EP1046969A1 - Method for controlling a stepping motor and means to apply this method - Google Patents

Abstract

Control procedure involves sub-dividing the stepper motor period into elementary periods and from calculations using the elementary periods determination of how the long the motor impulse has lasted and deciding whether the motor coil should be connected to a power source or not so that the motor is driven at the correct rate. Each motor impulse is chopped into a number of elementary periods of the same duration. For each elementary period an effec chopping rate (He) is determined where He = n1 divided by n2, where n1 is the total number of periods for which the motor coil h been connected to the source since the start of the motor impulse and n2 is the total number of periods since the start of the m impulse. If He is ≤ Hc, where Hc is the ordered stepper rate then the coil is connected if He greater than Hc then the motor is disconnected.

Description

The subject of the present invention is a method for controlling a stepper motor comprising a rotor provided with a permanent magnet and a coil magnetically coupled to said magnet, said method comprising applying a driving pulse to said coil each time said rotor must turn one step, said motor pulse comprising periods of connection during which said coil is connected to a source of electrical energy and disconnection periods during which said coil is disconnected from said source, the ratio between the total time of said connection periods and the total duration of said driving pulse being equal to a set hash rate.

The present invention also relates to a device for setting implementing this process.

Such a method and such a device are described, for example, in the US-A-4361410 where they are illustrated in Figures 8 to 11. In this document a circuit produces, after each driving pulse, a signal detection having a first or a second state depending on whether the load mechanical driven by the motor rotor during this driving impulse was relatively weak and that this rotor therefore turned correctly, or that this mechanical load was so great that this rotor did not rotate. A combinational logic circuit produces control pulses having a hash rate of 50% or 75% depending on whether this detection signal has its first or second state, and these control pulses are used to chop, with the same rate, the next driving impulse. The amount electrical energy supplied to the stepper motor coil is thus controlled mechanical load driven by the rotor of this motor, which decreases this amount of electrical energy.

It will be recalled that a chopped driving impulse has a certain number of periods during which the motor coil is connected to a source of electrical energy, these connection periods being separated the each other by periods of disconnection, that is to say during which the motor coil is disconnected from the source.

It will also be recalled that the hash rate of such an impulse motor is generally defined as the ratio between the total duration the connection periods just mentioned and the total duration of the driving impulse. It is this definition which will be used in the rest of this description.

It will also be noted that, in the patent US-A-4361410 mentioned above, the definition of the hash rate of motor pulses is the reverse of this generally accepted definition. It follows that the rates of 0% and 25% mentioned in this document are in fact, by this definition generally accepted, rates of 100% and, respectively, 75%.

Those skilled in the art will readily see that the enslavement achieved by the circuit of Figure 8 of US-A-4361410 succinctly described above is very basic, and that the decrease in electrical energy consumed by the motor which results from this enslavement is therefore very weak, because only two chopping rates of the driving pulses are provided.

It is obviously possible to increase the number of hash rates available, to improve the enslavement of the amount of energy electric supplied to the motor coil at the mechanical load driven by the rotor of the latter, and further decrease the total amount of this electrical energy consumed by this engine.

But the complexity of the combinatorial logic that produces the impulses control used to chop the driving impulses increases quickly with this number of hash rates available. It is good similarly heard of the place occupied by this logic in the integrated circuit where it is performed and therefore the cost price of the latter. We have found that in practice it is hardly possible to predict more than eight or ten separate hash rates if we want this cost price to remain within bearable limits. However it is often desirable to have a number higher hash rate in order to be able to decrease as much as possible the consumption of the stepper motor by very tightly controlling the amount of electrical energy supplied to it during each pulse driving mechanical load actually driven by its rotor. This is particularly the case when this motor is the one which drives the needles a timepiece whose source of electrical energy is consisting of a low volume battery or accumulator and therefore of fairly limited capacity.

It is also desirable to have a fairly high number of chopping rate when the motor supply voltage can vary by quite important, as is the case when this engine is the one that drives the hands of an electronic timepiece but where the source the latter is supplied by a rechargeable system, for example by solar cells or a generator-barrel system.

An object of the present invention is therefore to propose a method of control of a stepper motor by which the number of rates available for chopping the driving impulses applied to the coil of this motor can be much higher than when that the known process described above is used, without the complexity and therefore the cost price of the circuit allowing the implementation of this process are not increased too much, slaving the amount of electrical energy supplied to the coil of the motor with mechanical load driven by the latter's rotor which can thus be significantly improved and the total consumption of electrical energy by this engine can therefore be considerably reduced.

This object is achieved by the process, the characteristics of which are listed in claim 1 attached.

Another object of the present invention is to provide a circuit for control of a stepping motor implementing this method.

This goal is achieved by the circuit whose characteristics are listed in claim 6 attached.

As will be explained in detail later, these characteristics of the method according to the present invention and of the device which implements this process considerably increase the number of values the hash rate of motor impulses can take applied to the motor coil. It follows that the amount of energy electric which must be supplied to this coil can be slaved a lot more finely to the mechanical load driven by the rotor of this motor, this which results, all other things being equal, in a reduction of this amount of electrical energy.

• la figure 1 est un schéma d'une première forme d'exécution du dispositif selon la présente invention; et
• la figure 2 est un schéma d'une autre forme d'exécution du dispositif selon la présente invention.

Other objects and advantages of the present invention will be made evident by the description which follows and which will be made with the aid of the appended drawing in which:

• Figure 1 is a diagram of a first embodiment of the device according to the present invention; and
• Figure 2 is a diagram of another embodiment of the device according to the present invention.

Figure 1 shows schematically and by way of example not limiting a device according to the present invention in a case where it is used to control the stepper motor of a timepiece electronic. This timepiece, some of whose other components have also shown in Figure 1, is designated as a whole by reference 1.

To simplify the description which follows, the logical states "0" and "1" that can take the various signals existing in the device 1 will simply called state "0" and, respectively, state "1".

Timepiece 1 conventionally comprises a circuit for time base 2 formed by a quartz oscillator and a frequency divider which have not been shown separately and which will not be described further in detail, as they are well known to specialists.

We simply mention that the time base circuit 2 comprises, in this example, three outputs designated by the references 2a, 2b and 2c producing periodic signals in the form of square pulses having a frequency of 1Hz, 128 Hz and 16.384 Hz respectively. periods of these three signals are therefore respectively 1 second, 7.8 approximately milliseconds and approximately 61 microseconds.

