Classifications

• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03L—AUTOMATIC CONTROL, STARTING, SYNCHRONISATION OR STABILISATION OF GENERATORS OF ELECTRONIC OSCILLATIONS OR PULSES
  • H03L1/00—Stabilisation of generator output against variations of physical values, e.g. power supply
  • H03L1/02—Stabilisation of generator output against variations of physical values, e.g. power supply against variations of temperature only
  • H03L1/022—Stabilisation of generator output against variations of physical values, e.g. power supply against variations of temperature only by indirect stabilisation, i.e. by generating an electrical correction signal which is a function of the temperature

Definitions

• the disclosure relates to crystal oscillators and, more particularly, to techniques for estimating the frequency of crystal oscillators.
• Crystal oscillators are used in communications devices as frequency sources.
• a quartz crystal having a nominal resonant frequency is coupled to an oscillator circuit that generates a signal having a nominal output frequency.
• the crystal's resonant frequency and the circuit's output frequency may vary over time due to factors such as temperature, aging, drive level and vibration.
• An aspect of the present disclosure provides a method for computing coefficients for use in a polynomial approximation of a crystal oscillator frequency, the polynomial comprising a term c0' and a coefficient cl ' times a measured temperature T of the crystal oscillator, the method comprising measuring a first temperature Tl and a corresponding oscillator frequency Fm(Tl); measuring a second temperature T2 and a corresponding oscillator frequency Fm(T2); computing the coefficient c0' based on Fm(Tl); and computing the coefficient cl ' based on Tl, T2, Fm(Tl), and Fm(T2).
• Another aspect of the present disclosure provides a method for computing coefficients for use in a polynomial approximation of a crystal oscillator frequency, the polynomial comprising a term c0' and a coefficient cl ' times a measured temperature T of the crystal oscillator, the method comprising entering a state FIELDO, operations in the state FIELDO comprising computing the coefficient c0' if the measured temperature T is within a first range of temperatures; and entering a state FIELDl, operations in the state FIELDl comprising computing the coefficient cl ' if the measured temperature T is within a second range of temperatures.
• Yet another aspect of the present disclosure provides an apparatus for computing coefficients for use in a polynomial approximation of a crystal oscillator frequency, the polynomial comprising a term cO' and a coefficient cl ' times a measured temperature T of the crystal oscillator, the apparatus comprising a temperature measurement unit for measuring a first temperature Tl and a second temperature T2; a frequency measurement unit for measuring corresponding oscillator frequencies Fm(Tl) and Fm(T2); and a computing module for computing the coefficient cO' based on Fm(Tl), and for computing the coefficient cl ' based on Tl, T2, Fm(Tl), and Fm(T2).
• Yet another aspect of the present disclosure provides a computer program product for computing coefficients for use in a polynomial approximation of a crystal oscillator frequency, the polynomial comprising a term cO' and a coefficient cl ' times a measured temperature T of the crystal oscillator, the product comprising computer- readable medium comprising code for causing a computer to measure a first temperature Tl and a corresponding oscillator frequency Fm(Tl); code for causing a computer to measure a second temperature T2 and a corresponding oscillator frequency Fm(T2); code for causing a computer to compute the coefficient cO' based on Fm(Tl); and code for causing a computer to compute the coefficient cl ' based on Tl, T2, Fm(Tl), and Fm(T2).
• Yet another aspect of the present disclosure provides an apparatus for computing coefficients for use in a polynomial approximation of a crystal oscillator frequency, the polynomial comprising a term cO' and a coefficient cl ' times a measured temperature T of the crystal oscillator, the apparatus comprising means for entering a state FIELDO, operations in the state FIELDO comprising computing the coefficient cO' if the measured temperature T is within a first range of temperatures; and means for entering a state FIELDl, operations in the state FIELDl comprising computing the coefficient cl ' if the measured temperature T is within a second range of temperatures.
