To provide a motor drive signal for MEMS gyroscopes, a digital sinusoidal signal of frequency tO is generated by a numerically controlled dual- frequency oscillator (NCDFO). A command input to the oscillator is/ ? = cos (2rôt), where fs =1/T is a clock frequency of the oscillator. The frequency fa varies with changes in 8,,. The digital sinusoidal signal serves as the input to a drive circuit which, in turn, provides an analog signal to a gyroscope drive motor. Because the above described gyroscope motor drive configuration is within a closed-loop control system, the destabilizing effect of time delay, and an attendant phase shift resulting from the time delay, will cause an operational issue to result.

One known attempted solution is to pass the NCDFO output signal through a digital-to-analog converter (DAC), whose output is passed through a low pass, anti-aliasing filter to smooth the analog gyro-drive signal. Unfortunately, the time delay introduced by the combination of these operations is too long to permit solid closed- loop operation. A digital-to-analog-conversion scheme with lower phase shift is clearly needed.

BRIEF SUMMARY OF THE INVENTION In one aspect, an apparatus to reduce a time delay and a resultant phase shift in a gyroscope motor drive signal is provided. The motor drive signal originates from a numerically controlled oscillator, the oscillator output being sampled at a predetermined rate. The apparatus comprises a first element which upsamples the

oscillator output signal samples, a band pass filter configured to receive an output from the first element and remove spectral components of the output of the first element, a third element which generates a tuning parameter,/, to tune the band pass filter, and a scaling multiplier configured to normalize an output of the filter.

In another aspect, a method for reducing a time delay and a resultant phase shift in a gyroscope motor drive signal which originates from a numerically controlled oscillator is provided. The method comprises placing I-1 zero value samples between each pair of oscillator output samples, filtering spectral components from the combined oscillator output samples and zero value samples, generating a tuning parameter, ßO, for use in filtering, and scaling a filter ouput.

In still another aspect, an angular rate measurement system is provided.

The system comprises a gyroscope configured to sense an angular rate input and provide a modulated angular rate information signal and a sinusoidal demodulation reference signal. The system also comprises a numerically controlled oscillator (NCO) configured to receive as an input a tuning parameter, 8, which is a digitized signal derived from the sinusoidal demodulation reference signal. The NCO is further configured to provide output samples. The system also comprises an automatic gain control (AGC) circuit configured to amplify the output samples of the NCO, an interpolator, and a digital-to- analog converter and filter configured to produce a motor drive signal from an output of the interpolator. The interpolator is configured to place I-1 zero value samples between each pair of amplified output samples, and the interpolator comprises a filter configured to filter spectral components from the combined amplified output samples and zero value samples. The interpolator further generates a tuning parameter, ßO, for the filter, and scales the filtered samples to be output from the interpolator.

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 illustrates a gyroscope angular rate sensing system including an interpolator circuit for reducing a time delay in generating a gyro motor drive signal.

Figure 2 illustrates an embodiment of an interpolator circuit used in the angular rate sensing system of Figure 1.

DETAILED DESCRIPTION OF THE INVENTION Referring to Figure 1, an angular rate measurement system 10 as shown is built around gyroscope 20 which senses input angular rate 22. A first output 24 of gyroscope 20 is an electrical signal which is a double side band suppressed carrier (DSSC) modulated representation, at a fundamental frequency 2fi, of the input angular rate 22. First output 24 is input to an analog-to-digital conversion (ADC) system 26 including an internal analog anti-alias filter, a sampler, and a digitizer (none shown).

An output 28 from ADC system 26 is input to and demodulated by demodulator 30 which, as further described below, receives demodulating signals from numerically controlled dual frequency oscillator (NCDFO) 32. An output 34 from demodulator 30 is filtered with filter 36 whose output 38 is a base band digitized representation of angular input rate 22.

Gyroscope 20 provides a second output 40, which is a sinusoidal demodulation reference signal at a frequency 2fo. Second output 40 is connected to a second ADC system 42, functionally identical to ADC system 26. An output 44 from ADC 42 is then input to both a phase detector/servo equalizer 46 and an automatic gain control (AGC) 48. Phase detector/servo equalizer 46 is a combination fast-acting automatic gain control, phase shifter, phase detector, and servo equalizer. An output 50 of phase detector/servo equalizer 46 is a tuning parameter 8,, = cos (2 f determines the frequency of oscillation of NCDFO 32 (NCDFO 32 has a clock rate of 1/T) and is connected to a first input 52 of NCDFO 32. NCDFO 32 provides two outputs 54 and 56 in quadrature at frequency 2fo and another pair of outputs in quadrature at frequencyf,. In the embodiment shown, only one output 60 is connected to an input 62 of automatic-gain control (AGC) 48.

As stated above, output signal 44 from ADC 42 is connected to a second input 64 of AGC 48. Output signal 66 from AGC 48 is an amplified version of oscillator output 60, and is automatically adjusted in amplitude until the amplitude of signal 64 reaches a predetermined level. Signal 66 is connected to an input 68 of interpolator 70, which is described in further detail below. Output 72 of NCDFO 32 is the square of tuning parameterßO and is connected to a second input 74 of interpolator

70. Input signal 68 to interpolator 70 is a sinusoid of prescribed amplitude, frequency fo, and sampling frequency f,. Output signal 76 from interpolator 70 is a sinusoid of the same amplitude and frequency as input signal 68, but at a sampling frequency of I. f,, as interpolator 70 increases a sampling rate of input signal 68 by a factor of I.

