citations


Journal ArticleDOI
TL;DR: In this article, the cooling capacity, junction temperature, coefficient of performance, and required heat sink thermal resistance at the TEC hot side were computed for thermoelectric cooler applications in the electronic cooling.

287 citations


Proceedings ArticleDOI
26 Jan 2004
TL;DR: In this paper, a noncontact method for determining the junction temperature of phosphor-converted white LEDs was developed. But the method only considered the 5mm epoxy encapsulated GaN+YAG Cerium phosphor white LED.
Abstract: The goal of this study was to develop a non-contact method for determining the junction temperature of phosphor-converted white LEDs as a first step toward determining the useful life of systems using white LEDs. System manufacturers generally quote the same life values for their lighting systems that the LED manufacturers estimate for a single LED. However, the life of an LED system can be much different compared with the life of an LED tested under ideal conditions because system packaging can affect system life. Heat at the pn-junction is one of the key factors that affect the degradation rate, and thus the useful life, of GaN-based white LEDs. The non-contact method described in this manuscript, combined with LED degradation rates, can be used to predict white-LED system life without affecting the integrity of the lighting system or submitting it to long-term life tests that are time-consuming. Different types of LED packages would have different degradation mechanisms. Therefore, as a first step this study considered only the 5mm epoxy encapsulated GaN+YAG Cerium phosphor white LED. The method investigated here explored whether the spectral power distribution (SPD) of the white LED could provide the necessary information to estimate LED junction temperature. Based on past studies that have shown that heat affects the radiant energy emitted by the InGaN blue LED and the YAG Cerium phosphor differently, the authors hypothesized that the ratio of the total radiant energy (W) to the radiant energy within the blue emission (B) would be proportional to the junction temperature. Experiments conducted in this study verified this hypothesis and showed that the junction temperature can be measured non-invasively through spectral measurements.

139 citations


Patent
25 Jun 2004
TL;DR: In this paper, a system and method for determining the temperature of a semiconductor wafer at the time of thermal contact of the wafer with a temperature sensing element is presented.
Abstract: A system and method for determining the temperature of a semiconductor wafer at the time of thermal contact of the semiconductor wafer with a temperature sensing element. According to the invention, a temperature profile of the temperature sensing element is recorded from the time of thermal contact up to the time of thermal equilibrium between the semiconductor wafer and the temperature sensing element and the temperature of the semiconductor wafer at the time of thermal contact is determined on the basis of a time period between the time of thermal contact and the time of thermal equilibrium and the temperature T G of the semiconductor wafer reached at the time t G of thermal equilibrium is determined by back calculation with the aid of an equation derived from Newton's law of cooling.

123 citations


Proceedings ArticleDOI
26 Jan 2004
TL;DR: In this paper, the junction temperature of a 5mm epoxy encapsulated AlGaInP LEDs is estimated by measuring the spectral shift of the peak wavelengths of the LEDs, regardless of how the temperature is created at the junction.
Abstract: This study investigated a non-invasive method to determine the junction temperature of AlGaInP light-emitting diodes (LEDs) in a system. Because the primary cause for the AlGaInP LED degradation is junction temperature, this method can be used to predict LED life. Currently, life estimates of LED lighting systems quoted by manufacturers (commonly 100,000 hours) are based on the average life of a single LED measured under specific laboratory conditions. In reality, rates of degradation are much different for LEDs in a system than for those in a laboratory environment because the packaging and the environmental conditions in which the system operates can affect LED performance. Current practices for estimation require time-consuming life tests to accurately predict the life of LEDs. Therefore, a rapid estimation method for LED life is needed. Based on previous studies, the authors chose to focus on the measurement of junction temperature and its relationship to LED degradation. The primary objective of this study was to verify that wavelength shift could be used to estimate accurately the junction temperature of 5mm epoxy encapsulated AlGaInP LEDs. In this study, the junction temperature was increased by changing the drive current while holding the ambient temperature surrounding the LED constant, and by changing the surrounding temperature while holding the drive current steady. Experimental results from this study showed that for commercial LEDs, peak wavelengths shift proportionally to junction temperature regardless of how the temperature is created at the junction, and that this linear relationship could be used as a direct measure of the junction temperature. Because the primary cause for the degradation of AlGaInP LEDs is junction heat, the light output degradation rate of these types of LEDs can be predicted by measuring the spectral shift. Therefore, LED systems can be evaluated without disassembly in their intended application.

