GB2062990A - Digital waveform generator - Google Patents

Abstract

A digital waveform generator comprising means (e.g. clock generator 1, programmable dividers 2,3 and bistables 4,5) for generating two pulse trains of different frequencies and means (e.g. EXCL-OR 7) for combining them to form a pulse width modulated pulse train (C, C') which has a "low frequency component" (D, D', D'') the frequency of which is equal to the difference between the frequencies of said two pulse trains and the form of which is determined by the said pulse width modulation itself dependant upon the duty cycles of the two pulse trains. For generating sine waves the low frequency component is of substantially trapezium waveform (D) with horizontal portions, interconnected by ramp portions, forming one-sixth of the wavelength of the trapezium waveform. Such a trapezium waveform approximates to a sine wave with less than 5% distortion. This sine wave is generated by combining two different frequency pulse trains (A and 13), one with a one-half duty cycle, one with a one-third or two-thirds duty cycle, in an Exclusive OR gate (7) and passing the result through a low-pass filter (8). The generator is easily realized in integrated circuit form and is suitable for use in Multi-frequency touch-tone dialling equipment. <IMAGE>

Description

SPECIFICATION Digital waveform generator The present invention relates to digital waveform generators and particularly to digital sine wave generators.

According to one aspect of the present invention there is provided a digital waveform generator comprising means for generating two pulse trains of different frequencies and means for combining said two pulse trains to form a pulse width modulated pulse train having a "low frequency component" the frequency of which is equal to the difference between the frequencies of said two pulse trains, and the form } of which is determined by the pulse width modulation of the pulse width modulated pulse train, the pulse width modulation of the pulse width modulated pulse train being dependant upon the duty cycles of the two pulse trains.

If the two pulse trains both have a duty cycle of about one-half then the "low frequency component" is a substantially triangular waveform. A sawtooth "low frequency component can be achieved by switching the polarity of one of the pulse trains at each position of coincident changes of state between the two waveforms.

According to a second aspect of the present invention there is provided a digital sine wave generator comprising means for generating a pulse train which is pulse width modulated in such a way that said pulse train has a "low frequency component" having a substantially trapezium waveform with horizontal portions interconnected by ramp portions, the horizontal portions having a length substantially one-sixth of the wavelength of the trapezium waveform.

In Fourier Analysis a trapezium waveform can be represented by an expansion consisting of odd order sine terms. A trapezium waveform having a horizontal trace part equal to one-sixth the wavelength of the waveform has a zero third order term and therefore gives a sine wave approximation with no distortion beiow the fifth order. The total distortion can in fact be calculated to be less than 4.6%. The physiological limit of audibility is 5% and the CITT limit for touch tone diallers is 7%, so this is well within accepted distortion limits.

A pulse width modulated pulse train of suitable form can be generated by combining a first pulse train having a one-half duty cycle and a second pulse train of different frequency to said first pulse train having a one-third or two-thirds duty cycle. The "low frequency component" has a frequency equal to the difference between the frequencies of the first and second pulse trains. Hence, in accordance with a third aspect of the present invention there is provided a digital sine wave generator comprising means for generating two pulse trains of different frequencies, one of said pulse trains having a one-half duty cycle and the other of said pulse trains having a one-third or two-thirds duty cycle, and Exclusive OR means for combining said two pulse trains to generate a pulse-width modulated waveform with a "low frequency component" having a substantially sine wave waveform.

Preferably the two pulse trains of different frequencies are generated from a common, single frequency, clock train, for example using half-cycle dividing circuits.

It will be seen, particularly from the ensuing description of a specific practical embodiment, that a waveform generator according to the present invention can be constructed to be simple and reliable, and can be easily manufactured in integrated circuit form with a good yield, low power consumption and high supply voltage tolerance.

Reference will now be made to the accompanying drawings in which: Figure 1 is a circuit diagram of a particular practical implementation of a waveform generator according to the present invention arranged for generating sine waves; Figure 2 illustrates waveforms pertaining to the circuit of Figure 1; Figure 3 illustrates aiternative waveforms for the circuit of Figure 1 when used to generate other waveforms.

Figure 1 illustrates a clock frequency generator 1 connected to divider circuits 2 and 3 which are connected to bistable circuits 4 and 5 respectively. The outputs of bistable circuits 4 and 5 are connected to respective inputs of an exclusive OR gate 7 the output of which is connected to an output 9 via a low pass filter circuit 8.