The outputs 2a and 2b of the time base 2 are respectively connected at the S and R inputs of a flip-flop, or flip-flop, which is of the R-S type well known and which is designated by reference 3.

The direct output Q of the flip-flop 3 is connected to the clock input C of a type D flip-flop designated by the reference 4, as well as a first entry of four doors AND respectively 5, 6, 7 and 8, and at the entrance of a inverter 9.

The direct output Q of the flip-flop 4 is connected to a second input of door 5, while its reverse output Q is connected to its information input D and to a second input of door 6.

The output 2c of the time base 2 is connected to the clock input C another flip-flop D, designated by the reference 10, as well as at the entrance of a inverter 11, the output of which is connected to a second input of doors 7 and 8.

A person skilled in the art will note that the reverser 11 can be made of preferably by a plurality of reversing doors connected in series to form a reversing circuit with a large reaction time, so that the delay of signal Q of flip-flop 10 compared to signal C is less than that of the signal leaving the inverter 11 with respect to this signal C.

The direct output Q of the flip-flop 10 is connected to a third input of the doors 5, 6 and 7.

The outputs of doors 5 and 6 are respectively connected to a first input 12a and to a second input 12b of a forming circuit of driving pulses 12 having two outputs 12c and 12d.

The stepper motor driving the hands of timepiece 1 is only shown very schematically in Figure 1 where it is designated by the reference 13. The motor 13 comprises, conventionally, a rotor provided of a permanent magnet, a coil and a stator magnetically coupling this coil and this magnet. Only the coil of this motor 13 has been shown in Figure 1 where it is designated by the reference 14. The two terminals of this coil 14 are respectively connected to the output 12c and to the trainer output 12d 12.

The trainer 12 will not be described in detail here, since it is a circuit well known to specialists. It will simply be mentioned that it is arranged so that when its inputs 12a and 12b are both in state "0", the coil 14, or at least one of its terminals, is disconnected from the source of electrical energy which powers the various circuits of device 1 and which is shown schematically with the reference 15. In this case, the coil 14 is also short-circuited in a conventional manner.

The trainer 12 is further arranged so that when his inputs 12a and 12b are respectively in state "1" and in state "0", the coil 14 is connected to the source 15, this connection being such that a current flows at through this coil 14 for example from terminal 12c to terminal 12d of trainer 12. Similarly, when inputs 12a and 12b of trainer 12 are respectively in state "0" and in state "1", coil 14 is also connected to the source 15. A current therefore also flows in the coil 14, but in the same example, from terminal 12d to terminal 12c of formatter 12.

The trainer 12 furthermore has an outlet 12e which is connected to a input 16a of a detection circuit 16 and which supplies the latter with a signal representative, for example, of the intensity of the current flowing in the coil 14.

The detection circuit 16 will also not be described in detail, because it can be carried out in various ways well known to specialists. We simply mention here that it still has a command entry 16b connected to the output of the inverter 9 and an output 16c, and that it is arranged to so as to provide this output 16c in response to the signal it receives from the output 12e of formatter 12, a signal taking, after each pulse motor applied to the coil 14 by the trainer 12, a first or a second state depending on whether the rotor of motor 13 has turned correctly or has not turned in response to this driving impulse.

The output 16c of the detector 16 is connected to an input E which comprises a determination circuit 17 having outputs S whose states "0" and "1" form a binary number. We will see later that this binary number is equal to the value that the hash rate of the driving pulses must have applied to the coil 14 by the trainer 12. This number will therefore be called set hash rate and will be designated by Hc.

Note that this set hash rate Hc is a number always positive and less than or equal to 1.

The determination circuit 17 will not be described in detail, because it can be carried out in various ways and without difficulty by a person skilled in the art. It will simply be mentioned that the determination circuit 17 is arranged, in the present example, so that the number Hc decreases by an amount determined up to a predetermined minimum value, each time the detection signal provided by the output 16c of circuit 16 takes its first state at the end of a motor pulse because this motor pulse has caused correct rotation of the motor rotor 13. In addition, the number Hc increases to its maximum value each time the signal detection takes its second state at the end of a motor pulse because the latter did not cause the motor rotor to rotate correctly 13.

The output of gate 7 is connected to the counting input C of a counter 18 formed, in this example, of seven flip-flops connected in cascade in a conventional manner and which have not been shown separately. The binary number formed by the states "0" or "1" of the direct outputs of these seven flip-flops, which constitute the outputs S of the counter 18, can therefore take values ranging, when expressed in decimal notation, from zero to 127. This binary number will be called number n1 in the rest of this description.

The counter 18 has an input R connected to the output of the inverter 9, and it is arranged so that the number n1 mentioned above is maintained at zero as long as this entry R is in state "1".

The output of gate 8 is connected to the counting input C of a counter 19 which is identical to counter 18 and which will therefore not be described in more detail here. We will simply mention that the binary number present at the outputs S of the counter 19 will be called number n2 in the rest of this description, and that this number n2 is also kept at zero as long as the input R of the counter 19, which is also connected to the output of the inverter 9, is found in state "1".

As will be described in detail below, the numbers n1 and n2 which just mentioned vary during each motor impulse applied to the coil 14 of the motor 13, the number n2 always being greater or equal to the number n1. For a reason which will be made clear later, the n1 / n2 ratio, which also varies during each motor pulse, will be called effective hash rate and will be designated by the He reference.

We will also see that, in the present example, this ratio n1 / n2, and so the effective hash rate He, can take a very large number of separate values, all positive and less than or equal to 1.

The outputs S of the counters 18 and 19 are respectively connected to inputs E1 and to inputs E2 that a calculation circuit 20 comprises. This computation circuit 20 will also not be described in detail here, as it can be carried out in various ways and without difficulty by a person skilled in the art. We will simply mention that the computing circuit 20 is arranged so as to divide the number n1 by the number n2 and supply to its outputs S, in binary form, the result of this division, i.e. the number He. It will also be mentioned that the calculation circuit 20 is arranged so that the number He is equal to zero when the numbers n1 and n2 are themselves equal to zero.

For a reason which will be made clear later, the outputs S of the calculation circuit 20 and the outputs S of the determination circuit 17 are respectively connected to inputs E1 and to inputs E2 which comprises a comparator circuit 21 having an output S connected to the information input D of the flip-flop 10.

Comparator 21 will also not be described in detail. We will simply mention that it is arranged so that its output S is at the state "0" when the number He present at its inputs E1 is greater than number Hc present at its inputs E2, and that this output S is in state "1" when this number He is less than or equal to the number Hc.

