Battery temperature detection

Abstract

A method and a temperature detection circuit are disclosed. An example of the method includes driving an alternating current with a first frequency into a battery and detecting an imaginary part of a battery impedance at the first frequency; driving an alternating current with a second frequency different from the first frequency into the battery and detecting an imaginary part of the battery impedance at the second frequency; and calculating an intercept frequency at which the imaginary part equals a predefined value at least based on the imaginary part obtained at the first frequency and the imaginary part obtained at the second frequency.

Claims

1. A method comprising: driving an alternating input current with a first frequency into a battery, the first frequency having a first predetermined value, and detecting a first imaginary part of an impedance of the battery at the first frequency; driving the alternating input current with a second frequency into the battery, the second frequency having a second predetermined value different from the first predetermined value of the first frequency, and detecting a second imaginary part of the impedance of the battery at the second frequency; and calculating, by a control and calculation circuit, an intercept frequency at which a third imaginary part of the impedance of the battery at the intercept frequency equals a predefined value at least based on the first imaginary part of the impedance of the battery at the first frequency and the second imaginary part of the impedance of the battery at the second frequency.

2. The method of claim 1, wherein the predefined value is zero.

3. The method of claim 1, wherein the predefined value is different from zero.

4. The method of claim 1, further comprising obtaining temperature information from a look-up table that includes a plurality of frequency-temperature information pairs.

5. The method of claim 1, wherein calculating the intercept frequency comprises: calculating a straight line based on the first imaginary part of the impedance of the battery at the first frequency and the second imaginary part of the impedance of the battery at the second frequency; and calculating the intercept frequency at which the calculated straight line intercepts the predefined value.

6. The method of claim 1, wherein detecting the first imaginary part of the impedance of the battery and the second imaginary part of the impedance of the battery at each of the first and second frequencies comprises: measuring a voltage across the battery to obtain a measurement signal; demodulating the measurement signal to obtain a demodulated measurement signal; and low pass filtering the demodulated measurement signal.

7. The method of claim 6, wherein detecting the first imaginary part of the impedance of the battery and the second imaginary part of the impedance of the battery at each of the first and second frequencies further comprises: measuring the alternating input current to obtain a further measurement signal; detecting a phase shift based on the further measurement signal; and detecting the respective imaginary part of the impedance of the battery based on the measured voltage and the detected phase shift.

8. The method of claim 6, further comprising performing a calibration routine before detecting the first imaginary part of the impedance of the battery and the second imaginary part of the impedance of the battery at each of the first and second frequencies, wherein the calibration routine comprises detecting a phase shift, and wherein detecting the respective imaginary part of the impedance of the battery comprises detecting the imaginary part of the impedance of the battery based on the measured voltage and the detected phase shift.

9. The method of claim 6, wherein demodulating the measurement signal comprises multiplying the measurement signal with a sinusoidal signal.

10. The method of claim 9, wherein a phase shift between the alternating input current and the sinusoidal signal is 90.

11. The method of claim 6, wherein demodulating the measurement signal comprises: multiplying the measurement signal with a first sinusoidal signal; and multiplying the measurement signal with a second sinusoidal signal, wherein a phase shift between the first sinusoidal signal and the second sinusoidal signal is 90.

12. The method of claim 1, further comprising: driving, at least once, the alternating input current with a further frequency into the battery, the further frequency having a further predetermined value different from the first predetermined value of the first frequency and the second predetermined value of the second frequency, and detecting a further imaginary part of the impedance of the battery at the further frequency; and wherein the intercept frequency is further calculated based on the further imaginary part of the impedance of the battery at the further frequency.

13. The method of claim 12, wherein calculating the intercept frequency comprises calculating a linear function based on a least square method.

14. The method of claim 12, wherein calculating the intercept frequency comprises calculating a non-linear function.

15. The method of claim 1, wherein the battery comprises at least one battery cell.

16. The method of claim 15, wherein the battery comprises two or more battery cells connected in series.

17. The method of claim 15, wherein the battery comprises two or more battery cells connected in parallel.

18. The method of claim 1, wherein at least one additional battery is connected in series with the battery.

19. A temperature detection circuit comprising a control and calculation circuit, wherein the temperature detection circuit is configured to: drive an alternating current with a first frequency into a battery, the first frequency having a first predetermined value, and detect a first imaginary part of an impedance of the battery at the first frequency; and drive the alternating current with a second frequency into the battery, the second frequency having a second predetermined value different from the first predetermined value of the first frequency, and detect a second imaginary part of the impedance of the battery at the second frequency, wherein the control and calculation circuit is configured to calculate an intercept frequency at which a third imaginary part of the impedance of the battery at the intercept frequency equals a predefined value at least based on the first imaginary part of the impedance of the battery at the first frequency and the second imaginary part of the impedance of the battery at the second frequency.

20. The temperature detection circuit of claim 19, wherein the predefined value is zero.

21. The temperature detection circuit of claim 19, wherein the predefined value is different from zero.

22. The temperature detection circuit of claim 19, wherein the temperature detection circuit is further configured to obtain temperature information from a look-up table that includes a plurality of frequency-temperature information pairs.

23. The temperature detection circuit of claim 19, wherein the temperature detection circuit is configured to calculate the intercept frequency using the steps of: calculating a straight line based on the first imaginary part of the impedance of the battery at the first frequency and the second imaginary part of the impedance of the battery at the second frequency; and calculating the intercept frequency at which the calculated straight line intercepts the predefined value.

24. The temperature detection circuit of claim 19, wherein the temperature detection circuit is configured to detect the first imaginary part of the impedance of the battery and the second imaginary part of the impedance of the battery at each of the first and second frequencies using the steps of: measuring a voltage across the battery to obtain a measurement signal; demodulating the measurement signal to obtain a demodulated measurement signal; and low pass filtering the demodulated measurement signal.

25. The temperature detection circuit of claim 24, wherein the temperature detection circuit is configured to detect the first imaginary part of the impedance of the battery and the second imaginary part of the impedance of the battery at each of the first and second frequencies further using the steps of: measuring the alternating current to obtain a further measurement signal; detecting a phase based on the further measurement signal; and detecting the respective imaginary part of the impedance of the battery based on the measured voltage and the detected phase shift.

26. The temperature detection circuit of claim 24, wherein the temperature detection circuit is further configured to perform a calibration routine before detecting the first imaginary part of the impedance of the battery and the second imaginary part of the impedance of the battery at each of the first and second frequencies, wherein the calibration routine comprises detecting a phase, and wherein detecting a respective imaginary part of the impedance of the battery comprises detecting the respective imaginary part of the impedance of the battery based on the measured voltage and the detected phase shift.

