Method for measuring the thermal impedance in the frequency domain

Abstract

The present invention relates to a method for measuring the thermal impedance in the frequency domain. It comprises applying a periodical current input signal i(t) to a device under test with a given power at a frequency of interest ω; defining the thermal impedance in the frequency domain ZT (jω) as the ratio between a device temperature and the given power; calculating the temperature by multiplying each sample of vo(t) by a factor proportional to the inverse of a corresponding instantaneous level of i(t) and by a sinus / cosine which phase angle changes according to ω.t, and performing subsequent digitization and integration; calculating the given power by multiplying each sample of vo(t) by a factor proportional to the corresponding instantaneous level of i(t) and by a sinus / cosine which phase angle changes according to ω·t, and performing subsequent digitization and integration; and processing the calculated temperature and power.

Description

[0001]METHOD FOR MEASURING THE THERMAL IMPEDANCE IN THE FREQUENCY DOMAIN Field of the InventionThe present invention relates to methods for measuring thermal impedance. Particularly, thepresent invention relates to a method for measuring the thermal impedance in the frequencydomain.Background of the InventionMeasurement of the thermal impedance in the frequency domain is a technique used to characterize the thermal properties of materials and systems, especially in semiconductor engineering and thermal management of electronic devices.In general, thermal impedance is defined as ^^(^ω) where T(^ω) is the temperature ofa device under test and P(^ω) the power supplied to a device when the input has a frequencyω (period 2π / ω). Fig.1 shows an example of the circuit used.Furthermore, the relationship between the current signal applied i(t) and circuit response (Vo)is given by ^^ = ^^^^ ∗ ^(^), where RDUT generally represents a resistor that changes withtemperature, such as a platinum resistor, the behavior of which can be described as follows:^^^^ = ^^{1 + ^[^(^) − ^^]},where Ro is the resistor taken at temperature ^^ and “^” is a thermal coefficient.Based on the foregoing, it can be deduced that: ^(^) = + ^^.Therefore, temperature ^ depends on the division .On the other hand, the power supplied can be defined as ^(^) = , whereas powerdepends on the product ^^(^)^(^).In summary, obtaining the thermal impedance ^^(^ω) involves calculating the product anddivision of Vo(t) and i(t) at a given frequency.Patent EP 3594669-B1 discloses a method for determining the thermal impedance of a deviceunder test. According to this method, a device under test is heated to an initial temperatureand a pulsed power including a sequence of pulses is applied thereto. Temperature of the device is measured in a time-dependent manner. Finally, the thermal impedance of the deviceunder test is determined based on its temperature and the pulsed power.Furthermore, the method referred to as 3ω can also be used to measure thermal impedance.This method is based on the application of an alternating current (AC) at an angular frequencyω through a sample. The alternating current generates a temperature variation havingcomponents at the original frequency (1ω), the duplicate frequency (2ω), as well as a triplicatefrequency (3ω). The technique is referred to as “3-omega” because it focuses on the 3ωfrequency component of the temperature response. The third harmonic is the one used in theinference as it depends in the first order only on the magnitudes to be measured (thermalimpedance, properties of the materials or speed of the fluid in the case of anemometers). Thescientific article by Aleksandrova, Mariya et al.: “Implementation of 3ω Method for Studying theThermal Conductivity of Perovskite Thin Films”, Journal Crystals, Vol.12, 20 September 2022provides an application example thereof.The 3ω method allows measuring the thermal properties of materials with very low thermalconductivities and is applicable to a wide variety of materials. It is also used in absoluteanemometry (R. Heyd, et al., “Development of absolute hot-wire anemometry by the 3ωmethod”, Review of Scientific Instruments 81, 044901 (2010)). The main advantage is that, inthis case, measurement depends on air temperature in the second order only. However, itrequires a very high precision, which involves a complex and delicate circuitry.Therefore, new methods particularly for measuring the thermal impedance in the frequencydomain, allowing the integration thereof in ASIC, are needed.Summary of the InventionTo that end, embodiments of the present invention provide a method for measuring the thermalimpedance in the frequency domain as defined in claim 1.Particularly, the method comprises applying a periodical current input signal i(t) to a deviceunder test with a given power at a frequency of interest ω; defining the thermal impedance inthe frequency domain ZT (jω) as the ratio between a temperature of the device under test (forexample, a resistor that changes with temperature, such as a platinum resistor, among others)and the given power supplied to the device under test for the frequency of interest ω;calculating the temperature by the procedure of a) multiplying each sample of a responsesignal vo(t) by a factor proportional to the inverse of a corresponding instantaneous level of theapplied current input signal i(t) and by a sinus whose phase angle changes according to ω·t(i.e. as the function of the frequency of interest ω and the time “t”), and performing subsequentdigitization and integration of an obtained result; and b) multiplying each sample of theresponse signal vo(t) by a factor proportional to the inverse of the corresponding instantaneouslevel of the applied current input signal i(t) and by a cosine whose phase angle changesaccording to ω·t, and performing subsequent digitization and integration of an obtained result;calculating the given power by the procedure of c) multiplying each sample of the responsesignal vo(t) by a factor proportional to the corresponding instantaneous level of the applied current input signal i(t) and by a sinus whose phase angle changes according to ω·t, andperforming