WO2006061703A1

WO2006061703A1 - Method and apparatus for determining the resonant frequency of surface acoustic wave resonators

Info

Publication number: WO2006061703A1
Application number: PCT/IB2005/003713
Authority: WO
Inventors: Marc Lambrechts
Original assignee: Melexis Nv
Priority date: 2004-12-08
Filing date: 2005-12-08
Publication date: 2006-06-15
Also published as: GB0426915D0

Abstract

A torque sensing system for a shaft (not shown) comprises a sensor means (100), coupling means (105), interface means (110), and signal processing means (130). The sensor means (100) comprises a pair of SAW resonators (101, 102) mounted orthogonally to one another on said shaft connected to said interface means (110) and said signal processing means (130) via said coupling means (105). Interface means (110) also drives SAW resonators (101, 102) with an impulse RF signal (200) and detects output signals from each SAW resonator generated in response to said impulse signal (200). In order to determine the resonant frequency of each SAW resonator (101, 102) and hence the torque applied to the shaft, the out put signal from each SAW resonator (101, 102) is mixed with a first RF signal at a first frequency to produce an intermediate frequency (IF) signal. Said IF signal is then mixed with a second RF signal at a second frequency to provide a first interface signal and mixed with a third RF signal, said third RF signal having the same frequency as said second RF signal but having a known phase difference to said second RF signal, to produce a second interface signal. The interface signals are then used to determine the real and imaginary components of a first vector from said first and second interface signals and after a predetermined time determine the real and imaginary components of a second vector from said first and second interface signals. The phase angle between the real and imaginary components of said first and second vectors is compared with a calculated phase angle difference for a known reference frequency to determine the resonant frequency of said SAW resonator.

Description

Method and Apparatus for Determining the Resonant Frequency of Surface Acoustic

Wave Resonators

The invention relates to determining the resonant frequency of Surface Acoustic Wave (SAW) resonators.

SAW resonators may be used in the measurement of many physical or chemical properties including pressure, temperature, tensile strain or compressive strain, one particular application being to measure the torque transmitted by a rotating shaft. Torque measurement is of particular importance in an internal combustion engine as in order to manage the operation of an internal combustion engine in an effective and environmentally efficient manner, the engine management unit requires accurate information from sensors mounted on the drive shaft providing information relating to torque transmitted by the drive shaft.

In such applications, a pair of SAW resonators are mounted on a shaft such that when the shaft is rotated and transmitting torque one of the said SAW resonators is under tensile strain and the other SAW resonator is under compressive strain. As SAW resonators exhibit variation in their resonant frequency dependent on applied strain, by measuring the variation in the resonant frequency of each SAW resonator the strain applied to each SAW resonator can be determined and hence the torque transmitted by the shaft can be calculated. A torque sensor of this type is disclosed in US 5,585,571.

Conventionally, the determination of the resonant frequency involves driving the SAW resonator at a frequency close to its relaxed natural frequency, converting the SAW response signal to low frequency signals with RF receiver circuitry (low frequency signal is also called"down-converted signal), sampling the resultant outputs or down-converted signals from the RF receiver and then calculating the actual frequency of the output signals. In order to avoid aliasing problems when determining the frequency of the output signals, the output signals must be sampled for a minimum time period with a sampling rate of at least double the frequency of resonation. The frequency of the sampled signals are compared with a series of ideal signals calculated for a range of frequencies around the expected figure to determine the 'best fit and thereby determine the actual SAW resonant frequency. Such a method imposes heavy demands on the circuitry used for determining the resonant frequency. In particular, even with the use of a relatively expensive high speed, high accuracy analogue to digital converter and a relatively expensive high-speed digital signal processor, the speed and accuracy of the frequency determination can be limited.

It is therefore an object of the present invention to provide means for measuring the resonant frequency of an SAW resonator that overcomes or alleviates the above problem.