Before starting to describe the operation of the device shown in Figure 1, it will be noted that, in the present example, the flip-flops 3, 4 and 10 as well as the counters 18 and 19 react to the passage of state "1" to state "0" of their inputs S and R, respectively C. In others terms, the output Q of the flip-flop 3 takes the state "1" or the state "0" depending on whether its input S or its input R goes from state "1" to state "0". Similarly, the exit Q of flip-flops 4 and 10 take the state of their input D when their input C goes from state "1" to state "0", and the content of counters 18 and 19, that is to say the numbers n1 and, respectively, n2 increase by one each the counting input C of these counters goes from state "1" to state "0", provided of course that their input R is in the state "0".

To simplify the description which follows, the periodic signals provided by outputs 2a, 2b and 2c of time base 2 will be respectively signal 2a, signal 2b and signal 2c.

Furthermore, it will be admitted that, at the beginning of this description and to make this in a concrete case, the number Hc present at the outputs S of the circuit of determination 17 is equal to 0.7, or 70%, this value having been chosen arbitrarily. The circumstances under which this Hc number varies will be discussed below.

The description of the operation of the device in FIG. 1 will be done now by starting arbitrarily at a time when the signals 2a, 2b and 2c pass simultaneously from state "1" to state "0". This moment will be called instant T0.

It is well known that the signal 2c takes alternately and periodically the states "0" and "1". In the rest of this description, we will call instants T those where the signal 2c takes the state "0". Furthermore, these instants T will be numbered from time T0, which will therefore be followed by times T1, T2, T3, ... etc. Similarly, we will call instants J those where the signal 2c takes the state "1", and these instants J will also be numbered from time T0. This instant T0 will therefore be followed by instants J1, J 2, J3 ... etc, each of these last being located between two instants T.

To avoid having to repeat it several times in the rest of this description, we will note here that each instant T is separated from the previous one and the following by a delay equal to a period of signal 2c, that is to say approximately 61 μs in the this example. Similarly, it will be noted that each instant J is separated from instant T previous and instant T following by a delay equal to half a period of signal 2c, i.e. approximately 30.5 µs.

We will also admit that, at time T0, the output Q of flip-flop 4 is at state "1". We will see later in what circumstances this exit Q of the flip-flop 4 goes to state "0".

As will be made clear later, the Q output of flip-flop 3 is at the state "0" just before time T0. It follows that entries 12a and 12b of the formatter 12 are then also in state "0", so that the coil 14 is disconnected from source 15. It also follows that the numbers n1 and n2 are both zero since the output of the inverter 9, and therefore the inputs R counters 18 and 19 are in state "1".

The number He present at the outputs S of the calculation circuit 20 is therefore also zero and therefore less than the number Hc, which will be recalled to be worth 0.7 in this example. The output S of comparator 21 and, therefore, the input D of the flip-flop 10 are therefore in state "1".

At time T0, the output Q of the flip-flop 3 goes to state "1", which has no no effect on flip-flop 4 whose output Q remains in state "1". However, the output of the inverter 9 and the inputs R of the counters 18 and 19 pass to the state "0", so that these can start to function.

At time T0, signal 2c also goes to "0", so that the output Q of flip-flop 10, whose input D is then in state "1", takes this state "1".

The three inputs of door 5, and therefore the input 12a of the trainer 12, now being in state "1" while the entry 12b of the latter remains at state "0", a current begins to flow from output 12c of this formatter 12 at its output 12d through the coil 14 of the motor 13. In other words, this coil 14 is connected, by the formatter 12, to the power source 15. In other words, the trainer 12 begins to apply an impulse drive to coil 14 at time T0.

In addition, the inputs of doors 7 and 8 are all in the state "1", so The same is true for the counting inputs C of counters 18 and 19. The numbers n1 and n2 therefore do not change and both remain zero.

At time J1, i.e. around 30 µs after time T0, signal 2c passes again in the state "1", so that the output of the inverter 11 changes to the state "0", from same as the outputs of doors 7 and 8 and, therefore, the counting inputs C counters 18 and 19. The numbers n1 and n2 therefore both take the value 1.

The number He, which we will recall is equal to the ratio n1 / n2, therefore also takes the value 1 and therefore becomes greater than the number Hc. The output S of comparator 21 therefore takes the state "0", as does input D of flip-flop 10.

When signal 2c returns to state "0" at time T1, that is to say approximately 61 µs after time T0, the output Q of the flip-flop 10 returns to the state "0" since the input D of this flip-flop 10 is then itself in the state "0".

The input C of the counter 18 is therefore maintained in the state "0" although the output of the inverter 11 changes to state "1" at this time T1, while the input C of counter 19 returns to the state "1".

The passage of the output Q of the flip-flop 10 to the state "0" causes the passage of the input 12a of the formatter 12 also in the state "0". The trainer 12 therefore disconnects the coil 14 from the power source 15 and puts the latter in short circuit. Current flowing in coil 14 is therefore not abruptly interrupted, but decreases in a way that depends, as is well known to those skilled in the art, on the characteristics electric and magnetic motor 13.

At time J2, i.e. around 30.5 µs after time T1, signal 2c returns to state "1" and the output of the inverter 11 returns to state "0".

We see that only the input C of the counter 19 then goes from state "1" to state "0", since the input C of counter 19 has been maintained in state "0" as seen above.

It follows that, at this instant J2, the content of the counter 19, that is to say the number n2, takes the value 2 while the content of the counter 18, that is to say the number n1, remains equal to 1.

From this same instant J2, the value of the number He, which is equal to n1 / n2, therefore becomes equal to 0.5, that is to say less than the number Hc.

The output S of the comparator 21 and the input D of the flip-flop 10 resume therefore state "1", so that when signal 2c returns to state "0" at at time T2, the output Q of the flip-flop 10 returns to state "1". It follows that the formatter 12 again connects the coil 14 to the power source 15, and that the current passing through this coil 14 begins to increase again.

It also follows that the input C of the counter 18 also returns to the state "1", so that when the output of the inverter 11 returns to the state "0" at time J3, or approximately 30.5 µs after time T2, the content of the two counters 18 and 19 increases by one. The number n1 therefore takes the value 2 and the number n2 the value 3. It follows that the number He takes the value 0.66, which is still less than the value of the number Hc, which is 0.7. The output S of comparator 21 therefore remains in state "1". The Q output of the flip-flop 10 therefore remains in state "1" when signal 2c returns to state "0" at the moment T3.

The input 12a of the formatter 12 therefore remains in the state "1" after this instant T3, so that the coil 14 remains connected to the source 15.

