EA040762B1 - DEVICE AND METHOD FOR DETERMINING LIMITS OF WORKING RANGE OF CLASSICAL PHASE-LOCKED SYSTEMS - Google Patents

Description

The invention relates to the field of electrical engineering, in particular to radio electronics and computer architectures, can be used in transceivers and communication and control engineering, radio automatics, automatic control systems, in particular, when designing various types of phase locked loop systems (hereinafter PLL), characterized by the possibility determine the optimal parameters to achieve a synchronous mode within one beat and stable operation of PLL systems, which helps to increase noise immunity and improve the filtering properties of the system.

It is known that testing a real model is a laborious process and cannot guarantee the correct operation of the phase locked loop system for all possible values of the initial data and parameters of its components, such as the initial phase difference of the reference and adjustable oscillators, the initial state of the low-pass filter, so this method is rarely used. on practice.

It is known that the analysis of models of phase locked loop systems in the signal space is a difficult task, since these models are described by non-autonomous nonlinear differential equations [1].

It is known that the most common method used in the design and analysis of PLL systems is the method of modeling and analyzing the created models of phase lock in the phase space of signals [2, 3]. In particular, PLL models in the phase space of signals are used to find estimates of the range of frequency differences between the reference and adjustable oscillators corresponding to the mode in which synchronization is achieved within one beat both at the start of the PLL system and when the frequency of the reference oscillator is instantly switched. Such a range is called the capture band without slipping [4-6]. Despite the fact that finding such ranges is complex and laborious, estimates of the frequency tolerance exist [7]. However, due to the use of simplified low-pass filters in the design of such systems, the corresponding systems have insufficiently high noise immunity.

A phase-locked loop device [8] is known, the essence of which is to increase the stability that determines the frequency acquisition band, while maintaining high accuracy of phase synchronization. However, the known device is not sufficiently stable due to the fact that during its operation phase synchronization with beats is allowed, and also determining the capture band without slip using the known device is a difficult task.

There is a known scheme [9], the operation of which is based on the formation of two control signals using a phase detector, which receives two highly stable frequency signals generated by a reference and adjustable oscillator, and a frequency difference measurement unit connected to the output of the phase detector and generating a signal corresponding to the difference frequencies. However, the determination of the capture band without slipping using the known device is time-consuming and has insufficient accuracy.

A method is known for determining the operating parameters of a phase-locked-loop generator frequency and a device for its implementation [10], based on setting an additional signal depending on two given highly stable frequency oscillations of the reference and adjustable signal. An additional signal is used to determine the operating parameters of the phase locking system and reduces the complexity of their determination. The disadvantage of the known method and device is that the beats in the process of synchronization of the system are detected empirically, and such detection is time-consuming. In addition, the known method and device are not informative enough to determine the operating range in which phase synchronization is achieved within one beat.

There is a method for determining the boundaries of the operating range of a pulse generator of phase synchronization systems and a device for its implementation [11], the closest to the claimed group of inventions, taken as a prototype for the claimed invention. The essence of the known method is that two highly stable frequency oscillations of a rectangular signal are set, one of which is selected as a reference, and the second is adjustable, the frequency range of the first and second signals is selected from 20 kHz to 20 GHz, the first and second coefficients of the filter transfer function are set low frequencies, after which, according to the ratio of the reference and adjusted signals, an additional signal is set, which is filtered using a low-pass filter, its amplitude is increased using a DC amplifier, and the additional signal is used as a control signal, and the permissible deviation of the frequency of the adjusted signal from the reference is given by the appropriate formulas, the choice of which depends on the comparison function.

The disadvantages of this prototype are insufficient noise immunity due to the use of simplified low-pass filters, as well as the impossibility of applying the known method to systems with reference and adjustable harmonic signals.

The technical result achieved by the new solution is common to the entire group of objects of the claimed invention (a method for determining the boundaries of the operating range of classical phase-locked loop systems and a device for its implementation), and consists in increasing the stability against interference and noise by designing filters lower frequencies in a wider range of parameters.

