GB2101825A

GB2101825A - Low harmonic demodulator

Info

Publication number: GB2101825A
Application number: GB08214190A
Authority: GB
Inventors: Ernest Carl Wittke
Original assignee: Singer Co
Current assignee: Singer Co
Priority date: 1981-06-29
Filing date: 1982-05-14
Publication date: 1983-01-19
Also published as: JPS586648A; IT8222114A0; DE3221830A1; FR2508738A1; NO822098L; AU8532982A; SE8203989D0; IL65692A0; SE8203989L

Abstract

An apparatus and method for demodulating a synchronous signal utilising a pulse width-modulated equivalent of a modified square wave function to eliminate lower order harmonic distortion. The apparatus includes a switching demodulator 12 which is controlled by a function generator 16 which is synchronised to the input signal. The function generator produces a controlling function which is a square wave function having a fundamental component and an infinite series of odd harmonics of said fundamental component, less at least one of said odd harmonics. The function generator comprises an addressable memory 14 in which the controlling function is stored. The first one of the infinite series of odd harmonics is deleted from the square wave function. In a further example the third, fifth, seventh and ninth harmonics are deleted from the square wave function. <IMAGE>

Description

SPECIFICATION Low Harmonic demodulator means This invention relates to devices for demodulating synchronously encoded data. In particular, this device may be used for decoding the outputs of accelerometers, gyroscopes and the like, whose outputs are suppressed carrier amplitude modulated signals. The input to such an instrument, generally a steady-state function, is multiplied by the angular rate of the carrier signal. This produces an output function of the general form: D=Acos(o)t+0) (1) where D is the modulated signal, A is the amplitude of the disturbance, ea is the modulation frequency, and o is the phase angle.

To recover the input information, the output signal is demodulated by multiplying it by an appropriate demodulation function.

At present, switching demodulators are employed to carry out the multiplication process. A switching demodulator is nothing more than a simple reversing switch, having an "on" state and an "off" state. The operation of the switching demodulator can be represented by a square wave. It is responsive to a signal at the desired fundamental frequency as well as to any odd harmonic of the fundamental frequency that may be present. The usual remedy for curing harmonic response is the employment of a low pass or band pass filter. For many applications, such a filter produces a satisfactory result.

In rotational equipment such as accelerometers, bearings and other factors generate harmonics of significant magnitude which will appear in the instrument output signal. These harmonics are aliased into the fundamental (rotational) frequency, altering the magnitude of the desired fundamental component and thus giving a false output. An obvious solution to this problem is to filter out the harmonics. However, a filter capable of reducing the harmonics to an acceptable level will introduce a large degree of phase shift. In the case of an instrument having a single input axis, signal phase angle is not overly critical, since phase error affects instrument output in proportion to the cosine of the error angle. However, in the case of an instrument having two orthogonal input axes with a common signal, phase error affects the instrument output as an apparent rotation of the sensing axes.

The user of the instrument is thus faced with a dilemma. On the one hand, the presence of significant high order harmonics will lead to error if they are not filtered out. On the other hand, filtering produces phase shift which will also result in an error. It is therefore proposed to develop a demodulator that does not produce significant harmonics below an arbitrary nth order. For instance, one might eliminate the third, fifth, seventh, and the ninth harmonics. Then, a filter may be employed for harmonics above that level. The design for a filter for reducing the eleventh harmonic by fifty db is much less severe than one which is required to reduce the third harmonic by sixty db. The former produces minimal phase shift, and, in turn, significantly less error will appear in the output.

Summary of the invention In accordance with the invention, there is provided a switching demodulator controlled by a function generator synchronized to the input signal. In the preferred embodiment, the function generator produces a pulse width modulated equivalent of a square wave function not having at least one of the harmonics above the fundamental component. A phase locked loop synchronizes the function generator to the instrument's rotational rate.

This invention also contemplates a method that functions in accordance with the apparatus.

For a better understanding of the present invention together with other and further objects, reference is made to the following description taken in conjunction with the accompanying drawing, and its scope will be pointed out in the appended claims.

Brief description of the drawing Figure 7 is a block diagram of the demodulator apparatus.

Description of the preferred embodiment The switching demodulator multiplies its input signal by plus or minus one. This is equivalent to multiplying the input by the fundamental frequency and by odd harmonics of that frequency as well. The multiplying function is the square wave which can be represented by the following summation:

This summation can be expanded to show the individual components ofthe series: a . a f(t) = a sin wt + 3 sin 3(ot + 5 sin 5(out... (3) The above equations indicate that the switch is responsive to odd harmonics of the input signal. Where there is a great deal of noise, the harmonic components will be very significant. When these harmonics are processed, they are aliased into the fundamental frequency component and produce error.If a conventional low pass or band pass filter is employed, the phase shift introduced by the filter results in error that is equivalent to a physical rotation of the instrument.

To overcome this problem, it is proposed to operate the switching demodulator in such a manner as to eliminate certain of the troublesome harmonics. Instead of switching the demodulator at the fundamental frequency, producing a characteristic as in equations 2 and 3, the demodulator is operated at a much faster rate and in a manner that causes it to be insensitive to the undesired odd harmonics.

Specifically, a square wave function less certain lower order harmonics is used for demodulation. The higher order harmonics can then be filtered out in the conventional manner without incurring significant phase shift.