At time J4 when the signal 2c returns to state "1", the content of the two counters 18 and 19 again increases by one, so that the numbers n1 and n2 take the values 3 and 4 respectively.

The number He therefore takes the value 0.75, and therefore becomes greater than number Tc. The output S of comparator 21 therefore goes to state "0". AT at time T4, the output Q of the flip-flop 10 therefore returns to the state "0", and the trainer 12 again disconnects coil 14 from source 15.

The process described above continues to run until the signal 2b returns to state "0" about 7.8 ms after time T0, ie at the instant T128 as we can easily see. At this moment T128, the output Q of flip-flop 3 returns to state "0". We can easily see that this output Q of the flip-flop 3 remains in this state "0" until signal 2a returns itself in the state "0", that is to say 1 second after the instant T0 in the present example. During this time, the exits of doors 5 and 6 as well as the inputs 12a and 12b of formatter 12 are kept at state "0", so that the coil 14 is disconnected from the source 15. The driving pulse which had started at time T0 therefore ends at this time T128.

It is easy to see that, during this driving impulse, the rate of effective hash He oscillates on either side of the value of the hash rate Hc setpoint, i.e. 0.7 in this example. Furthermore, at the end of this driving impulse, this effective hash rate He practically reaches this value of the set hash rate Hc.

The passage of the output Q of the flip-flop 3 to the state "0", at time T128, also causes the flip-flop 4 to switch, the reverse output of which Q takes the state "1". It follows that, during the next driving pulse, which will start when the signal 2a returns to the state "0", it will be the output of the gate 6 and the input 12b of the formatter 12 which will alternately change state d 'a manner analogous to that which has been described above with regard to the output of the door 5 and the input 12a of the formatter 12, the latter then remaining in the state "0". The current which will circulate in the coil 14 when the input 12b of the formatter 12 is in the state "1" will then have the opposite direction to that which it had in the previous case.

The output Q of the flip-flop 3 being in the state "0" since the instant T128 mentioned above, the output of the inverter 9 then takes the state "1", so that the numbers n1 and n2 become zero again.

The transition to state "1" of the output of the inverter 9 causes also the production by circuit 16 of the detection signal already mentionned. In response to the first state of this detection signal, i.e. if the motor pulse which has just ended has caused a rotation motor rotor 13, the determination circuit 17 decreases the Hc number present at its outputs S and gives it, for example, the value 0.69.

During the next motor impulse, a process similar to that which has been described above will take place but the effective hash rate He which will calculated at each instant J of this next impulse will be compared to this new value, 0.69, of the set hash rate Hc.

At each instant T, during this new motor impulse, the trainer 12 will therefore connect coil 14 to source 15 or disconnect this coil 14 from this source 15 depending on whether, at this same instant T, the rate effective hash of He will either be 0.69 or less, or greater than this value.

The effective hash rate He will therefore oscillate on either side of 0.69 during this new motor impulse and, at the end of the latter, it will practically reach this value. At the end of this new impulse drive, the determination circuit 17 again decreases the value of the rate of setpoint hash Hc if this driving pulse caused a rotation motor rotor 13.

We see that as long as the motor impulses applied to the coil 14 cause correct rotation of the motor rotor 13, the rate set hash Hc, and therefore the effective hash rate He decreases, similarly of course that the amount of electrical energy consumed by the coil 14.

If, at the end of a driving pulse, the detection signal produced by the circuit 16 takes its second state because the rotor of motor 13 does not turned correctly in response to this driving impulse, the circuit of determination 17 gives the hash rate Hc present at its outputs S a predetermined value for the catch-up pulse, this value possibly be for example its maximum value, that is to say 1. It follows that, during this catch-up pulse, the effective hash rate He, which will be calculated as described above, will also be equal to 1 depending the previous example. The coil 14 of the motor 13 will therefore be connected in permanence at source 15.

The amount of electrical energy supplied to this coil 14 during this catch-up pulse will therefore be maximum, which will allow, in principle, the rotor of the motor 13 to catch up with the pitch that it did not execute in response to the previous driving impulse. Those skilled in the art will understand easily that means must be provided for the flip-flop 4 to resume, during this catch-up motor impulse, the state it had during the previous driving impulse, and so that this catch-up impulse is applied to coil 14 as soon as possible after the end of this pulse previous. These means have not been shown, because they have no direct relationship with the present invention and that their realization does not pose of a problem specific to a person skilled in the art.

In the aforementioned case of a missed step (i.e. the case where the rotor of the motor 13 has not turned correctly in response to a driving impulse), the set hash rate Hc is increased for the driving pulse next.

In the example of the device according to the present invention which has just been described, each motor impulse is subdivided into 128 elementary periods each starting at one of the instants T0 to T127, and the coil 14 is either connected to the source 15 is disconnected from the latter during each of these elementary periods.

The number of elementary periods during which the coil 14 is connected to source 15 can therefore vary, theoretically at least, from 1 to 128. The number of different values that the rate of effective chopping of the driving impulses is therefore, always theoretically, equal to 128, these values ranging from 1/128, or about 0.008, to 128/128, that is to say 1.

Obviously, in practice, the hash rate of an impulse motor cannot have a value lower than a minimum value which depends on various factors such as the characteristics of the motor ordered by this impulse, the importance of the mechanical load caused by its rotor or the voltage supplied by the source which supplies the device. The Applicant has found that, in general, it is necessary for the coil of a motor such as those commonly used in timepieces small volume, in wristwatches for example, or at least connected to its power source for about 20 periods elementary, which corresponds to a hash rate of about 0.16. There are none nevertheless, despite this limitation, the number of different values that can take the hash rate, which is greater than 100 in this example, is much larger than in known devices.

We also see that the resolution of hash rates is worth approximately 0.008, which is a significant improvement over known devices.

It follows from the above that the amount of electrical energy consumed by the stepper motor can be controlled by the load mechanical actually driven by the rotor thereof in a way much finer than in known devices.

This amount of electrical energy consumed by the stepper motor not can therefore be reduced even more than in known devices, this which results in an increase in the lifespan of the source that provides this energy or, for the same lifetime of this source, by a decrease in volume it should have.

It should be noted that these advantages of the device according to the present invention are obtained without the latter having to include a logic circuit complex and bulky combinatorial, which would be the case if we wanted increase, in a known device, the number of different values of the rate hash of the driving impulses.

It will also be readily seen that, in a device according to the present invention such as that just described, the periods elementary during which the coil 14 is connected to the source 15 are distributed regularly over the duration of the motor pulse whatever the hash rate of the latter, and this without the need to take any special measures to that effect.