The specified technical result is achieved by the fact that in the method for determining the boundaries of the operating range of phase-locked loop systems, in which two highly stable frequency oscillations of the signal are set, one of which is chosen as a reference, and the second is chosen as adjustable, and their frequency range is chosen from 20 kHz to 20 GHz , after which, according to the ratio of these two signals, an additional signal is set, which is filtered using a low-pass filter, and the additional signal is used as a control signal, in accordance with the claimed invention, the shapes of the reference and adjustable signals are chosen to be sinusoidal and cosine, respectively, and as a filter low-pass select a second-order low-pass filter with a transfer function of the form:

H(s) = bcs+c s(s+a) + C, where H(s) is the low pass filter transfer function, s is a complex variable, a>0, b>0 and c>0 are the first, second and third coefficients of the transfer function of the low-pass filter, satisfying the relations:

a(a+b)>1, ab%.

and the frequency of the tuned signal is chosen no more than ω _l from the frequency of the reference signal, and the permissible frequency deviation ω _l is given by the relation:

where K is the gain of the DC amplifier.

The specified technical result is also achieved by a new device for determining the boundaries of the operating range of phase locked loop systems, made in a housing containing a reference generator of highly stable oscillation frequency, the output of which is connected to the first input of the phase detector, which is made in the form of a multiplier of two signals, the output of the phase detector is connected to the first input of the low-pass filter, the output of the low-pass filter is connected to the first input of the DC amplifier, the output of the DC amplifier is connected to the control input of the adjustable oscillator of highly stable oscillation frequency, the output of the adjustable oscillator is connected to the second input of the phase detector, the block for determining the boundaries of the operating range, made in the form of an arithmetic controller with a calculation accuracy of at least four decimal places, the output of which is connected to a recorder that fixes the boundaries of the operating range of the phase locked loop system h frequency, the block for setting the gain of the DC amplifier, the first output of which is connected to the second input of the DC amplifier, the second output of the block for setting the gain of the DC amplifier is connected to the first input of the block for determining the boundaries of the operating range, in which, in accordance with the claimed invention, additionally a block for setting the first coefficient of the transfer function of the low-pass filter is installed, the first output of which is connected to the second input of the low-pass filter, and the second output of the block for setting the first coefficient of the transfer function of the low-pass filter is connected to the second input of the block for determining the boundaries of the operating range, the block for setting the second coefficient of the transfer function low-pass filter, the first output of which is connected to the third input of the low-pass filter, the second output of the block for setting the second coefficient of the low-pass filter transfer function is connected to the third input of the block for determining the boundaries of the operating range, block for setting the third coefficient of the low-pass filter transfer function, the first output of which is connected to the fourth input of the low-pass filter, the second output of the block for setting the third coefficient of the low-pass filter transfer function is connected to the fourth input of the block for determining the boundaries of the operating range.

The basis of the claimed invention is the technical problem of improving the accuracy, reliability and stability of the PLL system, reducing the complexity of determining the operating range when designing and testing a phase locked loop system.

The essence of the claimed method is illustrated in Fig. 2, fig. 3, which show the functional dependences of the reference and adjustable signals on time.

In the claimed method, one of the two highly stable frequency signals is selected as a reference one with a sinusoidal shape, which is shown in Fig. 2 as a function of time, where A1 is the amplitude, ωΓ is the frequency, and ^ω ι is the period of the signal. The second of the two high-frequency stability signals is chosen to be tunable with a cosine waveform, which is shown in FIG. 3 as a function of time, where A2 is the amplitude, ω2 is the frequency, and ^ω z is the period of the signal. An additional signal is chosen equal to half the sum of two sinusoidal signals with frequencies equal to ω1-ω2

- 2 040762 ¹ A A and ω ₁ + ω ₂ , and amplitudes equal to 2 ^{1 2}

The claimed invention was tested in the laboratory of St. Petersburg State University and the results of testing are given in the form of specific examples.

Examples of the implementation of the method for determining the boundaries of the operating range of the pulse generator of phase synchronization systems.