109 citations


Journal ArticleDOI
TL;DR: In this paper, the performance of high performance GaN-based laser diodes grown on LEO-GaN/ sapphire and free-standing GaN substrates was investigated.
Abstract: We investigated characteristics of high performance GaN-based laser diodes grown on LEO-GaN/ sapphire and free-standing GaN substrates. The maximum output power was 300 mW under cw operation. The operation current and voltage were 53 mA and 4.67 V, respectively, for 30 mW-output power. Thermal simulation and junction temperature measurement of laser diodes showed that epi-down bonding was essential for the use of sapphire substrate. It was proposed that Mg diffusion into active layers was responsible for the degradation mechanism of GaN-based laser diodes.

94 citations


Journal ArticleDOI
TL;DR: A new technique for measuring the temperature profiles of visible LED chips by use of a nematic liquid crystal with IR laser illumination and the insertion of a color filter in the optical path to block the high-intensity LED light is presented.
Abstract: We present a new technique for measuring the temperature profiles of visible LED chips by use of a nematic liquid crystal with IR laser illumination. The LEDs studied have a multi-quantum-well InGaN/GaN/sapphire structure. New features in this technique are the use of a high-power IR laser beam as the sensing light and the insertion of a color filter in the optical path to block the high-intensity LED light. For the LEDs measured, the conversion efficiency decreases by 70% when the junction temperature rises from 25 to 107 °C. This technique is a valuable tool for studying the performance of LEDs as a function of junction temperature.

89 citations


Journal ArticleDOI
TL;DR: In this article, analytical expressions for the electrothermal parameters governing thermal instability in bipolar transistors, i.e., thermal resistance R/sub TH/, critical temperature T/sub crit/ and critical current J/sub C,crit/, are established and verified by measurements on silicon-on-glass bipolar NPNs.
Abstract: Analytical expressions for the electrothermal parameters governing thermal instability in bipolar transistors, i.e., thermal resistance R/sub TH/, critical temperature T/sub crit/ and critical current J/sub C,crit/, are established and verified by measurements on silicon-on-glass bipolar NPNs. A minimum junction temperature increase above ambient due to selfheating that can cause thermal breakdown is identified and verified to be as low as 10-20/spl deg/C. The influence of internal and external series resistances and the thermal resistance explicitly included in the expressions for T/sub crit/ and J/sub C,crit/ becomes clear. The use of the derived expressions for determining the safe operating area of a device and for extracting the thermal resistance is demonstrated.

77 citations


Proceedings ArticleDOI
13 Dec 2004
TL;DR: In this article, the authors investigated the temperature dependence of thermal resistance in self-heating and showed that the increase in thermal resistance due to selfheating leads to a non-linear relation between temperature and power dissipation.
Abstract: We investigate the temperature dependence of thermal resistance. We extract the thermal resistance as a function of ambient temperature. The increase of thermal resistance due to self-heating leads to a non-linear relation between temperature and power dissipation. We show how to implement this in a compact model and what its effect is on simulations at high power dissipation.

76 citations


Journal ArticleDOI
TL;DR: In this paper, the junction temperature of multiquantum well (MQW) LEDs in InGaN-GaNsapphire structure is measured using a high power laser beam to enhance the contrast of the thermal image.
Abstract: In this letter, we present a new configuration with laser illumination to measure the temperature of visible light-emitting diode (LED) chips using nematic liquid crystals. This method is applied to measuring the junction temperature of multiquantum well (MQW) LEDs in InGaN-GaN-sapphire structure. A color filter is inserted in the optical path to attenuate the overwhelming LED light. A high-power laser beam is used as the sensing light to enhance the contrast of the thermal image on LED chips. This technique is nondestructive and can be performed in real-time during device operation. One objective is to investigate the effect of the junction temperature on the electrical and optical performance of the LED devices. For the LEDs measured, the conversion efficiency decreases by 67% when the junction temperature rises from 22/spl deg/C to 107/spl deg/C. The new measurement configuration is a valuable tool to study the thermal performance of GaN-based LED devices and subsequently to investigate the degradation on electrical and optical performance due to junction temperature increase.