27. The temperature detection circuit of claim 24, wherein demodulating the measurement signal comprises multiplying the measurement signal with a sinusoidal signal.

28. The temperature detection circuit of claim 27, wherein a phase shift between the alternating current and the sinusoidal signal is 90.

29. The temperature detection circuit of claim 24, wherein demodulating the measurement signal comprises: multiplying the measurement signal with a first sinusoidal signal; and multiplying the measurement signal with a second sinusoidal signal, wherein a phase shift between the first sinusoidal signal and the second sinusoidal signal is 90.

30. The temperature detection circuit of claim 19, wherein the temperature detection circuit is further configured to drive, at least once, the alternating current with a further frequency into the battery, the further frequency having a further predetermined value different from the first predetermined value of the first frequency and the second predetermined value of the second frequency, and detect a further imaginary part of the impedance of the battery at the further frequency, and wherein the control and calculation circuit is further configured to calculate the intercept frequency based on the imaginary part of the impedance of the battery at the further frequency.

31. The temperature detection circuit of claim 30, wherein the control and calculation circuit is configured to calculate the intercept frequency by calculating a linear function based on a least square method.

32. The temperature detection circuit of claim 30, wherein the control and calculation circuit is configured to calculate the intercept frequency by calculating a non-linear function.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Examples are explained below with reference to the drawings. The drawings serve to illustrate certain principles, so that only aspects necessary for understanding these principles are illustrated. The drawings are not to scale. In the drawings the same reference characters denote like features.

(2) FIG. 1 schematically illustrates an arrangement with a battery and temperature detection circuit connected to the battery and configured to detect a temperature of the battery;

(3) FIGS. 2A-2D show different examples of a battery;

(4) FIG. 3 schematically illustrates how an imaginary part of a complex battery impedance is dependent on a battery temperature and a frequency of a current driven into the battery;

(5) FIG. 4 illustrates one example of how a frequency at which the imaginary part of the battery equals a predefined value can be obtained based on imaginary parts of the battery impedance obtained at two different frequencies;

(6) FIG. 5 shows a flow diagram that illustrates one example of a method for detecting a battery temperature based on measuring the imaginary part of the battery impedance at two different frequencies;

(7) FIG. 6 illustrates one example of how a frequency at which the imaginary part of the battery equals a predefined value can be obtained based on imaginary parts of the battery impedance obtained at more than two different frequencies;

(8) FIG. 7 shows a temperature detection circuit according to one example;

(9) FIG. 8 shows a temperature detection circuit according to another example;

(10) FIG. 9 shows a temperature detection circuit according to yet another example;

(11) FIG. 10 shows an arrangement with a plurality of batteries connected in series and a plurality of battery detection circuits;

(12) FIG. 11 shows an arrangement with a plurality of batteries connected in series and one temperature detection circuit; and

(13) FIG. 12 shows an arrangement with a plurality of batteries connected in series and a temperature detection circuit according to a further example.

DETAILED DESCRIPTION

(14) In the following detailed description, reference is made to the accompanying drawings. The drawings form a part of the description and for the purpose of illustration show examples of how the invention may be used and implemented. It is to be understood that the features of the various embodiments described herein may be combined with each other, unless specifically noted otherwise.

(15) FIG. 1 schematically illustrates an arrangement with a battery 1 and a temperature detection circuit 2. The temperature detection circuit is connected to a first battery node 11 and a second battery node 12 of the battery 1 and is configured to detect a temperature of the battery 1 in a way explained in further detail herein below.

(16) The battery 1 is a lithium-ion (Li-ion) battery, for example. The battery 1 includes at least one battery cell. Some examples of how the battery 1 may be implemented are illustrated in FIGS. 2A to 2D.

(17) Referring to FIG. 2A, the battery 1 may include one battery cell 1.sub.11 connected between the first battery node 11 and the second battery node 12. According to another example shown in FIG. 2B, the battery 1 includes a plurality of battery cells 1.sub.11, 1.sub.21, 1.sub.n1 connected in series between the first battery node 11 and the second battery node 12. According to another example shown in FIG. 2C, the battery 1 includes a plurality of battery cells 1.sub.11, 1.sub.12, 1.sub.1m connected in parallel between the first battery node 11 and the second battery node 12. According to yet another example shown in FIG. 2D, the battery one includes a series circuit with two or more parallel circuits, wherein each of these parallel circuits includes two or more battery cells 1.sub.11, 1.sub.12, 1.sub.1m, 1.sub.n1, 1.sub.n2, 1.sub.nm.

(18) Detecting the battery temperature by the temperature detection circuit 2 shown in FIG. 1 includes driving an alternating current i(f,t) via the battery nodes 11, 12 into the battery 1 and measuring a complex impedance Z(f) of the battery 1. The current i(f,t) is also referred to as input current in the following. Measuring the impedance Z(f) includes measuring a voltage v(f,t) between the battery nodes 11, 12. When the current i(f,t) driven into the battery 1 is an alternating current the voltage v(f,t) between the battery nodes 11, 12 is an alternating voltage.

(19) As used herein, an alternating current is a current that includes an alternating current component and that, additionally, may include a direct current (DC) offset. According to one example, the alternating current component is a sinusoidal current component. In the following, an alternating current with a sinusoidal current component is referred to as sinusoidal current. A sinusoidal input current i(f,t) is given by
i(f,t)=I.sub.DC+I.sub.0.Math.sin(t)(1),
where I.sub.0 is an amplitude of the sinusoidal current component, =2.Math.f, and I.sub.DC is the optional DC offset. As used herein, driving a current into the battery may include driving only a positive current that charges the battery, only a negative current that discharges the battery, or alternatingly a positive current and a negative current. If in the example given in equation (1) the DC offset I.sub.DC is zero (I.sub.DC=0), there are time periods when the current is positive so that the battery 1 is charged and time periods when the current is negative so that the battery is discharged, wherein over each period of the sinusoidal input current i(f,t) the charging state of the battery 1 does not change. According to another example, the DC offset I.sub.DC is different from zero and selected such that the input current is either only positive or only negative, wherein the current direction of the input current i(f,t) can be adjusted by selecting the sign (positive or negative) of the DC offset I.sub.DC.

(20) Using a sinusoidal current as the alternating input current i(f,t) is only an example. Alternating currents with alternating current components that have a waveform different from a sinusoidal waveform may be used as well. Examples of these other types of waveforms include, but are not restricted to, a rectangular waveform, a triangular waveform, a sine square waveform, or the like.