Output signal 76 from interpolator 70 is connected to an input 78 of a signal conditioning element 80, whose output 82 is input to a digital-to-analog converter (DAC) and filter 84. An output 86 of DAC and filter 84 is input to an analog driver 88 which produces a motor-drive signal 90 for gyroscope 20.

Figure 2 is a block diagram of interpolator 70 including four elements. A first element upsamples an output signal from oscillator 32 (shown in Figure 1) by placing I-1 values of zero between each pair of samples from oscillator 32. The upsampled signal drives the second element, a Gray-Markel, lattice-based, second order, band pass interpolation filter, which is clocked at a frequency of IT to remove all extraneous spectral components of the upsampled signal. As further described below, a passband-width parameter, a, in a preferred embodiment, is set to 0.999 and a tuning parameter of the filter is set to ßo'=cos(2#foT/I)=cos[1/Icos-1(ßo)]. The third element tunes the filter by generating the filter tuning parameter ßO, via a three term power series where, 6,', Pt ao + au, qu + a2ßO4. The term ß027 is provided by oscillator 32.

A fourth element of interpolator 70 is a scaling multiplier which renormalizes the signal amplitude by a factor of Il2.

Referring specifically to Figure 2, interpolator 70 includes a three-input second-order band pass filter 100 and a power series calculation section 102. In the embodiment shown, band pass filter 100 is a Gray-Markel single-multiplier per order all pass structure whose output 104 is subtracted from an input 106 to provide band pass filtering. Input 106 is delivered to band pass filter 100 by sampling function 108.

Output 110 from band pass filter 100 is scaled by I/2 in multiplier 112 to generate output signal 76.

Input 106 is connected to an additive input 114 of a first subtraction element 116, an additive input 118 of a second subtraction element 120, and a first input

122 of a first adder 124. Output 126 of first adder 124 is connected to a first input 128 of a first multiplier 130. A second input 132 to first multiplier 130 is a, an externally supplied parameter. In a specific embodiment, a is set to a value of 0.999. An output 134 of first multiplier 130 is connected to a subtractive input 136 of first subtraction element 116 and a first input 138 of second adder 140. Output 104 of second adder 140 is connected to a subtractive input 142 of second subtraction element 120.

Output 150 of first subtraction element 116 is connected to an additive input 152 of third subtraction element 154 and to an additive input 156 of fourth subtraction element 158. A first input 160 of second multiplier 162 is connected to an output 164 of third subtraction element 154. A second input 166 to second multiplier 162 is 6', which is a tuning parameter for band pass filter 100. An output 168 of second multiplier 162 is connected to a subtractive input 170 of third subtraction element 158 and a subtractive input 172 of a fifth subtraction element 174.

An output 176 of fourth subtraction element 158 is connected to a first delay element 178. An output 180 of first delay element 178 is connected to a subtractive input 182 of third subtraction element 154 and to an additive input 184 of fifth subtraction element 174. An output 186 of fifth subtraction element 174 is connected to an input 188 of second delay element 190. Output 192 of second delay element 190 is connected to a second input 194 of first adder 124 and a second input 196 of second adder 140.

In operation, a sinusoid at a frequency fo7 is provided at input 68 at a sampling frequency of f,, to sampling function 108. The sinusoid at input 68 is modified at sampling function 108 by insertion of I-1 values of zero being input between each pair of input samples of the sinusoid. A new signal is created at a sampling rate of I 5. As described above, band pass filter 100 has as its second input 132 the parameter a, that determines a bandwidth for band pass filter 100. The bandwidth parameter,, has, in one embodiment, a nominal value of 0.999, where a is determined as a = tan (TfBwT/I), and where fBw is the 3dB bandwidth (in Hz) of the

pass band. A center of the pass band is tuned by input 166, the parameter ßO, where where 8,, is the input to NCDFO 32.

Direct calculation of ßO from ßO is difficult, but a Chebychev approximation can be obtained, in one embodiment, by a three-term power series, for example, 6,, #a0+a1ßo2+a2ßo4. This power series is mechanized in power series calculation section 102 whose input 74, fl2, is obtained directly from NCDFO 32. Input 74 is connected as a first input to third multiplier 200 and fourth multiplier 202. A second input 204 of third multiplier 200 is coefficient a2. An output 206 of third multiplier 200 is summed with coefficient a, in third adder 208, whose output 210 is connected to a second input 212 of fourth multiplier 202. Fourth adder 214 sums an output 216 of multiplier 202 with coefficient ao. An output 218 of adder 214 is the tuning parameter ßO. In one embodiment, ao, al, and a2, are computed utilizing a Chebychev approximation program as illustrated in Appendix A. In a specific embodiment, and as outlined in Appendix A, ao is 0. 9967032511, al is 0. 00526891, and a2 is-0.0021640344.

Numerically controlled, dual frequency oscillators (NCDFO) implemented in MEMS gyroscope motor drive systems, typically produce a sinusoid, whose frequency may not be constant, and which is sparsely sampled. Such a motor drive system can introduce an unacceptable amount of time delay and phase shift, as above described. One way to improve performance of such motor drive systems is to increase the sampling frequency of the NCDFO output signal through the use of interpolator 70. Implementation of system 10, including interpolator 70 allows an increase in the sampling frequency of the NCDFO output signal by a factor of I, where I is greater than one, and typically eight or more. The combined time delay of interpolator 70, a higher frequency DAC, and a simple low pass, anti-aliasing filter (DAC and filter 84) is less than the time delays in known gyroscope motor drive systems.

While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the claims.