The equation for the desired function is derived as follows. Since each quadrant of a symmetrical periodic function is a mirror image of the other three, then one need concentrate on only one quadrant. For a pure square wave having an amplitude of i 1, the equation for amplitude in the first quadrant is simply: v= 1 (4) The expression for a square wave less certain lower order harmonics, beginning with the third from equations 2 and 4, is:

where M is the number of harmonics to be cancelled.

Since the switch is a binary device, any switching function must also be binary in nature. If the amplitude is a constant, then the only other factor that may be varied is the duration of the pulse. Accordingly, the switching function employed is the pulse width modulated equivalent of the square wave function less the undesired lower harmonics. To derive the function, it is first necessary to choose a sampling rate, which is identically the switching rate mentioned previously. This rate is directly dependent upon the number of harmonics one desires to cancel, and, for a half cycle, it is ideally equal to the lowest common multiple of the harmonic numbers to be cancelled.For instance, to cancel the third, the fifth, the seventh, and the ninth harmonics, an entire cycle would be devided into 630 parts (2 x 3 > < x 5x 7 x 3). (Practical considerations may cause some other number of parts, such as 512, to be selected.) To convert the modified function, equation 5, to a pulse width modulated equivalent, the integral of the desired function from 0 to 3c/2 is compared to a summation of the pulses. The first pulse for the first interval is arbitrarily chosen to be plus one. The function is integrated from zero to the equivalent angle (n x z/2) and a comparison is made.If the integral of the function is greater than the summation of the pulses at any given point, the next pulse will be positive; if the summation of the pulses at a particular angle is greater than the integral of the desired function, then the next pulse will be negative. This comparison process is repeated for each successive interval from zero through 90% to complete one quadrant. The resulting function may be applied over the remaining three quadrants of the cycle, since those quadrants are mirror images of the first.

The switching pattern thus derived is used to operate the switching demodulator in phase synchronization with the instrument output. Because this function does not contain the lower order harmonics, any input to the switching demodulator at those frequencies will theoretically be rejected.

A practical implementation of the apparatus is illustrated in Figure 1. The instrument 10 produces an output which is demodulated by switching demodulator 12. The switching function derived above is digital and may be stored in a Read Only Memory (ROM) 14 or any other suitable memory having sufficient capacity and read out synchronously with the input to the switching demodulator. The size of the memory is simply determined by the sampling rate that was chosen previously. All that is necessary at this point is a method of synchronizing the generation of switching function to the instrument. A phase locked loop 16 performs this function well. The phase locked loop 16 receives a synchronizing signal on line 18, which is supplied to a phase comparator 20 that drives a voltage controlled oscillator 22 in the normal fashion of a phase locked loop.The output of the voltage controlled oscillator 22 is supplied to a counter 24, which has the dual function of acting as a frequency divider and an address generator. One output from the couter 24 is fed to the reference input 26 on the phase comparator 20. This feedback line 28 completes the phase locked loop 16. The output from the phase locked loop 30 is in digital form and supplies the address for the memory. In operation, the voltage controlled oscillator 22 is synchronized to the synchronizing signal on line 18; in turn, the counter 24 operates in synchronism with the voltage controlled oscillator 22 to provide a variable address from 1 to N that is synchronized with the instrument 10. The output of the memory 14 which is the pulse width modulated equivalent of the switching function is thus locked into the instrument 10 and provides a low harmonic output from the switching demodulator 12. Finally, a simple low pass filter, not shown, may be attached to remove the higher order harmonics.

While there has been described what is believed to be the preferred embodiment of the invention, those skilled in the art will recognize that other and further modifications may be made thereto without departing from the spirit of the invention, and it is intended to claim all such embodiments as fall within the true scope of the invention.

Claims

1. A demodulator for synchronously demodulating rotationally encoded information having an instantaneous phase angle, comprising: switch means; and control means for controlling said switch means, said control means comprising function generator means for generating a controlling function, whereby said switch means switches in accordance with said controlling function and where said controlling function is a square wave function, having a fundamental component and an infinite series of odd harmonics of said fundamental component, less at least one of said odd harmonics.

2. A demodulator as set forth in claim 1 wherein said controlling function is the pulse-width modulated equivalent of said square wave function.

3. A demodulator as set forth in claim 2 wherein said switch means comprises a switching demodulator.

4. A demodulator as set forth in claim 3 wherein said control means further comprises synchronizing means for phase synchronizing said function generator means with said instantaneous phase angle.

5. A demodulator as set forth in claim 4 wherein said function generator means comprises an addressable memory means in which said controlling function is stored, said addressable memory means being responsive to said synchronizing means.

6. A demodulator as set forth in claim 5 wherein said synchronizing means comprises a phase locked loop.

7. A demodulator as set forth in claim 6 wherein the first one of said infinite series of odd harmonics is deleted from said square wave function.

8. A demodulator as set forth in claim 6 wherein the first four of said infinite series of odd harmonics are deleted from said square wave function.

9. A method for synchronously demodulating rotationally encoded information comprising the steps of: generating a square wave function having a fundamental component and an infinite series of odd harmonics of said fundamental component, less at least one of said odd harmonics; phase synchronizing said square wave function with said rotationally encoded information; and multiplying said rotationally encoded information by said square wave function.

10. A demodulator substantially as hereinbefore described with reference to and as shown in the accompanying drawing.

11. A method for synchronously demodulating rotationally encoded information substantially as hereinbefore described.