(21) When the input current i(f,t) is a sinusoidal current as given in equation (1) the voltage v(f,t) between the battery nodes 11, 12 is an alternating voltage as follows:
v(f,t)=V.sub.0+Z.sub.0.Math.(I.sub.DC+I.sub.O.Math.sin(t+))(2),
where Z.sub.0 is the magnitude of a complex impedance of the battery 1, is a phase shift introduced by the complex impedance of the battery. Further, V.sub.0 is an optional offset of the battery voltage v(f,t). This offset V.sub.0 represents a charging state of the battery 1, that is V.sub.0 is the voltage that can be measured between the battery nodes 11, 12 when no input current (i(f,t)=0) is driven into the battery 1. In general, the complex impedance Z(f) of the battery 1 can be written as
Z(f)=Z.sub.0.Math.e.sup.j=Re{Z(f)}+j.Math.Im{Z(f)}=Z.sub.0.Math.cos +j.Math.Z.sub.0.Math.sin (3),
where Re{Z(f)} is the real part and Im{Z(f)} is the imaginary part of the complex battery impedance Z(f), and j is the imaginary unit. The real part Re{Z(f)} can also be referred to as resistance and the imaginary part Im{Z(f)} can also be referred to as reactance of the battery 1. The impedance Z(f) is dependent on the frequency f of the input current i(f,t), so that the magnitude Z.sub.0 and the phase of the impedance Z(f) are also dependent on the frequency (are a function of the frequency), that is, Z.sub.0=Z.sub.0(f) and =(f).

(22) It is known that the imaginary part Im{Z(f)} of the impedance Z(f) is dependent on the frequency f of the input current i(f,t) and the battery temperature T. This is schematically illustrated in FIG. 3. For the purpose of illustration, FIG. 3 illustrates three curves 101, 102, 103, wherein each of these curves represents the imaginary part Im{Z(f)} of the impedance Z(f) dependent on the frequency f of the input current i(f,t) at a certain temperature T1, T2, T3. As can be seen from FIG. 3 the imaginary part Im{Z(f)} of the impedance Z(f), at each of the temperatures T1, T2, T3 shown in FIG. 3, is essentially linearly dependent on the frequency f.

(23) The ZIF method explained above detects the frequency at which the imaginary part Im{Z(f)} is zero. Those frequencies are referred to ZIF1, ZIF2, ZIF3 in FIG. 3. Each of these frequencies, which are also referred to as zero intercept frequencies (ZIFs), is associated with one temperature (T1, T2, T3 in FIG. 3) so that based on these ZIFs the battery temperature can be detected. In the NZIF method explained above the frequency is detected where the imaginary part Im{Z(f)} equals a predefined value V that is different from zero. This frequency is referred to as non-zero intercept frequency (NZIF). In the example shown in FIG. 3 the NZIFs are referred to as NZIF1, NZIF2, NZIF3. Both, the ZIF method and the NZIF method, however, require that the imaginary part Im{Z(f)} of the battery impedance Z(f) is measured at a plurality of different frequencies f. This is time consuming.

(24) An alternative approach to detect the battery temperature is illustrated in FIG. 4. A flow chart of the method illustrated in FIG. 4 is shown in FIG. 5. Referring to FIGS. 4 and 5, the method includes determining an imaginary part Im{Z(f.sub.1)} of a battery impedance Z(f.sub.1) at a first frequency f1 (in step S101 shown in FIG. 5), and determining the imaginary part Im{Z(f.sub.2)} of the battery impedance Z(f.sub.2) at a second frequency f2 (in step S102 shown in FIG. 5). In this context, at a first frequency f1 means when driving an alternating input current i(f.sub.1,t) with the first frequency f.sub.1 into the battery 1, and at a second frequency f2 means when driving an alternating input current i(f.sub.2,t) with the second frequency f.sub.2 into the battery 1. Further, the method includes (in step S103 shown in FIG. 5) calculating a frequency f.sub.0 where the imaginary part Im{Z(f.sub.0)} of the battery impedance equals a predefined value P based on the imaginary parts Im{Z(f.sub.1)}, Im{Z(f.sub.2)} obtained at the first frequency f.sub.1 and the second frequency f.sub.2. According to one example, the predefined value P is zero (P=0). If the predefined value P is zero the frequency f.sub.0 is a zero intercept frequency (ZIF) as it defines a frequency at which the imaginary part is zero. As this ZIF is obtained by a calculation, such as an extrapolation based on two measured imaginary parts Im{Z(f.sub.1)}, Im{Z(f.sub.2)}, the frequency f.sub.0 may be referred to as extrapolated zero intercept frequency (EZIF).

(25) Based on the calculated frequency f.sub.0 the battery temperature can be detected (in step S104 in FIG. 5). Determining the battery temperature based on the frequency f.sub.0 may include looking up the temperature in a look-up table that holds a plurality of frequency-temperature pairs, wherein each of these frequency-temperature pairs includes a certain temperature and an associated frequency. The associated frequency is the frequency at which, at the certain temperature, the imaginary part of the battery impedance equals the predefined value P. These temperature-frequency pairs are the same for each battery type so that a look-up table for each battery type may be generated (by the battery manufacturer, for example) based on measurements applied to one or more batteries of this type. Those measurements may include detecting the imaginary part of the battery impedance at a plurality of different frequencies and at a plurality of different (known) battery temperatures and detecting, at each of the plurality of temperatures, the frequency at which the imaginary part equals the predefined value P. During these measurements, the battery temperature may be obtained using a temperature sensor arranged inside the battery.

(26) In the following the imaginary part Im{Z(f.sub.1)} obtained at the first frequency f.sub.1 is briefly referred to as first imaginary part Im.sub.1, and the imaginary part Im{Z(f.sub.2)} obtained at the second frequency f.sub.2 is briefly referred to as second imaginary part Im.sub.2. Calculating the frequency f.sub.0 at which the imaginary part equals P based on the first imaginary part Im.sub.1 and the second imaginary part Im.sub.2 is based on the fact that, at one temperature, the imaginary part of the battery impedance Z(f) is essentially linearly dependent on the frequency f, that is, the imaginary parts obtained at different frequencies are essentially located on a straight line in a diagram that shows the imaginary part over the frequency, such as a diagram of the type shown in FIG. 3. Based on this, the frequency f.sub.0 may be calculated based on the first imaginary part Im.sub.1, the second imaginary part Im.sub.2, the first frequency f.sub.1, the second frequency f.sub.2, and the predefined value P as follows:

(27) $\begin{array}{cc}{f}_0=f_1-\frac{{\mathrm{Im}}_1-P}{{\mathrm{Im}}_2-{\mathrm{Im}}_1}.Math.\left(f_2-f_1\right).& \left(4\right)\end{array}$
This is based on the assumption that the imaginary part Im{Z(f)} of the battery impedance can approximately be expressed by a linear function (first order function) as follows:

(28) $\begin{array}{cc}\mathrm{Im}\left\{Z\left(f\right)\right\}=P+\left(\frac{{\mathrm{Im}}_2-{\mathrm{Im}}_1}{f_2-f_1}\right).Math.f.& \left(5\right)\end{array}$

(29) Calculating f.sub.0 based on only two imaginary parts, such as the first imaginary part Im.sub.1 and the second imaginary part Im.sub.2 explained above, is only an example. According to another example, the method includes obtaining two or more imaginary parts Im.sub.1, Im.sub.2, Im.sub.n at different frequencies f.sub.1, f.sub.2, f.sub.n, calculating a linear or non-linear function of the imaginary part Im{Z(f)} based on these imaginary parts Im.sub.1, Im.sub.2, Im.sub.n and, based on the linear function or the non-linear function, calculating the frequency where the imaginary part Im{Z(f)} equals P, that is, calculating f.sub.0 so that Im{Z(f.sub.0)}=P.