subsequent digitization and integration of an obtained result; and d) multiplyingeach sample of the response signal vo(t) by a factor proportional to the corresponding instantaneous level of the applied current input signal i(t) and by a cosine whose phase angle changes according to ω·t, and performing subsequent digitization and integration of anobtained result; and calculating the thermal impedance in the frequency domain by means ofprocessing the calculated temperature and power.According to an embodiment, the current input signal i(t) is a square signal, particularly ofperiod T and 50% duty cycle, which ranges between two values IH and IL.In some embodiments, the calculation of the temperature is made in a temperature sensingdevice, which is independent of the device under test and from which the temperature isinferred. In this case, the temperature calculation comprises applying a measurement currentiT(t), for example, of constant value, to the temperature sensing device, and calculating thetemperature by means of: multiplying each sample of a response signal VT(t) by a factorproportional to the inverse of a corresponding instantaneous level of the measurement current iT(t) and by a sinus whose phase angle changes according to ω·t, and performing subsequentdigitization and integration of an obtained result; and multiplying each sample of the responsesignal VT(t) by a factor proportional to the inverse of the corresponding instantaneous level ofthe measurement current iT(t) and by a cosine whose phase angle changes according to ω·t, and performing subsequent digitization and integration of an obtained result.In some embodiments, calculation of the temperature and power comprises calculating boththeir real part and their imaginary part. Particularly, said calculation comprises calculating amagnitude M of the temperature and power and the phase ^ of their first harmonic.In some embodiments, the multiplications in procedures a) – d) are performed in a single stepusing an array of switched devices. Alternatively, the multiplications can be performed in twodifferent steps, for example, a first step in which an array of switched devices is used tocalculate the multiplication of each sample of the response signal vo(t) by the factor proportional to the inverse of the corresponding instantaneous level of the applied current inputsignal i(t) or by the factor proportional to the corresponding instantaneous level of the appliedcurrent input signal i(t), and a second step in which a modulator, for example, a modified sigma-delta modulator, is used to calculate a result of the previously calculated multiplication by thesinus or cosine. It should be noted that the order of the multiplication steps can beinterchanged, while the second one is embedded in the modulator. The switched devices maycomprise capacitors, resistors, transistors and / or transconductances.In some embodiments, the modified sigma-delta modulator comprises a first time-variabledevice X1, for example a circuit with switched capacitors, with weights associated with the sineor cosine, respectively, or other fixed factors.In some embodiments, the input signal i(t) is generated using a DAC, for example, of one ormore bits.Brief Description of the DrawingsThe foregoing and other features and advantages will be more completely understood basedon the following detailed description of several embodiments that is merely illustrative and non-limiting in reference to the attached drawings, in which:Figs.1A and 1B schematically illustrate the circuits used for measuring the thermal impedancein the frequency domain, according to different embodiments of the present invention. In Fig.1A the current input signal i(t) (10) comprises a square signal with values IH and IL, which isapplied to a device under test in order to measure its the temperature and power. In Fig.1B, right-side image, the temperature is measured using a constant measurement current iT(t), which is applied to a separate sensing device.Fig. 2 schematically illustrates the proposed diagram / architecture for measuring the thermalimpedance in the frequency domain, according to an embodiment of the present invention.Fig. 3 schematically illustrates the conceptual blocks implemented by the proposed method,according to an embodiment of the present invention.Fig. 4 schematically illustrates the input channel which includes the product block and thedigital conversion.Fig. 5 schematically illustrates a first-order sigma-delta modulator with the switched devicestechnique, according to an embodiment of the present invention.Fig. 6A shows an embodiment of the implementation of a variable capacitor with weightsassociated with a sine. The signals are digital controls. Fig.6B shows the levels that wouldcorrespond to the values of the capacitors to implement the sine. Note that the sign of the inputsignal must be inverted to generate negative lobes.Detailed Description of the Invention and EmbodimentsThermal impedance in the frequency domain ZT (jω), as explained above, is defined as theratio between the temperature of a device under test (100) and the power supplied to thedevice under test for a frequency of interest ω. In some embodiments, as illustrated in Fig.1A,particularly, the present invention proposes the use, as a current input signal i(t) (10), of asquare signal of period T and 50% duty cycle ranging between two values IH and IL. This inputsignal contains different harmonics, in addition to a direct or DC component, and can beexpressed according to the development thereof in Fourier series as follows: ^(^) = ^^^ +∑^ ^^^ ^^^sin (^^^) , of which only the first harmonic (k=1) is of interest and the rest of theharmonics must be filtered by the measurement system itself. Please note that in otherembodiments, the input signal i(t) can be any periodical signal, not necessarily square, to whicha given power at the frequency of interest ω is applied.In Fig. 1B, two separated devices (100 and 100 bis) are used respectively for power andtemperature measurement. The device under test on the left (100) is dedicated to powermeasurement. It is excited by the current input signal i(t) (10), and the power is determinedusing the response signal