SU1751846A1 - Method of and device for generating width-modulated pulse train - Google Patents

Abstract

The invention relates to the field of pulsed technology and can be used in automatic control devices, communications and measurement technology. The purpose of the invention is to expand the frequency range by suppressing the low frequency spectral zones of the frequency spectrum of the signal. The purpose of the invention is achieved by forming, on a time interval, additional 2K pulses with one-sided pulse-width modulation symmetrically arranged with respect to a central pulse, the amplitude and shift of which are determined using the above formula. The device for implementing the method contains a pulse-width modulator 2. The introduction of an additional synchronous control unit 1 and a multiplying digital-analog-1 converter 3 into it allows the formation of a pulse-width-modulated pulse sequence in accordance with the proposed formula. 3 il. Y t

Description

U0 +

2 Ui cos 2 n

t

-O, l 1. K.

n 1

A device for implementing a method for generating a pulse-width modulated pulse sequence comprises a pulse-width modulator, whose analog input is connected to the input bus, as well as a digital-to-analog converter and a synchronous control device, the output of which clock pulses are connected to the clock input of a pulse-width modulator, the output of which connected to the reference input of the D / A converter, the digital inputs of which are connected to the outputs of the synchronous control device, and you od - with an output device bus

The frequency spectrum of a signal with a tone-sided one-sided pulse-width modulation of the first kind (OSIMM1) is considered in detail in work 1, p. 216, 230-233, on the basis of which one can obtain the following

The type of the frequency spectrum of the signal with ERM1, obtained from relation (1), is shown in FIG. 1 When demodulating this signal using a low pass filter

(LPF), the idealized amplitude-frequency characteristic (AFC) of which is shown in FIG. 1 dotted, demodulation distortion inevitably occurs. These distortions are due to the fact that, in addition to the useful component of the spectrum with a frequency Q, the spectral components of the spectrum are primarily of the form - I Q,

Demodulation distortion can be

attenuate somewhat by reducing the frequency range of the signal to be converted and the corresponding decrease in the passband band of the low-pass filter, which is one of the drawbacks of the known signals with

OSHIM1.

By shaping the signals with OSIM1 according to the proposed method, it is possible not only to avoid reducing the frequency range of the signal being converted, but if necessary, to significantly expand it. This possibility is based on the suppression in the frequency spectrum of a number of low-frequency spectral zones formed by the first harmonics (a, 2 by the corresponding side components o) ± Q,

2y ± I Q Ko) ± I Q for which

". In this case, demodulation distortions can occur due to the components of the spectrum of the form (K + 1) CD-IQ, the level of which, due to the properties of the Bessel functions, is significantly lower than the components of the type o) I Q.

To carry out the planned suppression procedure, in particular, the first spectral zone of the frequency spectrum formed by the first harmonic of soy by the lateral components a ± Q, it suffices to add the original width-modulated pulse with amplitude Uo to the two width-modulated and symmetrically located pulses at each clock interval T with respect to the original pulse. In this case, the same amplitudes Ui of additional pulses, having the modulation coefficients t and the same moduli identical with the original duration TO the moving signal sin (Q t + f) must be chosen from the equation

Uo + 2lhcoswTi 0,

 (Uo + 2Ui) T0 (U

00

n 1

where t is the displacement (phase) of the leading fronts

excluding the sign of each of the two additional $ 3

pulses relative to anterior xma.sin (Qt) + 5)

of the front of the initial pulse with amplitude

Uo (fig. 2).

To prove the condition (2) you can

use the expression for the frequency-40 -Dgmax sin (Qt + y)}, the spectrum of 1, p.216 of the original pulse-width modulated pulse sequence with amplitude U0

x {sin n sh (t + -j-) - sin

From the relation (5 the spectral zone p, ra harmonics p (o and representing n w ± I Q in the next

UOoiunMl (t):

U0T0

- -mT-sln (Qt +) + 45

five

and. Ј J. {, Inna (t-Ј-n 1 P7G

-sin pof - y - DtMax sln (Qt + p)}

(3)

Using formula (3) as applied to sequences of pulse-width modulated additional pulses with amplitudes and taking into account the trigonometric ratio sln (a + / J) + sln (a fi) 2sin a -sin ft, it is possible to obtain an expression for the spectrum of the total signal of both sequences of additional pulses:

Junim1 (1) - 2 U Go + iryHn (Qt)

20

00

+1

t, - g- cos n WTI {sin n sh (t + 4

 4P LЈ.

25

Sin n (W t-4p- DGmax Sln (Qt + p)}

thirty

(four)

From expressions (3) and (4) find the frequency spectrum of all three sequences of pulses (Fig. 2):

UloilJHMl (t)

 (Uo + 2Ui) T0 (U0 + 2Ui) T0 v

T Irt fX

00

n 1

3 $

xma.sin (Qt) + 5)

2T

Up +2 Ui COS P (OT

P

Dgmax sin (Qt + y)},

x {sin n sh (t + -j-) - sin n -j

(five)

Dgmax sin (Qt + y)},

From relation (5), we can distinguish the spectral zone η located around the harmonic η (σ and represented by the components η ± ± I Q in the following form

- “1Д5 software and -1g 1 +

+ (Qt + y)},

which can be converted to mind

Uo TO. Do to

From expressions (5) and (6) it follows that, if the amplitude Ui had been properly amplified, additional pulses could be pressed in the signal spectrum (Fig. 2), either

4JQ I. Oh, / i, “w w ..-. ".. ..4..V V -I"

iooshim1 (+ 2 t mrs (spectral zone p w ± I Q. Condition

50

Wooin (t)

Uo +2 Ui cos nojTi n l

five

x {sin n ft) (t + -y-) - sin n w t- -y- -LGmax Sin (Qt +)},

(6)

From expressions (5) and (6), it follows that by appropriately choosing the amplitude Ui of additional pulses, any signal can be suppressed in the signal spectrum (Fig. 2).