(30) According to one example, a linear function is calculated based on the plurality of imaginary parts Im.sub.1, Im.sub.2, Im.sub.n. This is illustrated in FIG. 6. FIG. 6 shows n imaginary parts Im.sub.1, Im.sub.2, Im.sub.n obtained at different frequencies f.sub.1, f.sub.2, f.sub.n and a straight line (drawn as dashed line) that represents the linear function based on which f.sub.0 is calculated. Just for the purpose of illustration, n=3 in the example shown in FIG. 6; any number higher than n=3 may be used as well. The linear function may be calculated based on a least square method (LSM). Such method is known so that no further explanations are required. According to another example (not shown), a non-linear function is calculated based on n, where n3, imaginary parts. In particular this example includes calculating a function of order n1 based on n imaginary parts as follows:
Im{Z(f)}=a.sub.nf.sup.n+a.sub.n-1f.sup.n-1+ . . . +a.sub.1f+a.sub.0(6),
and calculating f.sub.0 based on this function such that Im{Z(f.sub.0)}=P. It is commonly known how based on n values, such as n imaginary parts explained above, a non-linear function of order n1 can be calculated. Thus, no further explanations are required in this regard.

(31) In the method explained with reference to FIGS. 4 and 5, the imaginary part of the battery impedance is to be detected (measured) only at two different frequencies, the first frequency f.sub.1 and the second frequency f.sub.2 explained before, wherein, referring to FIG. 6, more than two measurements at different frequencies f.sub.1, f.sub.2, f.sub.n may be performed. The at least two frequencies f.sub.1, f.sub.2, f.sub.n may be chosen arbitrarily. In particular, these frequencies may be chosen from a frequency range that, usually, is not effected by interferences in an application environment of the battery. According to one example, the at least two frequencies f.sub.1, f.sub.2, f.sub.n are each selected from a range of between 100 Hz and 10 kHz, in particular between 1 kHz and 10 kHz.

(32) FIG. 7 shows one example of a temperature detection circuit 2 that is configured to detect the battery temperature based on one of the methods explained with reference to FIGS. 4, 5 and 6. FIG. 7 shows a block diagram of the temperature detection circuit 2. It should be noted that this block diagram illustrates the functional blocks of the temperature detection circuit 2 rather than a specific implementation. Those functional blocks can be implemented in various ways. According to one example, these functional blocks are implemented using dedicated circuitry, such as analog circuits, digital circuits or analog and digital circuits. According to another example, the temperature detection circuit 2 is implemented using hardware and software. For example, the temperature detection circuit 2 includes a microcontroller and software running on the microcontroller.

(33) Referring to FIG. 7, the temperature detection circuit 2 includes a current source 21 configured to provide a direct current with a current level I.sub.0. A modulator 22 connected downstream the current source 21 is configured to modulate the current I.sub.0 provided by the current source 21 with a first alternating signal s1(t). Optionally, the DC offset I.sub.DC is added to an output signal of the modulator 22 by an optional adder 28. The current i(f,t) driven into the battery 1 is available at an output of the modulator 22 or an output of the adder 28. In general, this current i(f,t) is given by
i(f,t)=I.sub.DC+I.sub.0.Math.s1(t)(5).
According to one example, the first alternating signal s1(t) is a sinusoidal signal, so that the input current i(f,t) is given by equation (1). This, however, is only an example. Other alternating signal waveforms such as a rectangular waveform may be used as well. The first alternating signal s1(t) is generated by a modulation signal generator 23 in accordance with a frequency signal S.sub.f provided by a control and calculation circuit 27. The frequency signal S.sub.f defines the frequency of the alternating signal s1(t) provided by the modulation signal generator 23.

(34) Referring to FIG. 7, the temperature detection circuit 2 further includes a measurement unit 24 coupled to the battery nodes 11, 12 and configured to measure the battery voltage v(f,t). An output signal m(f,t) provided by the measurement circuit 24 is proportional to the battery voltage v(f,t) and is given by
m(f,t)=A.sub.0.Math.v(f,t)(6)
where A.sub.0 is an amplification factor (gain) of the measurement unit 24. A demodulator 25 receives the measurement signal m(f,t) from the measurement unit 24 and a second alternating signal s2(t). The second alternating signal s2(t) is also generated by the modulation signal generator 23 and is a phase shifted version of the first alternating signal s1(t). According to one example a phase shift between the first alternating signal s1(t) and the second alternating signal s2(t) is 90 (=/2), so that

(35) $\begin{array}{cc}s2\left(t\right)=s1\left(t\frac{}{2}\right)& \left(7\right)\end{array}$
According to one example, s1(t)=sin(t) and s2(t)=cos(t). In this example, an output signal s25(f,t) of the demodulator 25 is given by
s25(f,t)=A.sub.0.Math.v(f,t).Math.cos(t)=
=A.sub.0.Math.[V.sub.0+Z.sub.0.Math.(I.sub.DC+I.sub.0.Math.sin(t+))].Math.cos(t)(8a).
Using trigonometrical formulae, equation (8a) can be written as

(36) $\begin{array}{cc}s25\left(f,t\right)=A_0.Math.\left[\left(V_0+Z_0.Math.I_{\mathrm{DC}}\right)\cos \left(t\right)+\frac{Z_0.Math.I_0}{2}\left(\sin \left(2t+\right)\right)+\sin \left(\right)\right)].& \left(8b\right)\end{array}$
Referring to FIG. 7, the demodulator output signal s25(f,t) is received by a low pass filter 26. A cut of frequency of this low pass filter 26 is such that alternating components (that is, components with the frequency t or multiples of this frequency) of the demodulator output signal s25(f,t) are filtered out, so that an output signal of the low pass filter 26 is given by

(37) $\begin{array}{cc}s26\left(f,t\right)=A_0.Math.\left[\frac{Z_0{I}_0}{2}.Math.\sin \left(\right)\right],& \left(9\right)\end{array}$
which, referring to equation (3) is a scaled version of the imaginary part of the battery impedance Z(f). The low pass filter may be any type of low pass filter. According to one example, the low pass filter is a CIC (Cascaded Integrator Comb) filter.