Journal ArticleDOI
TL;DR: In this article, an epi-down-bonded single-mode 980-nm pump module was shown to reduce junction temperature and thermal resistance by up to 30% and achieved a lifetime test over 14 000 h at 500 mA and 80/spl deg/C.
Abstract: Epi-down and epi-up bonded high-power single-mode 980-nm lasers have been studied in terms of bonding process, thermal behavior, optical performances, and long-term laser reliability. We demonstrated that epi-down bonding can offer lower thermal resistance and improved optical performance without degrading the long-term laser reliability. An optical power of 630 mW was obtained for the first time from an epi-down bonded 980-nm pump module. Our studies have shown that epi-down bonding of single-mode 980-nm lasers can reduce junction temperature and thermal resistance by up to 30%. Experimental measurements showed over 20% in thermal rollover power improvement and over 25% reduction in wavelength shift versus current in epi-down mounted lasers compared to epi-up mounted lasers. Lifetime test over 14 000 h at 500 mA and 80/spl deg/C of the epi-down bonded lasers is reported for the first time.

Journal ArticleDOI
TL;DR: In this article, a revision of the technique to determine the junction temperature and thermal resistance of bipolar transistors is presented, based on the temperature sensitivity of the base-emitter voltage when biasing the device under constant emitter current.
Abstract: A revision is presented of the technique to determine the junction temperature and thermal resistance of bipolar transistors. It is based on the temperature sensitivity of the base-emitter voltage when biasing the device under constant emitter current. It accounts correctly for the self-heating of the device during the measurement. Results are obtained for devices fabricated on silicon-on-insulator (SOI) and bulk silicon having different emitter widths and lengths. An increment of the thermal resistance is found for SOI devices with respect to bulk.

Proceedings ArticleDOI
20 Oct 2004
TL;DR: In this paper, two life tests were conducted to compare the effects of drive current and ambient temperature on the degradation rate of 5 mm and high-flux white LEDs and showed that junction temperature increases produced by drive current had a greater effect on the rate of light output degradation than junction temperature from ambient heat.
Abstract: Two life tests were conducted to compare the effects of drive current and ambient temperature on the degradation rate of 5 mm and high-flux white LEDs. Tests of 5 mm white LED arrays showed that junction temperature increases produced by drive current had a greater effect on the rate of light output degradation than junction temperature increases from ambient heat. A preliminary test of high-flux white LEDs showed the opposite effect, with junction temperature increases from ambient heat leading to a faster depreciation. However, a second life test is necessary to verify this finding. The dissimilarity in temperature effect among 5 mm and high-flux LEDs is likely caused by packaging differences between the two device types.

Journal ArticleDOI
TL;DR: In this article, a verified three-dimensional finite-element thermal model has been used to analyze the thermal resistance of InP in the context of 80 and 160 Gb/sup -1/ integrated circuits.
Abstract: Bipolar transistor scaling laws indicate that the dissipated power per unit collector-junction area increases in proportion to the square of the transistor bandwidth, increasing to /spl sim/10/sup 6/ W/cm/sup 2/ for InP heterojunction bipolar transistors (HBTs) designed for 160 Gb/s operation. A verified three-dimensional finite-element thermal model has been used to analyze the thermal resistance of InP in the context of 80 and 160 Gb/sup -1/ integrated circuits. The simulations show that the maximum temperature in the device can be significantly higher than the experimentally determined base-emitter junction temperature. Devices suitable for 160-Gb/s circuits will be thermally possible if the InGaAs etch-stop or contacting layer is removed from the subcollector.