• le taux de hachage de consigne Hc est égal à N1/N2 dans lequel N2 est le nombre total des périodes élémentaires qui forment l'impulsion motrice et N1 est le nombre de ces périodes pendant lesquelles la bobine du moteur doit être connectée à la source d'alimentation du dispositif. N2 est évidemment aussi égal à la somme du nombre N1 et d'un nombre N3 qui est le nombre de périodes élémentaires pendant lesquelles la bobine du moteur doit être déconnectée de la source. On peut donc écrire : Hc = N1N1 + N3 la somme N1 + N3 étant bien entendu égale à N2. Pendant une impulsion motrice quelconque, N1, N2 et N3, de même bien entendu que Hc, sont des nombres constants,
• à un instant T quelconque, qui sera noté T(i) et qui est situé à la fin d'une période élémentaire P(i), on a : He(i) = n1(i)n2(i) où n1(i) est le nombre des périodes élémentaires de l'impulsion motrice pendant lesquelles la bobine 14 a été connectée à la source 15 entre l'instant T0, c'est-à-dire le début de cette impulsion motrice, et l'instant T(i), et n2(i) est le nombre total de périodes élémentaires qui se sont écoulées entre ces instants T0 et T(i).

Another embodiment of a device according to the present invention is based on the following considerations:

• the set chopping rate Hc is equal to N1 / N2 in which N2 is the total number of elementary periods which form the driving pulse and N1 is the number of these periods during which the motor coil must be connected to the source d power to the device. N2 is obviously also equal to the sum of the number N1 and a number N3 which is the number of elementary periods during which the motor coil must be disconnected from the source. We can therefore write: Hc = N1 N1 + N3 the sum N1 + N3 being of course equal to N2. During any motor impulse, N1, N2 and N3, just as of course as Hc, are constant numbers,
• at any time T, which will be noted T (i) and which is located at the end of an elementary period P (i), we have: He (i) = n1 (i) n2 (i) where n1 (i) is the number of elementary periods of the driving pulse during which the coil 14 has been connected to the source 15 between the instant T0, that is to say the start of this driving pulse, and l 'instant T (i), and n2 (i) is the total number of elementary periods which have passed between these instants T0 and T (i).

• selon le procédé de la présente invention, il faut savoir si, à cet instant T(i), He(i) est inférieur ou égal à Hc, ou si He(i) est supérieur à Hc. Dans le premier cas, il faudra connecter la bobine 14 à la source 15 pendant la période élémentaire suivante commençant à cet instant T(i), c'est-à-dire la période P(i+1). Dans le deuxième cas, il faudra déconnecter la bobine 14 de la source 15 pendant cette période P(i+1).

We can also write: He (i) = n1 (i) n1 (i) + n3 (i) where n3 (i) is the number of elementary periods during which the coil 14 has been disconnected from the source 15 between the instants T0 and T (i), the sum n1 (i) + n3 (i) being of course equal to n2 (i),

• according to the method of the present invention, it is necessary to know whether, at this instant T (i), He (i) is less than or equal to Hc, or if He (i) is greater than Hc. In the first case, it will be necessary to connect the coil 14 to the source 15 during the following elementary period starting at this instant T (i), that is to say the period P (i + 1). In the second case, it will be necessary to disconnect the coil 14 from the source 15 during this period P (i + 1).

• En utilisant les équations (1) et (2) ci-dessus, on voit que : He(i) - Hc = n1(i)n1(i) + n3(i) - N1N1 + N3

et après simplification : He(i) - Hc = n1(i)·N3-n3(i)·N1[n1(i) + n3(i)]· [N1 + N3] In other words, we must know, at time T (i) if we have: He (i) - Hc ≤ 0 or He (i) - Hc> 0

• Using equations (1) and (2) above, we see that: He (i) - Hc = n1 (i) n1 (i) + n3 (i) - N1 N1 + N3

and after simplification: He (i) - Hc = n1 (i) · N3-n3 (i) · N1 [n1 (i) + n3 (i)] · [N1 + N3]

We see that the denominator of this last fraction is always positive. The sign of the difference [He (i) - Hc] is therefore always that of the numerator of this same fraction, which will be designated by M (i). So we have : M (i) = n 1 (i) · N3 - n3 (i) · N1

We also see that the determination of the quantity M (i) at an instant T (i) indirectly constitutes a determination of the effective hash rate He (i) at this instant T (i). We also note that if M (i) is less than or equal at zero, the same applies to the difference He (i) - Hc, which means that He (i) is less than or equal to Hc. On the contrary, if M (i) is greater than zero, it is likewise of the difference He (i) - Hc, which means that He (i) is greater than Hc.

• Ce qui précède est évidemment valable pour tous les instants T, à l'exception de l'instant T0, pour lequel on admettra de préférence que M(0) = 0. A l'instant T(i-1) qui précède immédiatement l'instant T(i), on a donc : M(i-1) = n1(i-1) · N3 - n3(i-1) · N1
• Si, à l'instant T(i-1), on avait M(i-1) ≤ 0, la bobine 14 a été connectée à la source 14 pendant la période élémentaire P(i) qui a commencé à cet instant T(i-1). Donc, pendant cette période P(i), seul n1 a augmenté d'une unité, alors que n3 n'a pas changé. On a donc, à l'instant T(i) : n1(i) = n1(i-1) + 1 et n3(i) = n3(i-1) Il en découle dans ce cas que l'équation (5) devient : M(i) = [n1(i-1) + 1]·N3 - n3(i-1)·N1 et donc : M(i) = M(i-1) + N3
• Si par contre, à l'instant T(i - 1), on avait M(i-1)>0, la bobine 14 n'a pas été connectée à la source 15 pendant la période P(i). Pendant cette période P(i), n1 n'a donc pas changé, alors que n3 a augmenté d'une unité. On a donc, à l'instant T(i) : n1(i) = n1(i - 1) et n3(i) = n3(i -1) + 1 II en découle que, dans ce cas, l'équation (5) devient : M(i) = n1(i-1)·N3-[n3(i-1)+1]·N1 et donc : M(i) = M(i - 1) - N1 ou ce qui revient au même, M(i) = M(i-1) + (-N1)
• On voit que si on connaít la valeur et le signe de la grandeur M au début d'une période élémentaire quelconque, on peut facilement calculer la valeur et le signe de cette grandeur M à la fin de cette même période élémentaire, qui est aussi le début de la période élémentaire suivante.