According to a first aspect of the present invention there is provided a method suitable for determining the resonant frequency of an SAW resonator comprising the following steps: driving the SAW resonator with an impulse RF signal; detecting the resultant output signal of the SAW resonator; mixing said output signal with a first RF

signal at a first frequency to produce an intermediate frequency (IF) signal; mixing said IF signal with a second RF signal at a second frequency to provide a first interface signal; mixing said IF signal with a third RF signal, said third RF signal having the same frequency as said second RF signal but having a known phase difference to said second RF signal, to produce a second interface signal; determining the components of a first vector from said first and second interface signals; waiting a predetermined time interval and then determining the components of a second vector from said first and second interface signals; and comparing the phase angle between said first and second vectors with a calculated phase angle difference over the predetermined time interval for a known reference frequency to thereby determine the resonant frequency of said SAW resonator.

This method thus provides a method of determining the resonant frequency of an SAW resonator that requires less sampling of the output of the SAW resonator to determine its resonant frequency than known methods. This thereby allows more accurate results to be produced using slower and less costly analogue to digital conversion equipment and using slower and less costly digital processing circuitry (such as a microcontroller) than is required by known methods.

Preferably the first and second vectors are complex vectors, calculated by using the first interface signal to provide the real component of said vector and the second interface signal to provide the imaginary component of said vector. This thus allows the complex phase angle of said vector to be calculated. The real and imaginary components of said first and second vectors may be determined from the interface signals by: generating a pair of differential signals from each interface signal; then using a differential amplifier to determine the difference between said pair of differential signals, thus outputting a component signal; and then sampling said component signals. Generating a pair of differential signals in this manner reduces analogue noise.

In one embodiment, the method initially determines the frequency difference between the first and second interface signals and the reference frequency by comparing the recorded phase angle between the first and second vectors with a calculated phase angle difference for a reference frequency. By subsequently adding or subtracting this frequency difference from the sum of first RF signal frequency, the second RF signal frequency and the reference frequency, the actual resonant frequency of the SAW resonator is determined. The calculated phase angle difference varies with variations in frequency of the first, second and third RF signals, and the reference signal.

hi some embodiments, phase angle differences for a plurality of different reference frequencies may be stored in a look up table. The resonant frequency of the SAW resonator may thus be calculated by selecting the closest stored phase angle difference to the measured phase angle difference for use as a reference frequency.

Preferably, the impulse signal is a high frequency RF signal used to drive the

SAW resonator for a limited period. Preferably, this period is around 3-1 Oμs. In some embodiments, a series of said impulse signals may be applied consecutively.

The impulse signal may be amplified to increase its driving effect. The output signal may be buffered before being mixed with said first RF signal.

Preferably the impulse signal has a frequency that is close to the expected value of the resonant frequency. Preferably, the sum of said first frequency, the second frequency and the reference frequency is close to the expected value of the resonant frequency. The frequency of third RF signal is preferably the same as the frequency of second RF signal, and preferably has phase shift of 90 degrees relative to the second signal. This is so the total expected phase change between the first and second vectors over time, minus the phase change of the reference signal, is minimised thereby allowing greater accuracy of measurement. In one preferred embodiment, the frequency of the first RF signal is HMHz lower than the frequency of the impulse signals, the frequency of the second and third signals is 10 MHz, and the frequency of the reference signal is 1 MHz.

Preferably, the sampling to provide the first vector takes place shortly

(typically l-3μs) after the cessation of the impulse signal. This is to allow transients in the RF circuitry to subside before sampling. Preferably, the time interval between sampling the first and second interface signals to determine the components of the first vector and sampling the first and second interface signals to determine the components of the second vector is chosen so that the maximum expected variation in resonant frequency of the SAW resonator will not introduce the possibility of false results due to aliasing. The method may include the further steps of sampling the said interface signals on one or more additional occasions, each separated by said predetermined time interval, so that a composite estimate of the phase angle between said first and second vectors can be calculated. The composite estimate may be calculated by either using the plurality of samples to provide average values for said first and second vectors and thus allow the measurement of a phase angle between said average vectors or may be calculated by providing independently a plurality of pairs of first and second vectors, measuring the phase angle between each pair of vectors and taking the average of the plurality of phase angles. A further alternative is that the components of a plurality of vectors or a plurality of pairs of vectors resulting from samples at different times may be used to calculate a plurality of phase angles and least mean squares fitting may then be used to determine a best estimate of the phase angle. The best estimate may be calculated by performing a least mean squares calculation. The method may also include the further steps of sampling the interface signals at the end of the decay, when the signal strength (vector amplitude) is very low compared with the initial strength. Such sampled values can be used to correct the earlier sampled vectors in case a DC offset (possibly caused by the RF circuitry) is present in the signal outputs.