• Yet another aspect of the present disclosure provides a computer program product for computing coefficients for use in a polynomial approximation of a crystal oscillator frequency, the polynomial comprising a term cO' and a coefficient cl ' times a measured temperature T of the crystal oscillator, the product comprising computer- readable medium comprising code for causing a computer to enter a state FIELDO, operations in the state FIELDO comprising computing the coefficient cO' if the measured temperature T is within a first range of temperatures; and code for causing a computer to enter a state FIELDl, operations in the state FIELDl comprising computing the coefficient cl ' if the measured temperature T is within a second range of temperatures.
• FIG 1 shows a block diagram of a crystal 100 coupled to an oscillator circuit 110 to form a crystal oscillator.
• FIG IA plots a typical variation of a crystal's resonant frequency over temperature and crystal cutting angle.
• FIG 2 depicts steps according to the present disclosure for estimating the coefficients c0, cl, c2, c3.
• FIG 2A depicts an alternative embodiment of the present disclosure.
• FIG 2B depicts an embodiment of a technique for measuring a frequency offset
• FIG 3 A depicts a linear relationship between cl ' and c2' denoted by L 1/2.
• FIG 3B depicts a similar linear relationship between cl ' and c3' that can be used to compute an estimate of c3' from cl '.
• FIG 4 shows a state machine used to re-adjust an initially calibrated set of coefficients derived from, e.g., the procedure described in FIG 2.
• FIG 5 shows an embodiment of operations performed during state FIELDO.
• FIG 6 shows an embodiment of operations performed during state FIELDl.
• FIG 7 shows an embodiment of operations performed during state FIELD3.
• FIG 1 shows a block diagram of a crystal 100 coupled to an oscillator circuit 110 to form a crystal oscillator.
• the temperature of the crystal 100 is measured by temperature sensor 120, which generates a measured temperature T.
• the crystal oscillator generates an output signal 110a having a nominal reference frequency.
• the temperature T may be the temperature measured locally at the crystal.
• an additional temperature TQ corresponding to the oscillator circuit local temperature may be measured and provided to improve the frequency estimate, as further described hereinbelow.
• FIG IA plots a typical variation of a crystal's resonant frequency over temperature and crystal cutting angle.
• T represents the crystal temperature
• To represents a fixed reference temperature
• Fo(T, To) represents the predicted frequency shift of the signal 110a at temperature T relative to a reference frequency Foo
• To represents the oscillator temperature
• T 0 o represents a fixed oscillator reference temperature
• c0, cl, c2, c3 are coefficients characterizing the oscillator output signal 1 lOa's frequency dependence on crystal temperature
• cp is a coefficient characterizing the oscillator output signal 1 lOa's frequency dependence on oscillator temperature.
• the coefficient cp may depend on, e.g., the capacitance loading the oscillator circuit.
• the coefficient cp is derived by comparing a nominal F-T curve of the crystal provided by a crystal vendor with an F-T curve measured using a fully loaded crystal oscillator. The measurement may be done offline, e.g., in a laboratory.
• the crystal temperature may be fixed, while the oscillator temperature varied from a first temperature ToI to a second temperature To2.
• the corresponding oscillator output frequencies Fo(ToI) and Fo(To2) may be measured.
• FIG 2 depicts steps according to the present disclosure for estimating the coefficients cO, cl, c2, c3.
• the steps depicted in FIG 2 may be performed in the factory.
• initial values for cO, cl, c2, c3 are loaded from a memory.
• the initial values loaded are designated as c ⁇ init , cl init , c2 init , c3 init , respectively.
• c ⁇ init is set to zero.
• cl init , c2 init , c3 init are set to the values of the coefficients al, a2, a3, respectively, characterizing the crystal, according to Equation 1.
• the coefficients al, a2, a3 may be calculated from, e.g., data provided by the crystal vendor.
• the coefficients al, a2, a3 may be estimated by averaging data from multiple crystal samples as provided by the crystal vendor.