To know if, at time T (i), the coil 14 must be connected to the source 15 or not, it suffices to determine if, at this time T (i), M (i) is less than or equal to zero or, respectively, greater than zero, which can be done quite easily during the elementary period P (i) as will be seen below.

• The above is obviously valid for all times T, with the exception of time T0, for which we will preferably admit that M (0) = 0. At time T (i-1) which immediately precedes l 'instant T (i), we therefore have: M (i-1) = n1 (i-1) · N3 - n3 (i-1) · N1
• If, at time T (i-1), we had M (i-1) ≤ 0, the coil 14 was connected to the source 14 during the elementary period P (i) which started at this time T ( i-1). Therefore, during this period P (i), only n1 increased by one, while n3 has not changed. We therefore have, at time T (i): n1 (i) = n1 (i-1) + 1 and n3 (i) = n3 (i-1) In this case, it follows that equation (5) becomes: M (i) = [n1 (i-1) + 1] · N3 - n3 (i-1) · N1 and so : M (i) = M (i-1) + N3
• If on the other hand, at time T (i - 1), we had M (i-1)> 0, the coil 14 was not connected to the source 15 during the period P (i). During this period P (i), n1 has therefore not changed, while n3 has increased by one. We therefore have, at time T (i): n1 (i) = n1 (i - 1) and n3 (i) = n3 (i -1) + 1 It follows that, in this case, equation (5) becomes: M (i) = n1 (i-1) · N3- [n3 (i-1) +1] · N1 and so : M (i) = M (i - 1) - N1 or what is the same, M (i) = M (i-1) + (-N1)
• We see that if we know the value and the sign of the quantity M at the beginning of any elementary period, we can easily calculate the value and the sign of this quantity M at the end of this same elementary period, which is also the beginning of the next elementary period.

We also see that this calculation does not require, in both cases possible, than a simple addition, which is obviously easier to achieve that the division that is required in the form of execution depicted in the figure 1.

Figure 2 shows schematically and by way of example not limiting a device according to the present invention in which the hash rate effective He is calculated and compared to the set hash rate Hc of a indirectly and using the considerations just made.

As in the case of Figure 1, this device is used to control the stepper motor of an electronic timepiece which is designated by the general reference 22.

The various components of this timepiece 22 which are designated by the references 2 to 6 and 9 to 16 are respectively identical to the components of the timepiece 1 of FIG. 1 which are designated by the same references and will therefore not be described again here.

In the device of FIG. 2, the output 16c of the detection circuit 16 is connected to the input E of a determination circuit 23 having two groups of outputs designated respectively by S1 and S2.

As will be made clear later, the binary number formed by the states "0" and "1" of the outputs S1 of the circuit 23 is equal to the number (-N1), that is to say, the number, changed sign, of the elementary periods of each driving impulse during which the coil 14 must be connected to the source 15. Likewise, the binary number formed by the states "0" and "1" of the outputs S2 of circuit 23 is equal to the number N3 of the elementary periods of each drive pulse during which the coil 14 must be disconnected from source 15.

It will be recalled that the sum of the numbers N1 and N3 is equal to the total number, designated above by N2, of the elementary periods which form each motor impulse.

Like circuit 17 in Figure 1, circuit 23 therefore determines, from indirectly in this case, the set hash rate Hc that must have each driving pulse applied to the coil 14 of the motor 13.

The determination circuit 23 will not be described in detail, because it can be carried out without difficulty by a person skilled in the art. We will mention simply that it obviously has to be arranged so that the number N1 decreases to a predetermined minimum value, for example, by one each time the detection signal supplied by circuit 16 takes its first state at the end of a driving pulse, this signal thereby indicating that this driving impulse caused correct rotation of the motor rotor 13. In the same case, the number N3 must obviously increase by one. The determination circuit 23 must also be arranged so that the number N1 increases, for example, to its maximum value each time the detection signal takes its second state at the end of a pulse drive, this signal thereby indicating that the rotor of the motor 13 has not turned correctly in response to this driving impulse. In this same case, the number N3 must obviously decrease.

The outputs S1 and S2 of the determination circuit 23 are respectively connected to inputs E1 and E2 that a circuit has selector 24 which will also not be described in detail here, because it is a circuit well known to specialists. We will simply mention that the selector 24 further comprises outputs S and a control input C. In addition the selector 24 is arranged so as to connect its outputs S to its inputs E1 or to its inputs E2 depending on whether its control input C is in the "0" state or at state "1". In other words, the states "0" or "1" of the outputs S of the selector 24 form the number (-N1) or the number N3 depending on whether its entry of command C is in the state "0" or "1".

The outputs S of selector 24 are connected to first inputs E1 that includes an adder circuit 25 still having second inputs E2 and S outputs.

The adder 25 will also not be described in detail, since it is a circuit well known to specialists. We will simply mention that the adder 25 is arranged so that the states "0" or "1" of its outputs S permanently form a binary number equal to the sum of binary numbers formed by the states "0" or "1" of its inputs E1 and, respectively, of its E2 inputs.

The outputs S of the adder 25 are connected to inputs E that comprises a register 26 having in addition outputs S, an input of command C connected to the output of the inverter 11, and a setting input zero R.

Register 26 is also a well known circuit and therefore will not described in detail here. It will simply be mentioned that it is arranged so that all its outputs S are maintained in state "0" as long as its input R is in state "1". It will also be mentioned that when this entry R is in the state "0", the outputs S of register 26 take the same state as its inputs E in response to the passage of its control input C from state "1" to state "0". In other words, the binary number formed by the states "0" and "1" of outputs S of register 26 becomes equal to the binary number formed by the states "0" and "1" of its inputs E when its command input C changes from state "1" to state "0". As will be made clear later, the number binary formed by the states "0" or "1" of the outputs S of register 26 is the number M defined above.

The outputs S of register 26 are connected on the one hand to the inputs E2 of the adder 25 and, on the other hand, to the inputs E of a comparator 27 having an output S connected to the control input C of the selector 24 and to the input information D of the flip-flop 10. Comparator 27 will also not be described in detail, as it is also a well known circuit. We will mention simply that this comparator 27 is arranged so that its output S either in the logical state "0" when the binary number formed by the states "0" or "1" of its inputs E, that is to say the number M, is greater than zero, and that this output S is in state "1" when this binary number M is lower or equal to zero.

As in the description of the operation of the device in Figure 1, instants T will be called the instants when signal 2c goes from state "1" to state "0". In particular, the instant T when the two signals 2a and 2b pass also in state "0", that is to say the instant of the start of a driving pulse, will be called instant T0.