(38) Referring to FIG. 7, The low pass filter output signal s26(f,t) is received by the control and calculation circuit 27. The control and calculation circuit 27 is configured to control the modulation signal generator 23 such that in a first phase of the temperature detection process the modulation signal generator generates the first and second alternating signals s1(t), s2(t) with the first frequency f.sub.1. In this first phase, the low pass filter output signal s26(f,t) received by the control and calculation circuit 27 is proportional to the first imaginary part Im.sub.1 of the battery impedance, wherein a proportionality factor

(39) $\frac{A_0.Math.I_0}{2}$
is defined by the gain A.sub.0 of the measurement unit 24. In a second phase of the temperature detection process, the control and calculation circuit 27 controls the modulation signal generator 23 to generate the first and second alternating signals s1(t), s2(t) with the second frequency f.sub.2. Thus, in second phase the low pass filter signal s26(f,t) received by the control and calculation circuit 27 is proportional to the second imaginary part Im.sub.2 of the battery impedance. Based on these imaginary parts that are proportional to the first and second imaginary parts Im.sub.1, Im.sub.2 the control and calculation circuit 27 calculates the frequency f.sub.0 at which the imaginary part of the battery impedance equals the predefined value P. The control and calculation circuit 27 may calculate f.sub.0 based on equation (4), wherein the low pass filter output signal received by control and calculation circuit 27 may be divided by the proportionality factor

(40) $\frac{A_0.Math.I_0}{2}$
before applying equation (4) in order to calculate f.sub.0.

(41) If, for example, the predefined value P is zero (P=0) such division is not required, that is, the scaled versions

(42) $\frac{A_0{I}_0}{2}\sin \left(\left(f_1\right)\right)\mathrm{and}\frac{A_0{I}_0}{2}\sin \left(\left(f_2\right)\right)$
may be used in equation (4) instead of Im.sub.1=sin((f.sub.1)) and Im.sub.2=sin((f.sub.2)). The reason is that, if P=0, equation (4) can be written as

(43) $\begin{array}{cc}{f}_0=f_1-\frac{{\mathrm{Im}}_1}{{\mathrm{Im}}_2-{\mathrm{Im}}_1}.Math.\left(f_2-f_1\right),\mathrm{and}& \left(10\right)\\ \frac{{\mathrm{Im}}_1}{{\mathrm{Im}}_2-{\mathrm{Im}}_1}=\frac{\frac{A_0{I}_0}{2}{\mathrm{Im}}_1}{\frac{A_0{I}_0}{2}{\mathrm{Im}}_2-\frac{A_0{I}_0}{2}{\mathrm{Im}}_1}.& \left(11\right)\end{array}$
For the same reason, the method, if P=0, is very robust if it comes to variations of the amplification factor A of the measurement unit. Those variations may include variations either during operation of one temperature detection circuit or different amplification factors in different temperature detection circuits.

(44) According to one example, the control and calculation circuit 27 further includes a look-up table and is configured to look up a temperature associated with the calculated frequency f.sub.0, and to output a temperature signal S.sub.T that represents the temperature associated with the calculated frequency f.sub.0.

(45) The explanation provided above is based on the assumption that the only phase shift the amplifier output signal m(f,t) has relative to the first alternating signal s1(t) is the phase shift resulting from the battery 1. However, there may be an additional phase shift .sub.0 resulting from the temperature measurement circuit 2 itself, that is, for example, the amplifier 24, the modulator 22 and the optional adder 28. Thus, the amplifier output signal m(f,t) may in fact be given by
m(f,t)=A.sub.0.Math.[V.sub.0+Z.sub.0.Math.(I.sub.DC+I.sub.0.Math.sin(t+.sub.0+))](12).
The phase shift .sub.0 introduced by the temperature measurement circuit 2 may be compensated in various ways. Some examples are explained below. In two of these examples, the phase shift .sub.0 is measured in a calibration step before the temperature measurement circuit 2 is used to measure the battery temperature. The calibration step may include coupling an ohmic resistor instead of a battery 1 to the temperature measurement circuit 2 and calculating the phase shift .sub.0 based on the low pass filter output signal s26(f,t) which, in the calibration step, is given by

(46) 0$\begin{array}{cc}s26\left(f,t\right)=A_0.Math.\left[\frac{R_0{I}_0}{2}.Math.\sin \left({}_0\right)\right],& \left(13\right)\end{array}$
where R.sub.0 is a resistance of the resistor used in the calibration step. Based on equation (13), which is based on equation (9), the phase shift .sub.0 may be calculated by

(47) $\begin{array}{cc}{}_0=\arcsin \left(\frac{2.Math.s26\left(f,t\right)}{A.Math.{}_{0}R_0.Math.I_0}\right).& \left(14\right)\end{array}$

(48) According to one example that is illustrated in dashed lines in FIG. 7, the temperature measurement circuit 2 includes a phase shifter 29 that receives the second alternating signal s2(t) and provides a phase shifted version s2(t+.sub.0) of the second alternating signal to the demodulator 25, wherein the phase shifted version s2(t+.sub.0) of the second alternating signal takes into account the phase shift .sub.0 measured in the calibration process. The phase shift introduced by the temperature measurement circuit may be dependent on the frequency so that .sub.0=.sub.0(f). In this case, a calibration step may be performed at those different frequencies f.sub.1, f.sub.2 of the input current i(f,t) at which the at least two imaginary parts Im.sub.1, Im.sub.2 are obtained in operation of the temperature measurement circuit. In each calibration step one phase shift .sub.0(f.sub.1), .sub.0(f.sub.2) associated with the respective frequency f.sub.1, f.sub.2 is obtained and stored in the control and calculation circuit 27. In this case, during a temperature measurement operation of the temperature measurement circuit 2, the phase shifter 29 receives the correct phase shift information from the control and calculation circuit 27 in each of the at least two measurement phases in which the input current i(f,t) has different frequencies f1, f2.