hi some embodiments, the measurement of the resonant frequency may take place periodically.

The method may be used to determine the change in resonant frequency of SAW resonators used in devices for sensing pressure, temperature, tensile strain or compressive strain, torque or any other suitable physical property.

For greater dynamic range, a variable reference frequency may be selected, where the new reference frequency is the sum of the old reference frequency and the last calculated difference frequency. This method of relative tracking of SAW frequency reduces the possibility of false phase difference results.

In another, simplified embodiment the mixing of the output signal with the said first RF signal is omitted, thereby not using an intermediate frequency (IF). The output SAW signal is thus directly mixed with the said second RF signal and the said third RF signal by the RF circuitry. Preferably the frequency of said second RF signal and said third RF signal is close to the expected resonant SAW frequency. Preferably the frequency of the said second RF signal is the same as the frequency of the RF impulse signal, and hence the frequency of the said third RF signal is the same as the frequency of the said second RF signal, but the phase of the said third RF signal is 90 degrees shifted with respect to the phase of the said second RF signal.

In another embodiment, the calculation of the sensor output (e.g. torque output) is based not on the determined SAW frequency value, but on the initial phase difference value between the two vector samples; or on the further phase difference value between the two vector samples when taking into account the phase difference from the reference frequency; or on the frequency difference calculated from the phase angle difference.

In all of the above embodiments wherein a plurality of samples are taken, the method may include the additional step of monitoring the amplitude as well as the phase angle of the vector samples to detect the presence of a ripple in the monitored amplitudes. Such a ripple may be caused by parasitic intermodulations or distortions potentially caused by beats frequencies, the sampling process, the driving process or other processes. Preferably, only vector samples from the maxima or minima of the ripple are selected for use in calculating the phase angle as these vector samples will have a minimal phase distortion due to the parasitic intermodulations. According to a second aspect of the present invention there is provided an apparatus suitable for carrying out the method of the first aspect of the present invention comprising: signal generating means for generating an impulse RF signal for driving an SAW resonator, a first RF signal of a first frequency for input to a first mixing means; a second RF signal, a second RF signal of a second frequency for input to a second mixing means and a third RF signal of said second frequency but having a known phase difference to said second RF signal; signal detecting means, for detecting an output signal from said SAW resonator in response to said impulse RF signal; signal mixing means for mixing said first RF signal with said output signal to produce an intermediate frequency (IF) signal, said second RF signal with said IF signal to provide a first interface signal, said third RF signal with said IF signal to provide a second interface signal; and means, for determining the components of a vector from said first and second interface signals, operable to determine a the components of a first vector and after a predetermined time interval to determine the components of a second vector and for comparing the phase difference between said first and second vectors with a calculated phase difference for a reference frequency during the same predetermined time interval and thereby determining the resonant frequency of the SAW resonator.

The apparatus according to the second aspect of the present invention may incorporate any or all features of the first embodiment of the present invention as desired or as appropriate.

Preferably the signal mixing means comprises first, second and third signal mixing means: the first signal mixing means for mixing said first RF signal with said output signal to produce said intermediate frequency (IF) signal; the second signal mixing means for mixing said second RF signal with said IF signal to provide said first interface signal; and said third signal mixing means for mixing said third RF signal with said IF signal to provide said second interface signal.