Example 1

The boundaries of the operating range of a classical PLL system with a phase detector of the multiplier type were simulated for two highly stable frequency signals, one of which was adopted as a reference with a sinusoidal shape, and the second was adopted as an adjustable one with a cosine shape. Here, the first, second, and third low-pass filter transfer coefficients were set to a=0.1, b=11, c=1, and the DC amplifier gain was set to K=10. The frequency of the reference signal was set equal to ω ₁ = 30 kHz. Permissible frequency deviation ω _l =10 Hz was obtained from the original formula presented in the application. The frequency deviation of the tuned signal from the frequency of the reference signal was chosen not to exceed the permissible frequency deviation: oj'ee = 10 Hz. According to the results of the PLL operation, the obtained value (the frequency of the tuned signal ω/'Ν equal to 30.01 kHz) belongs to the operating range of the PLL, for which synchronization occurs within one beat. In this case, when choosing the deviation of the frequency of the adjusted signal from the frequency of the reference signal (0) / ^ = 15 Hz, exceeding the permissible frequency deviation, choosing the frequency of the adjusted signal (o2 ^free = 30.015 kHz and instantaneous change in the frequency of the reference signal ω1 from 30 kHz to 30.03 kHz, the PLL resynchronization occurred with beats, while choosing the transfer function coefficients a=0.1, b=1, violating the required inequality a(a+b)>1, choosing the frequency of the tuned signal o2 ^free =30.01 kHz and instantaneous frequency change reference signal ω1 from 30 kHz to 30.02 kHz synchronization was not observed.

The versatility of the proposed invention is based on the implementation of a change in the allowable deviation of the frequency of the tuned signal from the frequency of the reference signal, depending on the values of the coefficients of the low-pass filter transfer function and the gain of the DC amplifier, according to the original formula presented in the application. To do this, as can be seen from the claimed method, the allowable frequency deviation is determined and the frequency deviation of the tuned signal is selected, which does not exceed the received allowable value.

As the results of the study of example 1 show, the use of a single method for calculating the allowable frequency deviation allows you to effectively select the frequency deviations of the tuned signal, which guarantee the achievement of a synchronous mode within one beat, which significantly reduces the complexity.

Example 2

The claimed method is also illustrated by a specific example of using a device for implementing this method, the scheme of which is shown in Fig. 1.

A device for determining the boundaries of the operating range of phase locked loop systems, made in a housing (1) and containing a reference generator of a highly stable frequency oscillation (2), the output of which is connected to the first input of the phase detector (3), which is made in the form of a multiplier of two signals, the output of the phase of the detector is connected to the first input of the low-pass filter (4), the output of the low-pass filter is connected to the first input of the DC amplifier (5), the output of the DC amplifier is connected to the control input of the adjustable oscillator of highly stable oscillation frequency (6), the output of the adjustable oscillator is connected to to the second input of the phase detector, a block for determining the boundaries of the operating range (11), made in the form of an arithmetic controller with a calculation accuracy of at least four decimal places, the output of which is connected to a recorder (12), which fixes the boundaries of the operating range of the phase locked loop system, the block assignments to gain coefficient of the DC amplifier (10), the first output of which is connected to the second input of the DC amplifier, the second output of the block for setting the gain of the DC amplifier is connected to the first input of the block for determining the boundaries of the operating range, the device also contains a block for setting the first coefficient of the transfer function of the low-pass filter frequencies (7), the first output of which is connected to the second input of the low-pass filter, and the second output of the block for setting the first coefficient of the transfer function of the low-pass filter is connected to the second input of the block for determining the boundaries of the operating range, the block for setting the second coefficient of the transfer function of the low-pass filter (8) , the first output of which is connected to the third input of the low-pass filter, the second output of the block for setting the second coefficient of the transfer function of the low-pass filter is connected to the third input of the block for determining the boundaries of the operating range, the block for setting the third coefficient of the transfer function of the filter low-pass filter (9), the first output of which is connected to the fourth input of the low-pass filter, the second output of the block for setting the third coefficient of the low-pass filter transfer function is connected to the fourth input of the block for determining the boundaries of the operating range.