• the coefficients al, a2, a3 may be estimated from a nominal F-T curve provided by the crystal vendor.
• the temperature Tl of the crystal at an arbitrary time tl is measured, e.g., using temperature sensor 120 in FIG 1. Also measured is the corresponding oscillator frequency offset Fm(Tl) from the reference frequency Foo-
• the frequency offset Fm(Tl) may be measured by injecting a single tone of known frequency Fl into a receiver, tuning the crystal oscillator nominally to the frequency Fl, and observing the frequency of the signal after downconversion, as depicted in FIG 2B. The frequency of the signal after downconversion can be used to derive the frequency offset Fm(Tl).
• an estimated coefficient cO' is computed based on the information gathered at step 202.
• the oscillator frequency at a second temperature T2 is measured, yielding Fm(T2).
• the temperature T2 is preferably sufficiently separated from Tl to allow accurate estimation of the slope of the F-T curve, but sufficiently near Tl to minimize the effect of the second- and third-order terms.
• the separation between Tl and T2 may be chosen to be at least one degree Celsius.
• the temperature T2 may be sampled after waiting a predetermined amount of time after time tl at which Tl is sampled.
• a plurality of temperature-frequency data points may be sampled over a time interval, and the lowest temperature may be taken to be Tl, and the highest temperature may be taken to be T2.
• a heat source may be turned on after step 202, to raise the oscillator temperature.
• the heat source may be a power amplifier.
• an estimated coefficient cl ' is computed.
• estimated coefficients c2' and c3' are computed.
• c2' and c3' are assumed to be functions of cl ', such that specifying cl ' uniquely specifies c2' and c3'.
• c2' and c3' are assumed to be linearly related to cl ' as follows (Equation 6): wherein the linear coefficients m C 2', m C 3', b c r, b C 3> may be empirically determined and/or pre-stored in memory.
• FIG 3A depicts a linear relationship between cl ' and c2' denoted by Ll/2.
• the coefficients rn ⁇ and b c2 ' characterizing the linear relationship may be derived from multiple crystal data samples as provided by the crystal vendor. These multiple data samples are shown in FIG 3 A as a scatter plot superimposed on the line
• the estimated coefficients m c2 ' and b c2 ' may be determined according to predetermined optimality criteria, e.g., minimum mean square error between the line L 1/2 and the data samples in the scatter plot.
• FIG 3B depicts a similar linear relationship between cl ' and c3' that can be used to compute an estimate of c3' from cl '.
• crystal samples manufactured by the same crystal vendor as the crystal being calibrated may be included to estimate the coefficients m c2' , b c2 >, m c3' .
• crystal samples from multiple vendors may be included.
• an updated estimate c0" for the coefficient cO may be obtained based on the estimated coefficients c0', cl ', c2' and c3' derived in steps 204, 208, and 210.
• step 214 the coefficients c0, cl, c2, c3 may be updated to the values of the computed coefficients c0", cl ', c2', c3', respectively.
• the updated coefficients may be stored in a memory.
• FIG 2A depicts an alternative embodiment of the present disclosure.
• steps 202-212 are each performed a total of N+l times to obtain multiple estimates of the coefficients c0, cl, c2, c3.
• Numbered steps in FIG 2A correspond to similarly numbered steps in FIG 2.
• step 200 initializes the coefficients. In an embodiment, this may be done in the same manner as earlier described with reference to FIG 2.
• an iteration index n is set to 0. Steps 202-212 proceed as described earlier with reference to FIG 2, with [n] representing the computed coefficient corresponding to each iteration index.
• the algorithm checks for whether the iteration index n has reached N. If not, then the algorithm increments n, and returns to step 202 for the next iteration. If n has reached N, then the algorithm proceeds to step 214.
• steps 202-212 may be repeated to derive a set of coefficients c ⁇ '[n], cl '[n], c2'[n], c3'[n], c ⁇ "[n] associated with each iteration index n.