The signal generating means may be a single signal generating means or may be two or more signal generating means each operable to generate at least one of the impulse signal, the first RF signal, the second RF signal or the third RF signal. In a preferred embodiment, there are two signal generating means, a first signal generating means for generating said impulse signal and said first RF signal and a second signal generating means for generating said second and third RF signals. Most preferably, said first signal generating means and said second signal generating means are connected to a single oscillator input with a very stable frequency.

Preferably, a control means is provided operable to control the operation of any one of or all of the first, second and third mixing means and the first and second signal generating means.

Preferably, an amplifier is provided for amplifying said impulse signal before driving said SAW resonator. Preferably, a buffering amplifier is provided before said output signal is input to said first mixing means.

Preferably, the first, second and third mixing means and the first and second signal generating means, the control means, the amplifier and the buffering amplifier are provided in a single interface means. The interface means may comprise a single

integrated circuit. The processing means may also comprise a single integrated circuit and is preferably a digital processing means and most preferably a digital microprocessor.

If the apparatus is used to determine the resonant frequency of more than one SAW resonator the interface means is adapted to generate first and second interface signals from the output signals of each SAW resonator independently. This is preferably achieved by providing independent first, second and third mixing means for each output signal. Preferably, said processing means is also adapted to process the interface signals generated from each output signal independently.

Preferably said apparatus can be used to measure the change in resonant frequency of an SAW resonator in an apparatus for sensing pressure, temperature, tensile strain or compressive strain, torque or any other suitable physical property.

The apparatus may be used in a torque sensing means of the kind comprising a pair of SAW resonators mounted on a shaft, said resonators being connected to interface and processing circuitry by way of a coupling means. In such embodiments, preferably the interface and processing circuitry comprises an interface means and a processing means according to the invention. Most preferably, the interface means is adapted to generate first and second interface signals from the output signals of each SAW resonator independently and said processing means is also adapted to process the interface signals generated from each output signal independently. Additionally, said processing means is preferably further adapted to determine the torque

transmitted by said shaft from the determined resonant frequencies of each SAW resonator. In order that it may be more clearly understood the invention will be described further herein below, by way of example only, and with reference to the following drawings, in which:

Figure 1 shows a block diagram of a typical torque sensing means incorporating an SAW resonator;

Figure 2 shows a schematic diagram of an apparatus according to the present invention suitable for determining the resonant frequency of an SAW resonator;

Figure 3 shows typical first and second interface signals generated when performing the method of the present invention; and

Figure 4 shows first and second vectors calculated from sampling said first and second interface signals plotted on a phase diagram along with a calculated vector for a reference frequency.

Referring now to figure 1, a torque sensing system for a shaft (not shown) comprises a sensor means 100, coupling means 105, interface means 110, and signal processing means 130. The sensor means 100 comprises a pair of SAW resonators

101, 102 mounted orthogonally to one another and at 45 degrees to the axis of said shaft. Electrical connections are provided between each SAW resonator 101, 102 and a first antenna or coil 103 forming part of the coupling means 105 and being mounted on the shaft along with said SAW resonators 101, 102. A second antenna or coil 104 forming part of the coupling means 105 is mounted coaxially with said shaft and adjacent to said first antenna or coil 103. The second antenna or coil 103 is electrically connected to said interface means 110. RF coupling between said first and second antennas or coils 103, 104 allows signals to be passed between said SAW resonators 101, 102 and said interface means 110.

Interface means 110 drives SAW resonators 101, 102 with an impulse RF signal 200 and detects output signals from each SAW resonator generated in response to said impulse signal 200. The interface means 110 is also operative to generate interface signals from said output signals, the interface signals then being passed to the processing means.

Referring now to figures 2 and 3, said interface means 110 incorporates a control means 112, a signal generator means 113 and an amplifier 111, for the generation of said impulse signal 200. The signal generator 113 is operable to generate and output an RF signal of a first frequency. The output of the signal generator 113 is fed to the amplifier 111, and in turn the output of the amplifier is fed to the SAW resonators via said coupling means 105. The control means 112 is operable to control the output of an RF signal by the signal generator 113 and to control the gain of said amplifier 111.