“W w ..-. ".. ..4..V V -I"

spectral zone n w ± I Q. Condition

suppression of such a zone arises from equality

(6):

U0 + 2Uicosn w ri 0 (7)

The condition for suppressing the first zone (w ± I Q) is fulfilled with n 1. Then, from equation (7), one finds the relationship U0 + + 2Uicosn at n 0. coinciding with equality (2).

Having proved condition (2), it can be concluded that to suppress the first zones of the frequency spectrum of a signal with OSIM1, it is necessary to form such a signal from 2K + 1 sequences with OSIM1, having the same duration t0 of unmodulated pulses, the same modulation factors Gl-g and one the same modulating signal sln (Q t + f. In this case, at each clock interval T 2K pulses are positioned symmetrically (on the leading edges) relative to the average pulse with amplitude Uo, the amplitudes Ui are symmetrically disposable pulses and their phases m must be Choose according to the system of equations in which the ratio is used

Uo + |

n 1

2Uicos 2l-p - 0, 1 1, K,

(eight)

2l

which is a generalization of condition (7).

The system of equations (8) has an infinitely large number of solutions, which can be reduced by introducing some real restrictions. In particular, such a restriction is the choice of the amplitudes Ui of pulses with ER1, taking two values + Uo or -Uo. which allows to simplify the formation of pulse sequences. In this case, from the system of equations (2), the values of the phases are

In other cases, due to the convenience of forming, it may be advisable to evenly (along the leading fronts) position with a step g of all 2K + 1 pulses at each clock interval, i.e. r t. At the same time, in order to exclude the overlap of individual impulses of sequences with OSIM1, it is necessary to consider

t nv JL 1 With this, condition (8) will take

/ IX T 1

following view:

Ј 2 Ui cos 2n n

n 1

IT T

 0.1 1, K (9)

Example. A pulse width modulated pulse signal is formed by the proposed method, which provides suppression in the frequency spectrum of the first

spectral zone (K 1).

In the first example, it will be necessary to form three impulses in each transformation interval T, for which condition (8) takes the following form:

U0 + 2Uicos 2D - 0,

(ten)

Prin in T b t, from equation (10) find

Uo + 2Uicos 60 ° 0, whence Ui -U0. A device is proposed for carrying out the above method of forming a width-modulated sequence, the functional diagram of the device is shown in FIG. 3. The device consists of a synchronous control unit 1, a pulse-width modulator 2 and a multiplying digital-analog converter

(DAC) 3, while the output of the triggering pulses of the synchronous control unit 1 is connected to the triggering input of the pulse-width modulator 2, the output of which is connected to the input of the reference signal of the DAC 3,

the digital inputs of which are connected to the outputs of the synchronous control unit, and the output to the output bus of the device.

The device works as follows.

At each clock interval T, the modulator 2 is started from the synchronous control unit 1 (2K + 1) times and generates (2K + 1) non-overlapping pulses with QLLJHM1 respectively at the output. These pulses, modulated in duration and having a fixed amplitude U0 at the time of formation of the pulses and equal to zero at the rest of the time, are fed to the input of the reference signal of the DAC 3. In the intervals between each of the (2K + 1) starts of the modulator 2, the synchronous control unit 1 generates codes in parallel form, arriving at the digital inputs of the DAC 3. In this case, the amplitude and polarity of the output

the pulse signals of the DAC 3 will be determined by the values of the codes on its digital inputs, and the long pulse outputs will be set by the output signals of the pulse width modulator 2. With appropriate selection and generation of codes in the synchronous control unit 1, as well as the start intervals of the modulator 2 , at the output of the DAC 3, a pulse-width modulated pulse sequence can be formed in full

according to the conditions for the above method of forming a pulse width modulated pulse sequence.

Claims (2)

Claim 1. Method of forming a pulse-widthd pulse sequence, including the formation at equal clock intervals of duration T pulses with amplitude U0 and with one-sided pulse-width modulation, characterized in that, in order to expand the frequency range of the signal being converted, at each clock interval with a duration of T, an additional 2K pulses with one-sided pulse-width modulation are formed, all 2K + 1 pulses being located on a time interval of uniform phase-shifted by an amount t, the average amplitude of the pulse is set equal to Do. and the amplitude DI of the remaining pulses symmetrically located in both sides of the mean impulse are set according to the system of equations U0 + n 1 2 Ut cos In n - 0,1 rr. 2. A device for generating a pulse-width modulated pulse sequence containing a pulse-width modulator, the analog input of which is connected to the input bus, characterized in that a digital-to-analog converter and a synchronous control unit are added to it, the output of the trigger pulses of which is connected to the starting the input of a pulse-width modulator, the output of which is connected to the input of the reference signal of a digital-to-analog converter, whose digital inputs are connected to the outputs of synchronous control unit, and the output - with the output bus device.