The divider circuits 2 and 3 may be implemented by programmable counters, for example Motorola's MC 14526, and may be provided with a selector switch for programming them to divide by any one of a plurality of divisors in order that the sine wave generator be operable to generate any one of a plurality of different frequencies. In the example illustrated in Figure 1 this selecting function is represented by switch 6 which is provided on the divider circuit 3 and enables the output frequency appearing at output 9 to be chosen to be either of two values, i.e. either 984Hz or 1084Hz.

The clock frequency generator 1 may be used to generate any suitable frequency but is conveniently chosen to generate a standard frequency such as 3579kHz or 455kHz. 455kHz is used in this described embodiment as it requires less critical and less consumptive divider circuits.

The 455kHz pulse train generated by generator 1 is divided in divider circuits 2 and 3. Divider circuit 2 divides the pulse train frequency by 7. Divider circuit 3 divides the pulse train frequency by 11 or by 10 depending on whether the frequency 1084Hz or 984Hz respectively has been selected by means of the switch 6. In Figure 1 the frequency 984Hz has been selected so divider 3 will divide by 10.

Bistable arrangements 4 and 5, which may be formed from circuits as CD 4013, then divide the resulting pulse trains by 3 and by 2 respectively, producing pulse trains of the form illustrated in Figure 2 at lines A and B respectively. As can be seen in Figure 2, bistable arrangement 4 generates a pulse train with a one-third or two-thirds duty cycle at 455/21 kHz = 21 .667kHz, and bistable arrangement 5 generates a pulse train with a one-half duty cycle at 455120kHz - 22.750kHz.

These pulse trains A and B are combined in Exclusive OR gate 7 to produce a pulse train of the form illustrate at line C in Figure 2. This pulse train C has a high frequency component of 42.349kHz (the sum of the two gated pulse train frequencies) and a pulse-modulation frequency, defined as the average of two consecutive pulse cycles, of approximately 21kHz (i.e. half the high frequenc). It is pulse width modulated in such a way that it has a "low frequency component" of generally trapezium form with a horizontal part substantially equal to half the ramp part, i.e. substantially one-sixth of the wavelength of the trapezium waveform. This trapezium waveform is illustrated at line D of Figure 2.It is the "low frequency component" which is the waveform which would be produced at the output of a theoretical low-pass filter, i.e. a filter having a flat response up to a cut-off frequency between maximum audio frequency and the pulse-width modulation (pwm) frequency, with a perfectly sharp transistion to zero at that cut-off frequency.

As previously explained, such a trapezium wave-form approximates to a sine wave with less than 5% distortion. Such a sine wave is generated at the output 9 of the filter circuit 8. The frequency of this sine wave is equal to the difference between the frequencies of the pulse trains A and B, as would be expected from a consideration of a standard beat frequency techniques. In the illustrated example therefore this beat frequency is 22.750kHz - 21.666kHz = 984Hz.

In many practical applications the low pass filter 9 in Figure 1 would not be implemented electronically because the human ear and acoustical loads such as speakers and headphones act as inductive andlor mechanical low pass filters, i.e. as natural filters. Hence, in applications such as organs or horns it can be advantageous to feed the pulse output directly to a switching amplifier. This is more economical than the conventional analogue way because the circuit is simpie and electric-to-acoustic energy converting is more effective by driving the transducer directly from a switcher-output. If the difference between the highest "low frequency component" and the lowest "pulse modulation frequency" is large enough even a natural filter with a rather low-pass response will be sufficient.

A wide range of sine wave frequencies can be generated by suitable choice of dividing circuits 2 and 3.

Special half-cycle dividers are particularly useful in this respect and with them it is possible to generate all of the 8 frequencies used in MF touch-tone dialling equipment to with 1%, as shown in the table below. This is well within acceptable deviations as the limit of aberration is 1.5%.

Nominal Actual Error Divisor pwm freq.

1633 Hz 1649.551 + 0.95% 11.5/12 39kHz 1477 Hz 1486.928 +0.67% 17/18 26kHz 1336 Hz 1330.409 0.42% 18/19 24 kHz 1209 Hz 1203.703 - 0.44% 13.5/14 33 kHz 941 Hz 940.568 - 0.05% 21.5/22.5 21 kHz 852 Hz 86a.520 + 1.00% 22.5/23.5 20 kHz 770 Hz 764.705 - 0.69% 17117.5 26 kHz 697 Hz 700.000 + 0.43% 25/26 18 kHz Half cycle dividers can be constructed by adapting the odd number dividing technique described in "Electronic Design", 21st June, 1975 and 19th January, 1976, to count half cycles. For example, to divide by 11.5 the output of the counter must be high for 11 clock half-cycles and low for 12 clock half-cycles.The resulting waveform is of course not quite symmetrical but so long as reasonably high divisors are used, this does not result in any significant low-frequency distortion.