The impulse signal drives the SAW resonators for a preset time interval. After the impulse signal has ended, the SAW resonators 101, 102 continue to oscillate with decaying amplitude for a plurality of cycles. Typically, to avoid cross coupling only one SAW resonator will be significantly excited and will continue to oscillate for say

10,000 or more cycles whilst the other SAW resonator does not oscillate significantly. The outputs of the SAW resonators are passed via coupling means 105 to the interface means 110. The coupling is typically provided by coaxial coupling but may alternatively be carried out by and other form of RF coupling.

When the coupled output signal reaches the interface means it is input to a buffer amplifier 116 provided as part of the interface means 110.

The coupled SAW output is mixed with a first RF signal of a first frequency in a first signal mixing means 117 to produce an intermediate frequency (IF) signal. The first RF signal is also generated and output by signal generator 113.

The IF signal output from first signal mixing means 117 is split by splitting means 118 and input to second signal mixing means 119 and third signal mixing means 120. An oscillator means 121 is provides the signals for mixing with the output of the splitting means 118. The oscillator means 121 generates and outputs a pair of signals in quadrature. The pair of signal are a second RF signal at a second frequency, input to said second signal mixing means 119; and a third RF signal at said second frequency but having a 90° phase difference from said second RF signal, input to said third signal mixing means 120. Oscillator means 121 is connected to and used as a frequency input for signal generator 113.

The resultant output of said second signal mixing means 119 is a first interface signal 124. The resultant output of said third signal mixing means 120 is a second interface signal 127. A first pair of differential signals I+, I- is generated from the first interface signal 124 by amplifier 123. A second pair of differential signals Q+,

Q- is generated from the second interface signal 127 by amplifier 126. Generating differential signals in this manner reduces analogue noise. Band pass filters 122, 125 are provided to filter out noise from signals input to the amplifiers 123, 126. The filters 122, 125 are typically set to filter out noise and parasitic signals at high frequency, and offset noise at low frequency. Typically for a 1 MHz signal input to the amplifiers 123, 126, the lower limit would be around 100 kHz and the upper limit would be around 4 MHz. If the signal is of very low frequency, the band pass filters 122, 125 can be replaced with low pass filters.

Each pair of differential signals I+, I- and Q+, Q- is passed to a dedicated differential amplifier arrangement 128, 129. The differential amplifiers 128, 129 are operable to determine the difference between the pairs of differential signals I+, I- and Q+, Q- and to thereby output vector component signals 201, 202. In the embodiment shown in figure 2, the differential amplifiers 128, 129 are provided on a dedicated integrated circuit positioned between the interface means 110 and the processing means 130. It is of course possible for said differential amplifiers to be incorporated into either the interface means 110 or the processing means 130 if desired or appropriate.

Processing means 130 is provided with an analogue to digital converter (not shown) operable to sample the vector component signals 201 and 202 at a first time

203 in the time period shortly (typically l-3μs) after the cessation of the impulse signal 200. The sampled values 211, 212 of the vector component signals provide the real (I) and imaginary (Q) components of a first vector 301. After a predetermined time interval, at a time 204, the processing means 130 is again operable to sample the first and second vector component signals 124, 127. The sampled values 213, 214 of the vector component signals provide the real (I) and imaginary (Q) components of a first vector 301.

After the sampling is complete, the processing means is operable to calculate a third vector 303. The third vector 303 corresponds to the expected vector, using the first vector as start position and rotating this first vector over a phase difference, generated by a known reference frequency over the same time interval.

By way of example, where: RFl = frequency of the first RF signal; RF2 = frequency of the second and third RF signals; RF_REF = Reference frequency; RF_SAW = actual SAW frequency, to be measured; RF_IMPULSE = frequency of impulse RF; RF_DIFF = calculated frequency difference; PBMDIFF = calculated phase difference (in radians); and PHJTIME = predetermined time interval, the formula for calculating RF_SAW is:

RF_SAW = RFl + RF2 + RF_REF + RF_DIFF and the formula for calculating RF_DIFF is: RF_DIFF = PFHDIFF / PH_TIME*2π

In one example: RFl = 423MHz; RF2 = 10MHz; RF_REF = IMHz; and the phase difference is measured as 0.628 radians in lOμs. In such an example, RF_DIFF = 0.01 MHz (0.628/10*6.28) and thus RF_SAW = 434.01 MHz.