(49) FIG. 8 shows a modification of the temperature detection circuit 2 shown in FIG. 7. The temperature detection circuit shown in FIG. 8 is different from the one shown in FIG. 7 in that it includes a first demodulator 25.sub.I and a second demodulator 25.sub.Q that each receive the measurement signal m(f,t). A first low pass filter 26.sub.I is connected downstream the first demodulator 25.sub.I, and a second low pass filter 26.sub.Q is connected downstream the second demodulator 25.sub.Q. The first demodulator 25.sub.I receives a third alternating signal s1(t) and the second demodulator 25.sub.Q receives the second alternating signal s2(t). The third alternating signal s1(t) and the second alternating signal s2(t) are selected such that there is a phase shift of /2 (=90) between the third alternating signal s1(t) and the second alternating signal s2(t). The third alternating signal s1(t) may be in phase with the first alternating signal s1(t). This, however, is not mandatory. If there is a phase shift between the first signal s1(t) and the third signal s1(t) such phase shift can be considered as part of the phase shift introduced by the temperature detection circuit and is compensated by the mechanism explained below. According to one example, the third alternating signal s1(t) and the second alternating signal s2(t) have a sinusoidal waveform so that, for example, s1(t)=sin(t) and s2(t)=cos(t). In this case, output signals s25.sub.I(f,t), s25.sub.Q(f,t) of the demodulators 25.sub.I, 25.sub.Q are as follows:
s25.sub.I(f,t)=A.sub.0.Math.v(f,t).Math.s1(t)=A.sub.0.Math.v(f,t).Math.sin(t)(15a)
s25.sub.Q(f,t)=A.sub.0.Math.v(f,t).Math.s2(t)=A.sub.0.Math.v(f,t).Math.cos(t)(15b).
If the input current i(f,t) is a sinusoidal current, the first alternating signal s1(t) and the third alternating signal s1(t) may be identical. If, for example, v(f,t) is in accordance with equation (2) and there is an additional phase shift .sub.0 introduced by the temperature detection circuit 2 the demodulator output signals s25.sub.I(f,t), s25.sub.Q(f,t) are
s25.sub.I(f,t)=A.sub.0.Math.[V.sub.0+Z.sub.0.Math.(I.sub.DC+I.sub.0.Math.sin(t+.sub.0+))].Math.sin(t)(16a)
s25.sub.Q(f,t)=A.sub.0.Math.[V.sub.0+Z.sub.0.Math.(I.sub.DC+I.sub.0.Math.sin(t+.sub.0+))].Math.cos(t)(16b).
The low pass filters 26.sub.I, 26.sub.Q are configured to filter signal components with a frequency t and higher. Output signals s26.sub.I(f,t), s26.sub.Q(f,t), which are also referred to as inphase component V.sub.I and quadrature component V.sub.Q in the following, of these low pass filters 26.sub.I, 26.sub.Q are given by

(50) $\begin{array}{cc}s{26}_I\left(f,t\right)=V_I=\frac{A_0.Math.Z_0.Math.I_0}{2}\cos \left({}_0+\right)& \left(17a\right)\\ s{26}_Q\left(f,t\right)=V_Q=\frac{A_0.Math.Z_0.Math.I_0}{2}\sin \left({}_0+\right).& \left(17b\right)\end{array}$

(51) According to one example, the control and calculation circuit 27 is configured to divide the inphase and quadrature component by

(52) $\frac{I_0}{2}$
to obtain
s26.sub.1(f,t)=V.sub.I=A.sub.0.Math.Z.sub.0.Math.cos(.sub.0+)(18a)
s26.sub.Q(f,t)=V.sub.Q=A.sub.0.Math.Z.sub.0.Math.sin(.sub.0+)(18b),
wherein these signals (values) can be considered as the real part and the imaginary part of a product of a complex impedance Z of the battery 1 and a complex gain A of the amplifier 24. The complex gain also takes into account the overall phase shift .sub.0 introduced by the temperature detection circuit 2. Thus,
V.sub.I+jV.sub.Q=A.Math.Z=(A.sub.0.Math.e.sup.j.sup.0).Math.(Z.sub.0.Math.e.sup.j)(19),
According to one example, the complex gain A, which includes the magnitude A.sub.0 and the phase shift .sub.0, is determined in one or more calibration steps and stored in the control and calculation unit. Based on A.sub.0 and .sub.0 and on V.sub.I and V.sub.Q the control and calculation unit circuit 27 may calculate the magnitude Z.sub.0 and phase of the battery resistance Z as follows:

(53) $\begin{array}{cc}{Z}_0=\frac{\sqrt{{\left(V_I^{}\right)}^2+{\left(V_Q^{}\right)}^2}}{A_0}& \left(20a\right)\\ =\arctan \left(\frac{V_Q^{}}{V_I^{}}\right)-{}_0.& \left(20b\right)\end{array}$
Referring to the above, the magnitude Z.sub.0 and phase are dependent on the frequency, that is, Z.sub.0=Z.sub.0(f) and =(f) so that the control and calculation circuit 27 calculates Z.sub.0 and at at least two different frequency f1, f2 and calculates the imaginary part Im{Z(f)} at each of these frequencies based on
Im{Z(f)}=Z.sub.0.Math.sin()(21).
The complex gain A may be dependent on the frequency, that is, A.sub.0=A.sub.0(f) and .sub.0=.sub.0(f). In this case, A.sub.0(f) and .sub.0(f) may be obtained in a calibration routine for each of the at least two frequencies f.sub.1, f.sub.2 and stored in the control and calculation circuit 27. The control and calculation circuit 27 then, for example, uses A.sub.0(f1) and .sub.0(f1) to calculate Z.sub.0(f1) and (f1) based on equations (20a) and (20b) and A.sub.0(f2) and .sub.0(f2) to calculate Z.sub.0(f2) and (f2) based on equations (20a) and (20b). The calibration routine may include connecting an ohmic resistor with a resistance R.sub.0 instead of a battery to the temperature detection circuit 2. Signals s26.sub.I(f,t) and s26.sub.Q(f,t) explained with reference to equations (18a) and (18b) are then given by
s26.sub.I(f,t)=V.sub.I=A.sub.0.Math.R.sub.0.Math.cos(.sub.0)(22a)
s26.sub.Q(f,t)=V.sub.Q=A.sub.0.Math.R.sub.0.Math.sin(.sub.0)(22b).
Based on these signals s26.sub.I(f,t) and s26.sub.Q(f,t) magnitude A.sub.0 and phase .sub.0 of the complex amplification may be calculated by

(54) $\begin{array}{cc}{A}_0=\frac{\sqrt{{\left(V_I^{}\right)}^2+{\left(V_Q^{}\right)}^2}}{R_0}& \left(23a\right)\\ {}_0=\arctan \left(\frac{V_Q^{}}{V_I^{}}\right).& \left(23b\right)\end{array}$

(55) Although equations (15a) to (23b) illustrate/explain a method of detecting the imaginary part of the battery resistance based on a sinusoidal input current i(f,t) the method is not restricted to a sinusoidal input current, but any other type of alternating input current, such as a rectangular input current may be used as well. In each case the second and third alternating signals s2(t) and s1(t) can be sinusoidal signals, such as s2(t)=cos(t) and s1(t)=sin(t).