Journal ArticleDOI
TL;DR: In this paper, a mathematical expression of the chip junction temperature in terms of chip spatial location and size for effective thermal characterization of ball grid array (BGA) typed multichip modules (MCMs) is created through the integration of the finite element (FE) analysis and the response surface methods (RSMs).
Abstract: This paper presents a mathematical expression of the chip junction temperature in terms of chip spatial location and size for effective thermal characterization of ball grid array (BGA) typed multichip modules (MCMs). It is created through the integration of the finite element (FE) analysis and the response surface methods (RSMs) that introduce an approximation of the chip junction temperature in the form of a global response surface. In place of FE simulations, the global response surface is then used to effectively characterize the thermal performance of MCMs, and facilitate the thermal management and the finding of the optimal thermal design of MCMs. To create a set of response data, a rigorous three-dimensional (3D) FE modeling of the MCM package is first established for thermal analysis. The surface loads of the FE model for the heat conduction problems are described by using existing heat transfer (HT) coefficient correlation models. The validity of the proposed FE modeling is substantiated by both the IR thermography-based thermal characterization (IRTTC) approach and the thermal test die measurement based on joint electron device engineering council (JEDEC) specification under a natural convection environment. The uncertainty of the specific power supply applied in the study and the thermal test die measurement is also analyzed. To demonstrate the proposed methodology, two types of MCM thermal design problems are fulfilled, each of which corresponds to a different chip layout. It turns out that the mathematical expression could not only effectively define the relation of the thermal performance and design parameters but also highlight their combinatorial effect.

Journal ArticleDOI
TL;DR: In this paper, the effect of junction temperature on device reliability, aging, and burn-in procedure optimization is discussed, as well as the impact of device thermal runaway and the requirements it forces on commercial burnin ovens, device package and device cooling.
Abstract: This article describes how CMOS IC technology scaling impacts semiconductor burn-in and burn-in procedures. Burn-in is a quality improvement procedure challenged by the high leakage currents that are rapidly increasing with IC technology scaling. These currents are expected to increase even more under the new burn-in environments leading to higher junction temperatures, possible thermal runaway, and yield loss of good parts during burn-in. The paper discusses the effect of junction temperature on device reliability, aging, and burn-in procedure optimization. The effect of device thermal runaway and the requirements it forces on commercial burn-in ovens, device package, and device cooling are also described.

Patent
01 Jul 2004
TL;DR: In this article, a motor control system includes a control section that performs operating range limiting processing in which a junction temperature of switching element of an electric power converter is calculated and compared with a preset temperature limit, and junction temperature reduction processing is performed to make the junction temperature equal to or less than the temperature limit.
Abstract: A motor control system includes a control section that performs operating range limiting processing in which a junction temperature of switching element of an electric power converter is calculated and compared with a preset temperature limit, and when the junction temperature exceeds the temperature limit, junction temperature reduction processing is performed to make the junction temperature equal to or less than the temperature limit, whereby the switching elements can effectively used to their maximum temperature limit irrespective of a temperature detected by a temperature sensor, thus expanding the operating range of a motor

Patent
01 Mar 2004
TL;DR: In this article, the body bias voltage applied to each device under test can be adjusted device-by-device to achieve essentially the same junction temperature at each device, which can be used to control junction temperature.
Abstract: Systems and methods for reducing temperature dissipation during burn-in testing are described. Devices under test are each subject to a body bias voltage. The body bias voltage can be used to control junction temperature (e.g., temperature measured at the device under test). The body bias voltage applied to each device under test can be adjusted device-by-device to achieve essentially the same junction temperature at each device.

Proceedings ArticleDOI
01 Nov 2004
TL;DR: In this article, simple simulation methods to calculate power semiconductor loss and instantaneous junction -case temperature difference in a power module of a matrix converter are proposed, and the validity of the proposed simulation method for loss calculation is confirmed through experiment using a 22 kW test set up of the matrix converter.
Abstract: In this paper, simple simulation methods to calculate power semiconductor loss and instantaneous junction - case temperature difference in a power module of a matrix converter are proposed. The validity of the proposed simulation method for loss calculation is confirmed through experiment using a 22 kW test set-up of the matrix converter. By using the simulation method for temperature calculating, the influence of the output frequency on the junction - case temperature difference is investigated. Moreover, the effect of using a novel IGBT (RB-IGBT) that has reverse blocking capability is discussed. It is shown that the efficiency of a matrix converter using the RB-IGBT is higher by 1.3 points than that of a conventional PWM rectifier and inverter system.