Turning now to figure 4, each of the vectors 301, 302, and 303 are shown plotted on a phase diagram. The difference 304 in the phase angle between said first vector 301 and said second vector 302 compared with the phase angle between said first vector 301 and said third vector 303 enables processing means 130 to determine the actual frequency of the SAW resonator. For greater accuracy, more samples may be taken, each at regular intervals, and averaged values used to provide the first and second vectors 301 , 302.

It is also possible to calculate the sensor output (e.g. torque output) is based not on the determined SAW frequency value, but: on the initial phase difference value between the two vector samples, the phase angle difference labelled 305 in figure 4; or on the further phase difference value between the two vector samples when taking into account the phase difference from the reference frequency. In such cases, the phase angle difference 304 (PH_DIFF) is calculated by subtracting phase difference 306 (the calculated phase angle difference for the reference frequency 303 during the predetermined time interval, using the first vector 301 as start position) from the phase angle difference 305 (phase angle difference between the two vectors 301, 302). As a further alternative, the sensor output can be calculated from the frequency difference calculated from the phase angle difference 304, using the above formula.

In either of the above techniques, it is possible for a plurality of samples to be taken to determine a plurality of phase angles and phase differences. This plurality of phase angles or phase differences can be used to determine a best estimate phase angle or phase difference by any suitable technique such as averaging or least mean squares fitting. In some embodiments only selected samples from the plurality of samples are used. These samples are typically selected on the basis of monitoring of the amplitude of the vectors to detect any 'ripple' variation over time and selecting for further analysis only those vectors for resulting from sampling at the maxima or minima of the 'ripples'.

It is of course to be understood that the invention is not to be limited to the details of the above embodiment which is described by way of example only.

Claims

1. A method suitable for determining the resonant frequency of an SAW resonator comprising the following steps: driving the SAW resonator with an impulse RF signal; detecting the resultant output signal of the SAW resonator; mixing said output signal with a first RF signal at a first frequency to produce an intermediate frequency (IF) signal; mixing said IF signal with a second RF signal at a second frequency to provide a first interface signal; mixing said IF signal with a third RF signal, said third RF signal having the same frequency as said second RF signal but having a known phase difference to said second RF signal, to produce a second interface signal; determining the components of a first vector from said first and second interface signals; waiting a predetermined time interval and then determining the components of a second vector from said first and second interface signals; and comparing the phase angle between said first and second vectors with a calculated phase angle difference over the predetermined time interval for a known reference frequency to thereby determine the resonant frequency of said SAW resonator.

2. A method as claimed in claim 1 wherein the first and second vectors are complex vectors, calculated by using the first interface signal to provide the real component of said vector and the second interface signal to provide the imaginary component of said vector.

3. A method as claimed in claim 2 wherein the real and imaginary components of said vectors may be determined from the first and second interface signals by: generating a pair of differential signals from each interface signal; then using a differential amplifier to determine the difference between said pair of differential signals, thus outputting a component signal; and then sampling said component signals.

4. A method as claimed in any preceding claim wherein the method determines the frequency difference between the first and second interface signals and the reference frequency by comparing the recorded phase angle between the first and second vectors with a calculated phase angle difference for a reference frequency.

5. A method as claimed in claim 4 wherein by subsequently adding or subtracting this frequency difference from the sum of first RF signal frequency, the second RF signal frequency and the reference frequency, the actual resonant frequency of the SAW resonator is determined.

6. A method as claimed in any preceding claim wherein phase angle differences for a plurality of different reference frequencies are stored in a look up table.