(56) FIG. 9 shows a modification of the temperature detection circuit 2 shown in FIG. 8. Besides measuring the voltage v(f,t) across the battery 1 the temperature detection circuit 2 shown in FIG. 9 also measures the input current i(f,t). For this, a current sense resistor 30 is connected in series with the modulator 22. A sense voltage v30(f,t) across the resistor is proportional to the input current i(f,t),
v30(f,t)=R.sub.30.Math.i(f,t)(24),
where R.sub.30 is a resistance of the sense resistor. The sense voltage v30(f,t) is processed in the same way as the battery voltage v(f,t). That is, a further sense amplifier 24.sub.2 receives the sense voltage v30(f,t) and provides a further measurement signal m2(f,t). A third modulator 2512 modulates the further measurement signal m2(f,t) with the third alternating signal s1(t) and a fourth modulator 25.sub.Q2 modulates the further measurement signal m2(f,t) with the second alternating signal s2(t). An output signal s25.sub.I2(f,t) of the third modulator 2512 is filtered by a third low pass filter 26.sub.I2, and an output signal s25.sub.Q2(f,t) of the fourth modulator 25.sub.Q2 is filtered by a fourth low pass filter 26.sub.Q2. Based on what is explained in context with equations (17a) and (17b) above it can be shown that the output signals (output values) of the first to fourth low pass filters 26.sub.I, 26.sub.Q, 26.sub.I2, 26.sub.Q2 are as follows:

(57) $\begin{array}{cc}{V}_I=\frac{A_0.Math.Z_0.Math.I_0}{2}\cos \left({}_0+\right)& \left(25a\right)\\ V_Q=\frac{A_0.Math.Z_0.Math.I_0}{2}\sin \left({}_0+\right)& \left(25b\right)\\ V_{I2}=\frac{A_{02}.Math.R_{30}.Math.I_0}{2}\cos \left({}_{02}\right)& \left(25c\right)\\ V_{Q2}=\frac{A_{02}.Math.R_{30}.Math.I_0}{2}\sin \left({}_{02}\right)& \left(25d\right)\end{array}$
According to one example, the sense amplifiers 24, 24.sub.2 are sense amplifiers of the same type with the same complex gain, so that A.sub.02=A.sub.0 and .sub.0=.sub.02. In this case, A.sub.0 and .sub.0 can be calculated by the control and calculation circuit 27 based on V.sub.I2 and V.sub.Q2 as follows:

(58) $\begin{array}{cc}{A}_0=A_{02}=2.Math.\frac{\sqrt{{\left(V_{I2}\right)}^2+{\left(V_{Q2}\right)}^2}}{R_{30}.Math.I_0}& \left(23a\right)\\ {}_0={}_{02}=\arctan \left(\frac{V_{Q2}}{V_{I2}}\right).& \left(23b\right)\end{array}$
Thus, in this example, a calibration routine is not required but A.sub.0 and .sub.0 are calculated by the control and calculation circuit 27 during the temperature measurement operation of the temperature detection circuit 27. Further, control and calculation circuit 27 calculates the imaginary part of the battery impedance Z(f) at each of the at least two frequencies based on equations (20a), (20b), and (21).

(59) Referring to FIG. 10, the battery 1 explained before may be part of a battery arrangement with a plurality of batteries 1, 1.sub.I, 1.sub.II connected in series. A temperature detection circuit 2, 2.sub.I, 2.sub.II may be connected to each of these batteries, wherein each of these temperature detection circuits 2, 2.sub.I, 2.sub.II is configured to detect the temperature of the battery 1, 1.sub.I, 1.sub.II it is connected to.

(60) FIG. 11 shows a modification of the arrangement shown in FIG. 10. In the arrangement shown in FIG. 11 there is only one temperature detection circuit 2 and a multiplexer 3. The multiplexer 3 is connected between the battery arrangement with the plurality of batteries 1, 1.sub.I, 1.sub.II and the temperature detection circuit 2. This multiplexer 3 is configured, at each time, to connect the temperature detection circuit with one of the several batteries 1, 1.sub.I, 1.sub.II and, in a timely successive fashion, connect the individual batteries 1, 1.sub.I, 1.sub.II of the arrangement to the temperature detection circuit 2. By this, the temperature detection circuit 2 in a timely successive fashion detects the temperatures of the individual batteries 1, 1.sub.I, 1.sub.II of the battery arrangement.

(61) FIG. 12 shows a battery arrangement with a plurality of batteries 1.sub.I, 1, 1.sub.II connected in series and a temperature detection circuit 2 according to another example. The temperature detection circuit shown in FIG. 12 is configured to drive one input current i(f,t) at at least two different frequencies f.sub.1, f.sub.2 into the battery series circuit, measure the voltage v.sub.I(f,t), v(f,t), v.sub.II(f,t) across each battery 1.sub.I, 1, 1.sub.II, and detect a temperature of each battery v.sub.I(f,t), v(f,t), v.sub.II(f,t) based on the measured voltage v.sub.I(f,t), v(f,t), v.sub.II(f,t) in accordance with any of the methods explained before.

(62) The following examples may illustrate one or more aspects of the disclosure.

Example 1

(63) A method, including: driving an alternating input current with a first frequency into a battery and detecting an imaginary part of a battery impedance at the first frequency; driving an alternating current with a second frequency different from the first frequency into the battery and detecting an imaginary part of the battery impedance at the second frequency; and calculating an intercept frequency at which the imaginary part equals a predefined value at least based on the imaginary part obtained at the first frequency and the imaginary part obtained at the second frequency.

Example 2

(64) The method of example 1, wherein the predefined value is zero.

Example 3

(65) The method of example 1 or 2, wherein the predefined value is different from zero.

Example 4

(66) The method of any combination of examples 1 to 3, further including: obtaining temperature information from a look-up table that includes a plurality of frequency-temperature information pairs.

Example 5

(67) The method of any combination of examples 1 to 4, wherein calculating the intercept frequency includes: calculating a straight line based on the imaginary part obtained at the first frequency and the imaginary part obtained at the second frequency; and calculating the frequency at which the calculated straight line intercepts the predefined value.

Example 6

(68) The method of any combination of examples 1 to 5, wherein detecting the imaginary part at each of the first and second frequencies includes: measuring a voltage across the battery to obtain a measurement signal; demodulating the measurement signal to obtain a demodulated measurement signal; and low pass filtering the demodulated measurement signal.

Example 7

(69) The method of example 6, wherein detecting the imaginary part at each of the first and second frequencies further includes: measuring the alternating input current to obtain a further measurement signal; detecting a phase shift based on the further measurement signal; and detecting the imaginary part based on the measured voltage and the detected phase shift.