Likewise, the instants when signal 2c returns from state "0" to state "1" will be called instants J.

Just before an instant T0, the output Q of the flip-flop 3 is in the state "0", of so that entry "R" in register 26 is state "1". The outputs S of this register 26 are therefore all in the state "0", so that the number M formed by these states of these outputs is zero. As we will easily see, this number M still has this zero value at time T0. It will therefore be called M0.

The number M0 being zero, always just before the instant T0, the outputs S of comparator 27 and information input D of flip-flop 10 are in the state "1". In addition, the selector 24 connects its inputs E2 to its outputs S so that the number N3 is present at the inputs E1 of the adder 25. The number M0 present at the inputs E2 of the adder 25 being zero, it is also the number N3 which is present at the outputs S of this adder 25 and therefore at the register entries E 26.

As in the case of the device in FIG. 1, it will be assumed that, always just before time T0, the output Q of flip-flop 4 is state "1".

It is easy to see that, as in the example in Figure 1, each motor impulse and subdivided into 128 elementary periods. We will admit arbitrarily and, to take a concrete example, that the number N1 of these elementary periods during which the coil 14 must be connected to the source 15 is equal to 90 in this example or, which is the same, as the number (-N1) present at the outputs S1 of the determination circuit 23 is equal to (-90). It follows that the number N3 present at the outputs S2 of this circuit of determination 23 is equal, in this example, to (128 - 90), that is to say to 38. We see that, in this case, the set hash rate Hc is equal to 90/128, or practically 0.7, i.e. it has the same value as in the example of figure 1.

At time T0, the signal 2a supplied by the time base 2 goes to the state "0", so that the output Q of flip-flop 3 changes to state "1". Simultaneously, signal 2c also goes to state "0". The input D of the flip-flop 10 then being in state "1", the output Q of this flip-flop 10 also changes to state "1". As in the case of FIG. 1, the formatter 12 then connects the coil 14 from motor 13 to source 15 so that current begins to flow in this coil 14.

At the instant J1 which immediately follows the instant T0, the signal 2c returns to state "1", so that entry C of register 26 changes to state "0". In response to this passage, the outputs S of register 26 take the state of inputs E of the latter. In other words, the number M takes a value M1 which is equal to the number N3, that is 38 in this example. This number M1 being so now greater than zero, the output S of comparator 27 takes the state "0", as well as input D of the flip-flop 10. In addition, the selector 24 now select the number (-N1) present at its inputs E1, so that this number (-N1) is applied to the inputs E1 of the adder 25. The outputs S of this adder 25 therefore now have an equal number to N3 + (-N1), in this example, a number equal to (38 - 90), that is to say (-52).

At the instant T1 which follows the instant J1, the signal 2c returns to the state "0". The output Q of flip-flop 10, whose input D is now in state "0", takes also this state "0", so that the formatter 12 disconnects the coil 14 of the source 15. At the next instant J, that is to say the instant J2, the signal 2c returns to state "1", so that entry C in register 26 changes to state "0". The number M therefore takes a value M2 which is that of the number present at this instant at the entries E of this register, that is (-52) in this example.

This value M2 being less than zero, the output S of the comparator 27, as well as the input D of the flip-flop 10, resumes the state "1". It is therefore again the number N3 which is selected by the selector 24 and applied to the inputs E1 of the adder 25.

The number present at the outputs S of this adder 25 therefore takes a value equal to M2 + N3 or, in this example, (-52 + 38), that is to say (-14).

At the next instant T, that is to say at the instant T2, the signal 2c resumes the state "0", so that the output Q of the flip-flop 10, whose input D is now in state "1", also takes state "1". Trainer 12 connects so again coil 14 at source 15.

At the next instant J, that is to say at the instant J3, the entry C of the register 26 returns to state "0", so that the number M takes a value M3 equal to that of the number present at the outputs S of the adder 25, that is (-14) in this example.

The number M being still negative, it is still the number N3 which is applied to the inputs E1 of the adder 25, so that the outputs S of this adder 25 now have a number equal to (-14 + 38), i.e. 24.

For the same reason, the output Q of the flip-flop 10 remains in the state "1" at the following instant T, that is to say at the instant T3, so that the coil 14 remains connected to source 15.

At time J4, the number M takes a value M4 which is equal to 24 in this example. This value being positive, it is now the number (-N1) which is applied to the inputs E1 of the adder 25, so that the S outputs of the latter have a number equal to (24 - 90), or (-66).

Furthermore, the number M always having this positive value M4 at the instant T4, the output Q of the flip-flop 10 returns to the state "0" at this instant T4 and the trainer 12 disconnects the coil 14 from the source 15.

As in the case of FIG. 1, the process which has just been described continues to run until signal 2b returns to state "0" at the instant T128, or approximately 7.8 ms after the instant T0.

The effects of the transition to state "0" of the output Q of the flip-flop 3 at this instant T128 are practically the same as in the case of this figure 1 and will not be described again. We will simply note that, at this moment T128, the transition to state "1" of the output of the inverter 9 has the effect that the number M present at the outputs S of register 26 returns to its value M0 of which saw that it is zero.

In addition, the determination circuit 23 gives a new value to the numbers N1 and N3 in response to the detection signal it receives from the detector 16 just after time T128, this new value being determined from the as described above.

We see that the device according to the present invention shown in the Figure 2 is even simpler than that of Figure 1, while presenting the same advantages as the latter compared to known devices.

In summary, it can be seen that in the method according to the present invention, each driving impulse is subdivided into a certain number of periods elementary, 128 in this example, all having the same duration. In in addition, one calculates directly or indirectly, with each elementary period, the value that the effective hash rate He takes at the start of the period next elementary, and we compare this value, also directly or indirectly, to that of the set hash rate Hc. Finally, at this beginning of the next elementary period, we connect the coil of the stepper motor to the source that powers the device or we disconnect this coil from this source according to the above comparison shows that the hash rate effective He is less than or equal to the set hash rate Hc or that this He rate is higher than this Hc rate.

Obviously many changes can be made to the device according to the present invention, two examples of which have been described above, without departing from the scope of this invention. So by example, the comparator 21 of the device of FIG. 1 can be replaced by a subtractor circuit operating the subtraction of the set rate Hc of the effective rate He. In this case, the device must also include a circuit comparing the result of this subtraction with zero and providing the input D of the flip-flop 10 a signal having the state "1" if this result is less or equal to zero and the state "0" if this result is greater than zero.