7. A method as claimed in claim 6 wherein the resonant frequency of the SAW resonator is calculated by selecting the closest stored phase angle difference to the measured phase angle difference for use as a reference frequency.

8. A method as claimed in any preceding claim wherein the impulse signal is a high frequency RF signal used to drive the SAW resonator for a period of around 3-1 Oμs.

9. A method as claimed in any preceding claim wherein a series of said impulse signals are applied consecutively.

10. A method as claimed in any preceding claim wherein the impulse signal is amplified to increase its driving effect.

11. A method as claimed in any preceding claim wherein the output signal is buffered before being mixed with said first RF signal.

12. A method as claimed in any preceding claim 1 wherein the impulse signal has a frequency that is close to the expected value of the resonant frequency.

13. A method as claimed in any preceding claim wherein the sum of said first frequency, the second frequency and the reference frequency is close to the expected value of the resonant frequency.

14. A method as claimed in any preceding claim wherein the frequency of third RF signal is the same as the frequency of second RF signal, and has a phase shift of 90 degrees relative to the second RF signal.

15. A method as claimed in any preceding claim wherein the sampling to determine the components of the first vector takes place l-3μs after the cessation of the impulse signal.

16. A method as claimed in claim 15 wherein the time interval between sampling the first and second interface signals to determine the components of the first vector and sampling the first and second interface signals to determine the components of the second vector is chosen so that the maximum expected variation in resonant frequency of the SAW resonator will not introduce the possibility of false results due to aliasing.

17. A method as claimed in claim 16 wherein the method may include the further steps of sampling the said interface signals on one or more additional occasions, each separated by said predetermined time interval, so that a composite estimate of the phase angle between said first and second vectors can be calculated.

18. A method as claimed in claim 17 wherein the composite estimate is calculated by using the plurality of samples to provide average values for said first and second vectors and thus allow the measurement of a phase angle between said average vectors.

19. A method as claimed in claim 17 wherein the composite estimate is calculated by providing independently a plurality of pairs of first and second vectors, measuring the phase angle between each pair of vectors and taking the average of the plurality of phase angles.

20. A method as claimed in claim 17 wherein the composite estimate is calculated by using the plurality of samples to provide a plurality of vectors and using least mean squares fitting to determine the phase angle.

21. A method as claimed in any preceding claim wherein the method may also include the further steps of sampling the interface signals at the end of the decay, when the signal strength (vector amplitude) is very low compared with the initial strength.

22. A method as claimed in any preceding claim wherein the measurement of the resonant frequency may take place periodically.

23. A method as claimed in any preceding claim wherein a variable reference frequency may be selected, where the new reference frequency is the sum of the old reference frequency and the last calculated difference frequency.

24. A method as claimed in any preceding claim wherein the mixing of the output signal with the said first RF signal is omitted and the output SAW signal is then directly mixed with the said second RF signal and the said third RF signal by the RF circuitry.

25. A method as claimed in any preceding claim wherein the frequency of said second RF signal and said third RF signal is close to the expected resonant

SAW frequency.

26. A method as claimed in any preceding claim wherein the frequency of the said second RF signal is the same as the frequency of the RF impulse signal.

27. A method as claimed in any preceding claim wherein the method includes the further step of monitoring the amplitude as well as the phase angle of the vector samples to detect the presence of a ripple in the monitored amplitudes.

28. A method as claimed in claim 27 wherein only samples taken at the maxima or minima of the amplitude ripple are used for the determination of the phase difference.

29. A method as claimed in any preceding claim wherein the method is used to determine the change in resonant frequency of SAW resonators used in devices for sensing pressure, temperature, tensile strain or compressive strain, torque or any other suitable physical property.