• the set of coefficients derived for each iteration index n may be stored in memory for later processing.
• the coefficients cO", cl ', c2', c3' from all N+l iterations may be combined to generate an estimate for the coefficients cO, cl, c2, c3.
• [c0,cl,c2,c3] o id is the running estimate of the coefficients
• [cO,cl,c2,c3] C urrent is the estimate of coefficients computed for the current iteration n
• [c ⁇ ,cl,c2,c3] new is the updated estimate of coefficients.
• a joint probability maximization method may be employed to derive an optimal set of coefficients based on the N+l available sets of coefficients. For example, given the plurality of F-T data points sampled in the process of FIG 2A, an optimal set of coefficients c0 opt , cl opt , c2 opt , c3 opt yielding a minimum mean-squared error between the F(T) and the sampled data points may be derived.
• an optimal set of coefficients c0 opt , cl opt , c2 opt , c3 opt yielding a minimum mean-squared error between the F(T) and the sampled data points may be derived.
• a linear relationship may be assumed between cl opt and each of coefficients c2 opt and c3 opt , as described previously herein with reference to FIGs 3A and 3B.
• the steps shown in FIGs 2 and 2 A may be performed in the factory, prior to in-field operation of the oscillator circuit. Alternatively, the steps may be performed during in-field operation of the oscillator circuit.
• the steps depicted in FIGs 2 and 2A may be performed once during an initial calibration phase of a device utilizing the crystal oscillator, e.g., during assembly of the device at a factory. In alternative embodiments, the steps depicted in FIG 2 may be performed multiple times as needed.
• the estimates for coefficients cO, cl, c2, c3 may be periodically updated during normal operation to maintain their accuracy over time. Disclosed hereinbelow are techniques to periodically update the coefficient estimates.
• FIG 4 shows a state machine used to re-adjust an initially calibrated set of coefficients derived from, e.g., the procedure described in FIG 2.
• the re-adjustment may help mitigate the inaccuracies of factory calibration, as well as inaccuracies due to aging of the crystal and/or oscillator.
• the re-adjustment procedure begins at state FIELDO.
• the state FIELDO calibrates the coefficient c0.
• the calibration of cO may be done according to operations described later herein with reference to FIG 5.
• State FIELDO may transition to state FIELDl when a predetermined set of conditions (labeled "Done" in FIG 4) are met.
• State FIELDl may calibrate coefficient cl, as well as cO. In an embodiment, the calibration of cO and cl may be done according to operations described later herein with reference to FIG 6. State FIELDl may transition to state FIELD2 when a predetermined set of conditions are met. State FIELDl may also transition back to state
• the aging timer may track the amount of time elapsed since any coefficient has last been updated.
• the aging timer may be an electronic counter resident on a chip with the oscillator, or it may be a module that compares a time stamp stored during the last coefficient update with the current time stamp.
• the aging timer can be set to expire two years after a last calibration.
• state FIELD2 may calibrate coefficient c2, as well as coefficients cl and/or cO. State FIELD2 may transition to state FIELD3 when a predetermined set of conditions are met. State FIELD2 may also transition back to
• State FIELD3 may calibrate coefficient c3, as well as coefficients c2, cl, and/or cO. In an embodiment, the calibration of c3, c2, cl, cO may be done according to operations described later herein with reference to FIG 7. State FIELD3 may transition to state FIELD4 when a predetermined set of conditions are met. Alternatively, state
• state FIELD4 may be a sleep state. In the sleep state, the calibration mechanism may cease operation for a predetermined amount of time. In an embodiment, the predetermined amount of time may be one year.
• state FIELDl may skip FIELD2 and transition directly to state FIELD3 upon the predetermined set of conditions being met.
• the current state i.e., FIELDO, FIELDl, FIELD2, FIELD3, or FIELD4
• the crystal oscillator may be used in a wireless handset.