Proceedings ArticleDOI
21 Jun 2004
TL;DR: In this article, the junction temperature of white LEDs is measured from the (W/B) ratio, where W represents the total radiant energy of the white LED spectrum, and B represents the radiant energy within the blue emission peak.
Abstract: Performance of white light LEDs has improved significantly over the past few years. White LEDs are typically created by incorporating a layer of phosphor over the GaN-based blue emitter. Heat at the p-n junction seems to be the major factor that influences light output degradation in these devices. In an earlier paper, the principal authors of this manuscript demonstrated that the junction temperature of white LEDs could be measured from the (W/B) ratio, where W represents the total radiant energy of the white LED spectrum, and B represents the radiant energy within the blue emission peak. In that earlier study, the concept was verified using commercially available 5-mm type white LEDs. The goal of the study presented here was to evaluate whether the (W/B) ratio could be used to estimate junction temperature of new high-flux white LEDs. The results show that (W/B) ratio is proportional to the junction temperature of the high-flux white LED; however, the proportionality constants are different for the different white LED types.

Journal ArticleDOI
TL;DR: In this paper, a systematic assessment of predictive accuracy is presented for printed circuit board (PCB)-mounted component heat transfer, using a CFD code dedicated to the thermal analysis of electronic systems.
Abstract: This study aims to provide a perspective on the current capabilities of computational fluids dynamics (CFD) as a design tool to predict component operational temperature in electronic systems. A systematic assessment of predictive accuracy is presented for printed circuit board (PCB)-mounted component heat transfer, using a CFD code dedicated to the thermal analysis of electronic systems. Component operating temperature predictive accuracy ranges from +3/spl deg/C to -22/spl deg/C (up to 35%) of measurement, depending on component location on the board, airflow velocity and flow model applied. Combined with previous studies, the results highlight that component junction temperature needs to be experimentally measured when used for strategic product design decisions and reliability predictions. Potential development areas are discussed for improved analysis.

Journal ArticleDOI
TL;DR: In this article, the experimental methods of the determination of junction temperature and thermal resistance in GaN-based LEDs are described, and a micro thermocouple is embedded into the epoxy package for the investigation of its size effects on thermal behavior.
Abstract: This paper reports on the experimental methods of the determination of junction temperature and thermal resistance in GaN-based LEDs. For the direct temperature measurement and investigation of thermal distribution on the operating LED chip, nematic liquid crystal thermographic technique was employed. Hot spot was observed and its size was increasing with the driving input power. The initial hot spot with an anisotropic–isotropic transition of 29 °C appeared near the cathode region under the drive voltage of 2.95 V and the current of 8.1 mA. The size of the hot spot was increased with input power. Micro thermocouple was embedded into the epoxy package for the investigation of its size effects on thermal behavior. For the specific structure of LED package investigated the thermal resistances were calculated to be 265 °C/W and 215 °C/W for the low epoxy domed package and high epoxy domed package, respectively. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Proceedings ArticleDOI
04 May 2004
TL;DR: In this article, a comparison between a matrix converter and a back-to-back converter feeding a passive load is presented, with the aim of determining the converter topology which yields the highest output power per switches number.
Abstract: A comparison between a matrix converter and a back-to-back converter feeding a passive load is presented in this paper, with the aim of determining the converter topology which yields the highest output power per switches number. The comparison has been performed for different values of the output frequency. For each output frequency the load power has been increased until one of the switching devices reaches the maximum thermal stress, so defining the maximum output power of the converter. For this purpose, a simplified thermal model has been used to evaluate the junction temperature of the switches on the basis of the switch losses. An accurate computer model of both converters has been implemented taking into account the modulation laws and the real characteristics of the switching devices. Simulation results are presented showing the different behaviour of the two converters as a function of the output frequency. It has been verified that matrix converters perform better than back-to-back converters at low output frequencies.