Example 8

(70) The method of example 6 or 7, further including performing a calibration routine before detecting the imaginary part at each of the first and second frequencies, wherein the calibration routine includes detecting a phase shift, and

(71) wherein detecting the imaginary part comprises detecting the imaginary part based on the measured voltage and the detected phase shift.

Example 9

(72) The method of any combination of examples 6 to 8, wherein demodulating the measurement signal comprises multiplying the measurement signal with a sinusoidal signal.

Example 10

(73) The method of example 9, wherein a phase shift between the alternating input current and the sinusoidal signal is 90.

Example 11

(74) The method of any combination of examples 6 to 10, wherein demodulating the measurement signal includes: multiplying the measurement signal with a first sinusoidal signal; and multiplying the measurement signal with a second sinusoidal signal, wherein a phase shift between the first sinusoidal signal and the second sinusoidal signal is 90.

Example 12

(75) The method of any combination of examples 1 to 11, further including: driving, at least once, an alternating current with a further frequency different from the first frequency and the second frequency into the battery and detecting an imaginary part of the battery impedance at the further frequency, so as to obtain an imaginary part at at least one further frequency; and calculating the intercept frequency additionally based on the imaginary part obtained at the at least one further frequency.

Example 13

(76) The method of example 12, wherein calculating the intercept frequency includes calculating a linear function based on a least square method.

Example 14

(77) The method of example 12, wherein calculating the intercept frequency includes calculating a non-linear function.

Example 15

(78) The method of any combination of examples 1 to 14, wherein the battery includes at least one battery cell.

Example 16

(79) The method of example 15, wherein the battery includes two or more battery cells connected in series.

Example 17

(80) The method of example 15, wherein the battery includes two or more battery cells connected in parallel.

Example 18

(81) The method of any combination of examples 1 to 17, wherein at least one additional battery is connected in series with the battery.

Example 19

(82) A temperature detection circuit configured to drive an alternating current with a first frequency into a battery and detect an imaginary part of a battery impedance at the first frequency; drive an alternating current with a second frequency different from the first frequency into the battery and detect an imaginary part of the battery impedance at the second frequency; and calculate an intercept frequency at which the imaginary part equals a predefined value at least based on the imaginary part obtained at the first frequency and the imaginary part obtained at the second frequency.

Example 20

(83) The temperature detection circuit of example 19, wherein the predefined value is zero.

Example 21

(84) The temperature detection circuit of example 19, wherein the predefined value is different from zero.

Example 22

(85) The temperature detection circuit of any combination of examples 19 to 21, wherein the temperature detection circuit is further configured to obtain temperature information from a look-up table that includes a plurality of frequency-temperature information pairs.

Example 23

(86) The temperature detection circuit of any combination of examples 19 to 22, wherein the temperature detection circuit is configured to calculate the intercept frequency using the steps of calculating a straight line based on the imaginary part obtained at the first frequency and the imaginary part obtained at the second frequency; and calculating the frequency at which the calculated straight line intercepts the predefined value.

Example 24

(87) The temperature detection circuit of any combination of examples 19 to 23, wherein the temperature detection circuit is configured to detect the imaginary part at each of the first and second frequencies using the steps of measuring a voltage across the battery to obtain a measurement signal; demodulating the measurement signal to obtain a demodulated measurement signal; and low pass filtering the demodulated measurement signal.

Example 25

(88) The temperature detection circuit of example 24, wherein the temperature detection circuit is configured to detect the imaginary part at each of the first and second frequencies further using the steps of measuring the alternating input current to obtain a further measurement signal; detecting a phase based on the further measurement signal; and detecting the imaginary part based on the measured voltage and the detected phase shift.

Example 26

(89) The temperature detection circuit of example 24 or 25, wherein the temperature detection circuit is further configured to perform a calibration routine before detecting the imaginary part at each of the first and second frequencies, wherein the calibration routine includes detecting a phase, and wherein detecting the imaginary part includes detecting the imaginary part based on the measured voltage and the detected phase shift.

Example 27

(90) The temperature detection circuit of any combination of examples 19 to 26, wherein demodulating the measurement signal includes multiplying the measurement signal with a sinusoidal signal.

Example 28

(91) The temperature detection circuit of example 27, wherein a phase shift between the alternating input current and the sinusoidal signal is 90.

Example 29

(92) The method of any combination of examples 19 to 28, wherein demodulating the measurement signal includes: multiplying the measurement signal with a first sinusoidal signal; and multiplying the measurement signal with a second sinusoidal signal, wherein a phase shift between the first sinusoidal signal and the second sinusoidal signal is 90.

Example 30

(93) The temperature detection circuit of any combination of examples 19 to 29, wherein the temperature detection circuit is further configured to drive, at least once, an alternating current with a further frequency different from the first frequency and the second frequency into the battery and detecting an imaginary part of the battery impedance at the further frequency, so as to obtain an imaginary part at at least one further frequency; and calculate the intercept frequency additionally based on the imaginary part obtained at the at least one further frequency.

Example 31

(94) The temperature detection circuit of example 30, wherein calculating the intercept frequency includes calculating a linear function based on a least square method.

Example 32

(95) The temperature detection circuit of example 30, wherein calculating the intercept frequency includes calculating a non-linear function.

(96) Although various exemplary embodiments of the invention have been disclosed, it will be apparent to those skilled in the art that various changes and modifications can be made which will achieve some of the advantages of the invention without departing from the spirit and scope of the invention. It will be obvious to those reasonably skilled in the art that other components performing the same functions may be suitably substituted. It should be mentioned that features explained with reference to a specific figure may be combined with features of other figures, even in those cases in which this has not explicitly been mentioned. Further, the methods of the invention may be achieved in either all software implementations, using the appropriate processor instructions, or in hybrid implementations that utilize a combination of hardware logic and software logic to achieve the same results. Such modifications to the inventive concept are intended to be covered by the appended claims.

(97) Spatially relative terms such as under, below, lower, over, upper and the like, are used for ease of description to explain the positioning of one element relative to a second element. These terms are intended to encompass different orientations of the device in addition to different orientations than those depicted in the figures. Further, terms such as first, second and the like, are also used to describe various elements, regions, sections, etc. and are also not intended to be limiting. Like terms refer to like elements throughout the description.

(98) As used herein, the terms having, containing, including, comprising and the like are open ended terms that indicate the presence of stated elements or features, but do not preclude additional elements or features. The articles a, an and the are intended to include the plural as well as the singular, unless the context clearly indicates otherwise.

(99) With the above range of variations and applications in mind, it should be understood that the present invention is not limited by the foregoing description, nor is it limited by the accompanying drawings. Instead, the present invention is limited only by the following claims and their legal equivalents.