• FIG 5 shows an embodiment of operations performed during state FIELDO. Note the embodiment illustrated in FIG 5 is not meant to limit the scope of the disclosure to any particular set of operations in FIELDO. Rather, one of ordinary skill in the art will realize that any steps used to update an estimate of the coefficients may be performed during any of the states FIELDO, FIELDl, FIELD2, FIELD3, and FIELD4. Such embodiments are contemplated to be within the scope of the present disclosure.
• a counter n0 for counting iterations of a loop is initialized to zero.
• the state machine commences by waiting for a period of time
• FT updateO seconds At the end of FT updateO seconds, the temperature T (e.g., in degrees Celsius) of the crystal is measured. At step 510, it is checked whether the temperature T falls within a range
• T e.g., in degrees Celsius
• To is set to 30 degrees Celsius, and Ti is set to 15 degrees
• the coefficient cO[O] may be assumed to be the last cO stored in memory.
• the actual measured frequency of the oscillator fin may be derived from an automatic frequency control circuit used in, for example, a receiver apparatus for code-division multiple access (CDMA).
• CDMA code-division multiple access
• n0 is compared to a variable maxIterationsO. If n0 has reached a variable maxIterationsO, then the state machine exits state FIELDO and proceeds to the next state. If n0 has not reached maxIterationsO, then the state returns to step 500.
• FIG 6 shows an embodiment of operations performed during state FIELDl. In state FIELDl, a counter nl for counting the iterations is initially set to zero. At step 600, the state machine waits for a period of time FT updatel seconds. At the end of FT updatel seconds, the temperature T (e.g., in degrees Celsius) of the crystal is measured.
• T e.g., in degrees Celsius
• step 610 it is checked whether T falls within the range Ti ⁇
• cl [nl] may be updated as follows. Given the current value of c0, candidate values of cl[nl] may be assessed to determine the best cl candidate for the measured frequency and temperature, according to some optimality criteria.
• the optimality criteria may include the error between a measured temperature-frequency pair and the computed temperature-frequency characteristic, assuming the current value of cO and a candidate value of cl.
• the search for the best cl may be aided by assuming a linear relationship between cl and c2/c3, e.g., as described with reference to FIGs 3A and 3B.
• cl[nl] may be determined by computing the following metric:
• the HR weighting constant can be 256.
• nl is compared to a variable maxlterationsl. If nl has reached maxIterationsO, then the state machine exits state FIELDl and proceeds to the next state. If nl has not reached maxlterationsl, then the state returns to step 600.
• state FIELD2 may be implemented similarly to the states FIELDO and FIELD 1 previously described. In an alternative embodiment, FIELD2 need not be implemented if the coefficient c2 is predetermined to be close to zero. In this embodiment, state FIELDl may bypass FIELD2 and directly transition to FIELD3.
• FIG 7 shows an embodiment of the operations performed during state FIELD3.
• a counter n3 for counting the iterations is initially set to zero.
• the state machine waits for a period of time FT_update3 seconds.
• the temperature T e.g., in degrees Celsius
• the current estimate for c3 is updated at step 720.
• step 720 given the most recent values of c0, cl, and c2, candidate values of c3 may be assessed to determine the best c3 for the measured frequency and temperature, according to some optimality criteria. Once a best c3 is determined, it may be HR filtered with a previous estimate of c3. [0079] At step 730, n3 is compared to a variable maxlterations3. If n3 has reached maxIterationsO, then the state machine proceeds to the next state. If n3 has not reached maxlterations3, then the state returns to step 700.
• the state machine may transition to the next state upon detecting little or no change in the coefficient to be updated.
• the state machine may transition from FIELDO to FIELD 1 if c ⁇ [n ⁇ ] - c ⁇ [n ⁇ -l]
• the functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium.
• Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another.
• a storage media may be any available media that can be accessed by a computer.
• such computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer.
• any connection is properly termed a computer-readable medium.
• the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave
• the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of medium.
• Disk and disc includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk and blu-ray disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media.

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• 2008
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