Vo(t) (20) in combination with i(t) (10), as will be detailed below whenreferring to Fig.3. In contrast, the device on the right (100bis) is used to infer the temperature of the left-hand device (100). In this particular case, it is excited by a constant measurement current iT(t)(10bis), and the temperature is measured using a response signal VT(t) (20bis) and iT(t) (10bis).Particularly, by multiplying each sample of the response signal VT(t) (20bis) by a factor proportional to the inverse of a corresponding instantaneous level of the measurement currentiT(t) (10bis), and by a sine function whose phase angle varies with ω·t, followed by digitizationand integration of the resulting signal; and multiplying each sample of the response signal VT(t) (20bis) by a factor proportional to the inverse of the corresponding instantaneous level of themeasurement current iT(t) (10bis), and by a cosine function whose phase also varies with ω·t,followed again by digitization and integration.Fig.2 shows the architecture proposed for measuring / calculating the thermal impedance in thefrequency domain ZT (jω). In this case, it would be made up of respective conversion channelsto extract the real and imaginary parts of temperature and power, a digital processing block toextract thermal impedance, a digital control block to control A / D conversion paths and in turnto control the generation of the input signal i(t) (10) from a 1-bit DAC, for example, amongothers.According to the embodiment of Fig. 3, two channels are used to calculate temperature andtwo other channels are used to calculate power. To calculate temperature in one of thechannels, the product of the response signal vo(t) (20) is calculated by multiplying each of thesamples of the response signal vo(t) (20) by a factor proportional to the inverse of acorresponding instantaneous level of i(t) (10) and by a sinus whose phase angle changesaccording to ω·t, followed by the digitalization and integration of the obtained result by meansof the analog-digital converter. For the other channel, the product of the response signal vo(t)(20) is calculated by multiplying by a factor proportional to the inverse of the correspondinginstantaneous level of i(t) (10) and by a cosine whose phase angle changes according to ω·t,followed by the digitalization and integration of the obtained result. To calculate power in oneof the channels, the product of the response signal vo(t) (20) is calculated by multiplying by afactor proportional to the corresponding instantaneous level of i(t) and by a sinus whose phaseangle changes according to ω·t, followed by digitalization and integration of the obtained result.For the other channel, the product of the response signal vo(t) (20) is calculated by a factorproportional to the corresponding instantaneous level of i(t) and by a cosine whose phaseangle changes according to ω·t, followed by the digitalization and integration of the obtainedresult.Finally, calculation of the thermal impedance in the frequency domain is performed, forexample, by means of digital or arithmetic processing, in the digital domain, of the previouslycalculated temperature and power.According to the proposed method, the different products described above can be obtained bymeans of a single step or two different steps. If they are obtained by means of a single step,an array of switched devices, for example, capacitors, resistors, conductances, etc., can beused. If they are obtained by means of two different steps, the first step can use, for example,an array of switched devices to calculate the multiplication of each of the samples of theresponse signal vo(t) (20) by the factor that is proportional to the inverse of the correspondinginstantaneous level of i(t) of by the factor that is proportional to the correspondinginstantaneous level of i(t), and the second step can use a modified sigma-delta modulator (30),see Figs. 3 and 4, for calculating the result of the previously calculated multiplication by thesinus or cosine.Fig.5 shows an embodiment of the sigma-delta modulator (30) using, in this case, the switchedcapacitor or SC technique. To that end, the modulator includes an amplifier, an edge-triggeredcomparator, a time-variable capacitor (X1) with weights associated with the sine or cosine,capacitors C2 and CF, and switches controlled by two non-overlapping clock phases (^1 and^2). The input is the response signal vo(t) (20) and the digital output is d. Please note that forthis specific implementation, the ration X1 / C2 defines a scale gain factor “k”.Note that in other embodiments that are not illustrated, depending on the techniqueimplemented by the sigma-delta modulator (30), the time-variable device (X1) will be of onetype or another. For example, if the implemented technique is RC, the variable device can bea resistor, if the technique is Gm-C, the variable device can be a transconductance, and if thetechnique is MOSFET-C, the variable device can be a transistor.Figs. 6A and 6B show an embodiment of how the sinus or cosine can be implemented in adiscrete manner using a variable capacitor as a time-variable device. In this case, 16 periodlevels are used. Note that the larger / greater the number of levels, the smaller the introducederror will be. Due to the inherent properties of the circuit, to implement (in the absence of asign) all the steps of the period, only four capacitors are required, therefore one of them is null.In this way, the weight of the modulator input is in turn modulated with a capacitor the value ofwhich gradually changes according to a sine or cosine pattern. Given that negative capacitorscannot be made, the same effect is achieved with positive capacitors and the input signal isinverted (i.e., multiplied by -1) when said negative values should act. If positive and negativesignal values are available, it is immediate because exchanging the input lines by means of apair of switches is sufficient. Otherwise, a (readily implementable) inversion step must beintroduced. In any case, inversion of the input signal with appropriate control of the switchescan be implemented in a simple manner with the switched capacitors technique.The scope of the present invention is defined in the attached claims.