Proceedings ArticleDOI
20 Jun 2004
TL;DR: In this article, a physics-based Fourier solution IGCT model for circuit simulation with full temperature dependencies is presented, which can provide internal physical and electrical information of the device, such as the junction temperature, and the charge distribution.
Abstract: This paper presents a physics-based Fourier solution IGCT model for circuit simulation with full temperature dependencies. Besides the external electrical characteristics, the model can also provide internal physical and electrical information of the device, such as the junction temperature, and the charge distribution. The model is shown to give good agreement with experimental waveforms and accurately predicts the device behavior under changing temperatures.

Patent
03 Mar 2004
TL;DR: In this article, a temperature measurement circuit for a dual junction temperature sensor is provided, which includes two signal channels configured to provide an intermediate differential signal from a differential input signal that is received from the temperature sensor.
Abstract: A temperature measurement circuit for a dual junction temperature sensor is provided. The temperature measurement circuit is configured to provide separate bias currents to the junctions in the temperature sensor. The temperature measurement circuit includes two signal channels configured to provide an intermediate differential signal from a differential input signal that is received from the temperature sensor. Also, the temperature measurement circuit may include one or more multiplexer circuits that are configured to control the intermediate differential signal. The temperature sensor circuit further includes a control circuit configured to adjust the bias currents and to control the multiplexer circuits such that several different differential voltages can be provided by the signal channels. Additionally, the temperature measurement circuit includes a conversion circuit that is configured to convert the differential voltage to a temperature signal, and to perform error cancellation based on the different differential voltages provided by the signal channels.

Proceedings ArticleDOI
04 May 2004
TL;DR: In this paper, the authors present a thermal model suitable for a MOSFET power switch derived from the seven-layer physical structure of the device, which can be implemented in real-time and used to estimate temperature variations within the active region of the power switch.
Abstract: Temperature management and control are among the most critical functions in power electronic devices, as operating temperature and thermal cycling can affect device performance and reliability. Therefore, it is useful to develop a device thermal model, which can be implemented in real-time and used to estimate temperature variations within the active region of the device. This paper begins by presenting a device thermal model suitable for a MOSFET power-switch derived from the seven-layer physical structure of the device. However it is shown subsequently that a third-order thermal model can give satisfactory estimates of device temperature. Furthermore, computational efficiency can he improved if the model is implemented as a third-order difference equation. Modelling results are compared with real-time temperature device measurements.

Proceedings ArticleDOI
15 Nov 2004
TL;DR: In this paper, integrated micro-channel cooling, directly underneath an electronic circuit, for on-chip cooling with forced water convection has been investigated both theoretically and experimentally, and the minimum thermal resistance, which is measured, is 0.08 K/W for a power dissipation of 428 W at a flow rate of 1 l/min.
Abstract: Integrated micro-channel cooling, directly underneath an electronic circuit, for on-chip cooling with forced water convection has been investigated both theoretically and experimentally. In a 1-cm/sup 2/ experimental device, 370 W was dissipated without exceeding the critical junction temperature of 120/spl deg/C at a flow rate of only 0.1 l/min and a pressure drop of 0.15 bar. The minimum thermal resistance, which is measured, is 0.08 K/W for a power dissipation of 428 W at a flow rate of 1.1 l/min. This more than satisfies the requirements for cooling of next generation CPUs.

Journal ArticleDOI
Ming-C. Cheng1, Feixia Yu1, Lin Jun1, Min Shen1, Goodarz Ahmadi1 
TL;DR: Improved steady-state and dynamic SOI heat flow models based on the SOI film thermal resistance for efficient prediction of steady- state and dynamic temperature variations in SOI devices are presented.

Patent
30 Sep 2004
TL;DR: In this paper, the cold junction temperature of the channels on a multi-channel terminal block is accurately determined for each terminal pair without affixing a thermistor to each terminal.
Abstract: The cold junction temperature of the channels on a multi-channel terminal block are accurately determined for each terminal pair without affixing a thermistor to each terminal. One embodiment provides accurate cold junction measurement of a six channel device (12 terminals) by mounting or directly affixing only three sensors (e.g., thermistors). The present technique decreases cost by reducing the number of sensors to less than the number of channels or terminals, while providing for accurate cold junction measurement at each channel.