30. An apparatus suitable for carrying out the method of any one of claims 1 to 29 comprising: signal generating means for generating an impulse RF signal for driving an SAW resonator, a first RF signal of a first frequency for input to a first mixing means; a second RF signal, a second RF signal of a second frequency for input to a second mixing means and a third RF signal of said second frequency but having a known phase difference to said second RF signal; signal detecting means, for detecting an output signal from said SAW resonator in response to said impulse RF signal; signal mixing means for

mixing said first RF signal with said output signal to produce an intermediate frequency (IF) signal, said second RF signal with said IF signal to provide a first interface signal, said third RF signal with said IF signal to provide a second interface signal; and means, for determining the components of a vector from said first and second interface signals, operable to determine a the components of a first vector and after a predetermined time interval to determine the components of a second vector and for comparing the phase difference between said first and second vectors with a calculated phase difference for a reference frequency during the same predetermined time interval and thereby determining the resonant frequency of the SAW resonator.

31. An apparatus as claimed in claim 30 wherein the signal mixing means comprises first, second and third signal mixing means: the first signal mixing means for mixing said first RF signal with said output signal to produce said intermediate frequency (IF) signal; the second signal mixing means for mixing said second RF signal with said IF signal to provide said first interface signal; and said third signal mixing means for mixing said third RF signal with said IF signal to provide said second interface signal.

32. An apparatus as claimed in claim 30 or claim 31 wherein the signal generating means is a single signal generating means.

33. An apparatus as claimed in claim 30 or claim 31 wherein the signal generating means is two or more signal generating means each operable to generate at least one of the impulse signal, the first RF signal, the second RF signal or the third RF signal.

34. An apparatus as claimed in claim 30 or claim 31 wherein there are two signal generating means, a first signal generating means for generating said impulse signal and said first RP signal and a second signal generating means for generating said second and third RF signals.

35. An apparatus as claimed in claim 34 wherein said first signal generating means and said second signal generating means are connected to a single oscillator input with a very stable frequency.

36. An apparatus as claimed in claim 35 wherein a control means is provided operable to control the operation of any one of or all of the first, second and third mixing means and the first and second signal generating means.

37. An apparatus as claimed in any one of claims 30 to 36 wherein an amplifier is provided for amplifying said impulse signal before driving said SAW resonator.

38. An apparatus as claimed in any one of claims 30 to 37 wherein a buffering amplifier is provided before said output signal is input to said first mixing means.

39. An apparatus as claimed in any one of claims 30 to 38 wherein the first, second and third mixing means and the first and second signal generating means, the control means, the amplifier and the buffering amplifier are provided in a single interface means.

40. An apparatus as claimed in any one of claims 30 to 39 wherein the interface means comprises a single integrated circuit.

41. An apparatus as claimed in any one of claims 30 to 40 wherein the processing means comprises a single integrated circuit.

42. An apparatus as claimed in claim 41 wherein the processing means is a digital processing means or a digital microprocessor.

43. An apparatus as claimed in any one of claims 30 to 42 wherein if the apparatus is used to determine the resonant frequency of more than one SAW resonator the interface means is adapted to generate first and second interface signals from the output signals of each SAW resonator independently.

44. An apparatus as claimed in claim 43 wherein this is achieved by providing independent first, second and third mixing means for each output signal.

45. An apparatus as claimed in claim 43 or claim 44 wherein said processing means is adapted to process the interface signals generated from each output signal independently.

46. An apparatus as claimed in any one of claims 30 to 45 wherein said apparatus is used to measure the change in resonant frequency of an SAW resonator in an apparatus for sensing pressure, temperature, tensile strain or compressive strain, torque or any other suitable physical property.

47. An apparatus as claimed in claim 46 wherein the apparatus is used in a torque sensing means of the kind comprising a pair of SAW resonators mounted on a shaft, said resonators being connected to interface and processing circuitry by way of a coupling means.

48. An apparatus as claimed in claim 47 wherein the interface and processing circuitry comprises an interface means and a processing means according to the invention.

49. An apparatus as claimed in claim 48 wherein the interface means is adapted to generate first and second interface signals from the output signals of each SAW resonator independently and said processing means is also adapted to process the interface signals generated from each output signal independently.

50. An apparatus as claimed in claim 48 or claim 49 wherein said processing means is adapted to determine the torque transmitted by said shaft from the determined resonant frequencies of each SAW resonator.