The sine wave synthesis herein described can also be used to generate a mixture of two frequencies. Such a mixture is required in multi-frequency touch-tone dialling equipment because pairs of frequencies, one from a low group of 4 and one from a high group of 4 frequencies, are used as a form of code to define a particular digit.

Such a mixture can be accomplised using micro-sequence mixing, which is a technique known to those skilled in the art of complex sound generation using digital music-computers. It entails switching between the two pulse width modulated pulse trains to be mixed to generate a sequential train comprising a few periods of one train followed by a few periods of the other. This can be achieved by switching between frequencies at the programmable counters, for example using switch 6, or by using two separate circuits and switching between the pulse width modulated pulse trains generated by each, for example using a switch at C (Figure 1). The result, after filtering, sounds like an analogue mixture of the two and will give the same results as true analogue mixtures in analogue filters.Even preemphasis of the high group frequencies is possible because such frequency burst can be weighted by counting out the appropriate number of periods.

The decibel ratio should be chosen to take account of the response to the output low-pass filter and the time of a wave period.

The technique described herein, using a pulse train with a one-half duty cycle and another with a one-third or two-thirds duty cycle combined by an Exclusive OR gate, is not the only way of generating a pulse-width modulated pulse train having a suitable low-frequency component. It is however the most practical.

Complicated circuits could be devised to combine pulse trains having duty cycles other than as described above, or to combine more than two pulse trains, and combining could be achieved by means other than an Exclusive OR gate.

The apparatus illustrated in Figure 1 could also be used for generating a pulse width modulated pulse train at C having a "low frequency component" of triangular form. In this case bistable circuits 4 and 5 would both divide by 2 (or would be omitted altogether) so that the pulse train generated at A and B would both have duty cycles of one-half. Pulse trains pertaining to the apparatus of Figure 1 when used in this way are illustrated in Figure 3. A', B' and C' are the waveforms produced at A, B and C respectively and D' represents the triangular low frequency component of C'.

D" represents a sawtooth "low frequency component" produced by including a logic circuit in the apparatus of Figure 1 which detects the positions of coincident changes of state of A' and B', which are indicated by reference Tin Figure 3, and switches the polarity of A' or B' at those positions.

Claims (11)

1. A digital waveform generator comprising means for generating two pulse trains of different frequencies and means for combining said two pulse trains to form a pulse width modulated pulse train having a "low frequency component" the frequency of which is equal to the difference between the frequencies of said two pulse trains, and the form of which is determined by the pulse width modulation of the pulse width modulated pulse train, the pulse width modulation of the pulse width modulated pulse train being dependent upon the duty cycles of the two pulse trains.

2. A digital waveform generator according to claim 1 wherein said "low frequency component" has a triangular form and wherein said two pulse trains both have duty cycles of about a half.

3. A digital waveform generator according to claim 1 wherein said "low frequency component" has a sawtooth waveform and wherein said two pulse trains both have duty cycles of about a half and there is provided a logic circuit arranged to detect positions of coincident changes of state between the two pulse trains and, in response thereto, to switch the polarity of one of said two pulse trains.

4. A digital waveform generator according to claim 1 for generating sine waves wherein one of said two pulse trains has a duty cycle of about a half and the other of said two pulse trains has a duty cycle of about one-third or two-thirds so that said "low frequency component" has a substantially trapezium waveform.

5. A digital waveform generator according to claim 4wherein said combining means comprises an Exclusive OR gate.

6. A digital waveform generator according to claim 4 or claim 5 wherein said first and said second pulse trains are generated from a common, single frequency, clock train.

7. A digital waveform generator according to claim 6 comprising half-cycle dividing circuits for producing said first and second pulse trains from said single frequency.clocktrain.

8. A digital waveform generator comprising means for generating a pulse train which is pulse width modulated in such a way that said pulse train has a "low frequency component" having a substantially trapezium waveform with horizontal portions interconnected by ramp portions, the horizontal portions having a length substantially one-sixth of the wavelength of the trapezium waveform.

9. A digital waveform generator comprising means for generating two pulse trains of different frequencies, one of said pulse trains having a one-half duty cycle and the other of said pulse trains having a one-third or two-thirds duty cycle, and Exclusive OR means for combining said two pulse trains to generate a pulse width modulated pulse train with a "low frequency component" having a substantially sine wave waveform.

10. A digital waveform generator substantially as hereinbefore described with reference to Figures 1 and 2 of the accompanying drawings.

11. A method of generating waveforms using a digital waveform generator according to any one of the preceding claims.