Always for example, the duration of each motor impulse applied to the stepper motor coil may be different from the one it has in the examples above. Likewise, each motor impulse can be subdivided into a number of elementary periods different from that which has been used in the examples above.

In addition, calculating the effective hash rate He and comparing it with the set hash rate Hc, which are performed at times J located in the middle of each elementary period in the examples above, can very well be carried out at another time located elsewhere than in this environment of this elementary period.

In addition, the circuit for determining the set hash rate Hc can be arranged so that the latter rate varies differently from what has been described above in response to the signal from the detection circuit rotation or non-rotation of the motor rotor.

In addition, the invention can obviously be used in a device other than an electronic timepiece, the signal causing the application of a driving impulse to the motor coil, i.e. signal 2a in the examples above, which may very well have a different periodicity than this last, or even not be periodic.

Claims (9)

A method of controlling a stepping motor comprising a rotor provided with a permanent magnet and a coil magnetically coupled to said magnet, said method comprising applying a driving pulse to said coil each time said rotor is to rotate by a step, said driving pulse comprising connection periods during which said coil is connected to a source of electrical energy and disconnection periods during which said coil is disconnected from said source, the ratio between the total duration of said connection periods and the total duration of said driving pulse being equal to a set chopping rate (Hc), said method being characterized in that it comprises: the subdivision of said driving pulse into a first number (N2) of consecutive elementary periods, of durations at least substantially equal and each beginning at a determined instant (T); at least indirect determination, at each determined instant (T), of an effective hash rate (He) which is equal to the ratio between on the one hand a second number (n1) which is the number of said elementary periods which have elapsed since the start of said motor pulse and which are part of said connection periods and, on the other hand, a third number (n2) which is the total number of said elementary periods which have elapsed since the start of said motor pulse; at least indirect comparison, at each determined instant (T) between said effective hash rate (He) and said set hash rate (Hc); connecting said coil (14) to said source (15) at said determined time (T) if said comparison shows that said effective hash rate (He) is less than or equal to said set hash rate (Hc); and the disconnection of said coil (14) from said source (15) at said determined time (T) if said comparison shows that said effective hash rate (He) is greater than said set hash rate (Hc). Method according to claim 1, characterized in that the said second number (n1) and said third number (n2) are obtained by counting, from the start of said motor pulse, the periods elementary forming part of said periods of connection and, respectively, all the elementary periods, and by the fact that said rate effective hash (He) is obtained by dividing said second number (n1) by said third number (n2). Method according to claim 2, characterized in that it includes a direct comparison of said effective hash rate (He) to said set hash rate (Hc) by a comparator circuit (21). Method according to claim 2, characterized in that it involves subtracting said effective hash rate (He) and said rate set hash (Hc) and a comparison of said subtraction with zero. Method according to claim 1, characterized in that: that it involves the supply of a fourth number (-N1), which is always negative, and of a fifth number (N3), which is always positive or zero, said fourth (-N1) and fifth number (N3) being such that the ratio between, on the one hand, the absolute value (N1) of said fourth number (-N1) and, on the other hand, the sum of said absolute value (N1) and said fifth number (N3) is equal said set hash rate (Hc); that said determination of said effective hash rate (He) comprises the calculation, at each determined instant (T), of a sixth number (M) which is equal to the sum of a seventh and an eighth number, said seventh number being equal to the value that said sixth number (M) had during the elementary period immediately preceding said each determined instant (T) and said eighth number being equal to said fourth number (-N1) if said seventh number is greater than zero and being equal to said fifth number (N3) if said seventh number is less than or equal to zero; and which said comparison between said effective hash rate (He) and said set hash rate (Hc) includes the comparison of said sixth number (M) with zero. Device for carrying out the method of claim 1, comprising means for determining; (16, 17; 16, 23) for determining said set hash rate (Hc), characterized in that it further comprises: means (2) for producing a periodic signal (2c) for subdivision of said driving pulse, said signal (2c) defining said determined instants (T); calculation means (18 to 20; 24 to 26) responding to said periodic signal (2c) to calculate, at least indirectly, a quantity (He; M) representative of said effective hash rate (He) at each of said determined times (T ); comparison means (21; 27) responding to said quantity (He; M) for producing a comparison signal between said effective hash rate (He) and said set hash rate (Hc); hashing means (5, 6, 10, 12) responding to said comparison signal for connecting said coil (14) to said source (15) if said effective hash rate (He) is less than or equal to said set hash rate (Hc) and to disconnect said coil (14) from said source if said effective hash rate is greater than said set hash rate (Hc). Device according to claim 6, characterized in that said calculation means (18 to 20) include a first counter (18) responding to said periodic signal (2c) and to said hash signal for producing said second number (n1), a second counter (19) responding said periodic signal (2c) to produce said third number (n2) and a divider circuit (20) responding to said second (n1) and said third number (n2) to produce said effective hash rate (He). Device according to claim 7, characterized in that said comparison means (21) include a comparator circuit (21) responding to said effective hash rate (He) and to said hash rate of setpoint (Hc) for producing said comparison signal. Device according to claim 6, characterized in that: said determining means (23) are arranged to supply a fourth number (-N1) which is always negative, and a fifth number (N3) which is always positive or zero, said fourth (-N1) and fifth number (N3) being such that the ratio between, on the one hand, the absolute value (N1) of said fourth number (-N1) and, on the other hand, the sum of said absolute value (N1) and said fifth number (N3) is equal to said set hash rate (Hc); said calculation means (24 to 26) include a selector circuit (24) having first inputs receiving said fourth number (-N1), second inputs receiving said fifth number (N3) and outputs having a selected number which is equal to said fourth (-N1) or said fifth number (N3) depending on whether said comparison signal has a first or a second state, an adder circuit (25) having first inputs connected to the outputs of said selector circuit (24), second inputs receiving a sixth number (M) and outputs having, at each determined instant (T), the sum of a seventh and an eighth number, said seventh number being equal to said selected number and said eighth number being equal to the value that said sixth number (M) had during the elementary period immediately preceding said determined instant (T), and a register (26) having inputs connected to the outputs of said add circuit iterator (25) and outputs connected to the second inputs of said adder circuit (25) and having said sixth number (M) in response to said periodic signal (2c); and said comparison means (27) include a comparator circuit (27) having inputs connected to the outputs of said register (26), an output providing said comparison signal, and arranged so that said comparison signal has its first or second state depending on whether said sixth number (M) is less than or equal to zero, or that said sixth number (M) is greater than zero.

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