Claims

CLAIMS1. A method for measuring the thermal impedance in the frequency domain, the methodcomprising: -applying a periodical current input signal i(t) (10) to a device under test (100) with agiven power at a frequency of interest ω; -defining the thermal impedance in the frequency domain ZT (jω) as the ratio betweena temperature of the device under test (100) and the given power;- calculating said temperature by means of:a) multiplying each sample of a response signal vo(t) (20) by a factorproportional to the inverse of a corresponding instantaneous level of the applied current input signal i(t) (10) and by a sinus whose phase angle changes as a function of thefrequency of interest and time ω·t, and performing subsequent digitization andintegration of an obtained result; and b) multiplying each sample of the response signal vo(t) (20) by a factorproportional to the inverse of the corresponding instantaneous level of the applied current input signal i(t) (10) and by a cosine whose phase angle changes according toω·t, and performing subsequent digitization and integration of an obtained result;- calculating said given power by means of:c) multiplying each sample of the response signal vo(t) (20) by a factorproportional to the corresponding instantaneous level of the applied current input signal i(t) (10) and by a sinus whose phase angle changes according to ω·t, and performingsubsequent digitization and integration of an obtained result; and d) multiplying each sample of the response signal vo(t) (20) by a factorproportional to the corresponding instantaneous level of the applied current input signal i(t) (10) and by a cosine whose phase angle changes according to ω·t, and performingsubsequent digitization and integration of an obtained result; and -calculating the thermal impedance in the frequency domain by processing thecalculated temperature and power.

2. The method according to claim 1, wherein the calculation of the temperature is made in atemperature sensing device (100bis), and comprises:- applying a measurement current iT(t) (10bis) to the temperature sensing device(100bis); and -calculating said temperature by means of:multiplying each sample of a response signal vT(t) (20bis) by a factor proportional to the inverse of a corresponding instantaneous level of the measurementcurrent it(t) and by a sinus whose phase angle changes according to ω·t, andperforming subsequent digitization and integration of an obtained result; and multiplying each sample of the response signal vT(t) (20bis) by a factor proportional to the inverse of the corresponding instantaneous level of the measurement current iT(t) (10bis) and by a cosine whose phase angle changesaccording to ω·t, and performing subsequent digitization and integration of an obtained result.

3. The method according to claim 1, wherein the calculation of the temperature and powercomprises calculating both their magnitude M and the ^ phase of their first harmonic.

4. The method according to any one of the previous claims, wherein the current input signal i(t) is a square signal with values IH and IL.

5. The method according to any one of the previous claims, wherein the multiplications of stepsa) – d) are performed in a single step using an array of switched devices.

6. The method according to any one of the previous claims 1-4, wherein the multiplications ofsteps a) – d) are performed in two different steps, a first step in which an array of switcheddevices is used to calculate the multiplication of each sample of the response signal vo(t) (20)by the factor proportional to the inverse of the corresponding instantaneous level of the appliedcurrent input signal i(t) (10) or by the factor proportional to the corresponding instantaneouslevel of the applied current input signal i(t) (10), and a second step in which a modified sigma-delta modulator (30) is used to calculate a result of the previously calculated multiplication bythe sinus or cosine.

7. The method according to claim 5 or 6, wherein the switched devices comprise capacitors,resistors, transistors and / or transconductances.

8. The method according to claim 6, wherein the modified sigma-delta modulator (30)comprises a first time-variable device X1 with weights associated with the sinus or cosine,respectively.

9. The method according to any one of the previous claims, wherein the current input signali(t) is generated using a DAC of one or more bits.

10. The method according to any one of the previous claims, wherein the device under test(100) comprises a resistor that changes with temperature.

Images