- 3 040762

The operation of the claimed device is as follows. The low-pass filter is designed as a second-order low-pass filter with transfer function x bcs+c

H(x) = -—- + c, s(s+a) where H(s) is the low-pass filter transfer function, s is a complex variable, a, b, and c are the first, second, and third coefficients of the low-pass filter transfer function frequencies.

The DC amplifier gain setting block generates the gain value K, and the first, second, and third low-pass filter transfer function setting blocks generate the first, second, and third transfer function coefficients a>0, b>0, and c>0, satisfying the relationships : a(a+b)>1, ab^1.

The values of K, a, b and c are fed to the inputs of the block for determining the boundaries of the operating range, where the permissible deviation of the frequency of the signal of the adjustable generator from the frequency of the signal of the reference generator ωι is determined in accordance with the following relationship:

The registrar, connected to the output of the unit for determining the boundaries of the operating range, registers the permissible deviation of the frequency of the signal of the adjustable generator from the frequency of the signal of the reference generator.

The reference oscillator of a highly stable frequency oscillation generates a sinusoidal signal f ₁ (t) in the range of 20 kHz - 20 Hz with a frequency of ω ₁ , and the adjustable generator of a highly stable oscillation in frequency generates a cosine signal f ₂ (t) in the range of 20 kHz - 20 Hz with a frequency ω ₂ ^free , which is set by no more than ωι from the frequency ω1 of the reference signal.

The signals of the reference and adjustable oscillators are fed to the input of the phase detector, at the output of which a signal is obtained that satisfies the following relationship:

t= where f(t) is the output of the phase detector.

The signal from the output of the phase detector through the first input of the low-pass filter is fed to the series-connected low-pass filter, through the first input of the DC amplifier, and through the control input of the adjustable oscillator, which achieves the technical result, which consists in simplifying and reducing the complexity of determining the operating range of classical PLL systems, increasing the reliability and accuracy by achieving the synchronism mode within one beat, increasing the information content and stability of the system.

Below is an example of a specific implementation of a device for determining the boundaries of the PLL operating range, confirming the operability and achievement of the above technical result by the claimed method.

A specific example of the operation of a device for determining the boundaries of the operating range of the PLL is as follows: the reference and adjustable oscillators generate signals that have the following form:

= A ₁ sin (m ₁ t),

Λ (0 = A ₂ cos(m ₂ (t) t), where the frequency of the signal of the reference generator ω1=30 kHz, the frequency of the signal of the adjustable generator ω ₂ (t) varies depending on the control input, using the gain setting block, the coefficient is set gain of the DC amplifier K=10, and using the blocks for setting the first, second and third coefficients of the transfer function of the low-pass filter set a=0.1, b=11, c=1. the given values of the first, second and third coefficients of the transfer function of the low-pass filter are fed to the corresponding inputs of the low-pass filter.In addition, the given values of the gain, the first, second and third coefficients of the transfer function of the low-pass filter are fed to the corresponding inputs of the unit for determining the boundaries of the operating range. The value of the permissible frequency deviation ωι is calculated by the unit for determining the boundaries of the operating range on in accordance with the stated ratio, i.e. ωι=10 Hz. The calculated value of the permissible frequency deviation ωι is recorded by the recorder.

To achieve the claimed technical result, the frequency of the signal of the adjustable oscillator is set to no more than ωι from the frequency of the signal of the reference oscillator, i.e. ω2 ^ee =30.01 kHz. The signals from the reference and adjustable oscillators are fed to the corresponding inputs of the phase detector, made as a multiplier, at the output of which a signal of the following form is obtained:

/(O \u003d -A ₁ A ₂ (.zm ^w ₁ + ω ₂ (t))0 + 5ΐη ((ω ₁ - ω ₂ (t))ί))

Further, the received signal passes through a series-connected low-pass filter and a DC amplifier, forming a control signal that is fed to the control input of the adjustable oscillator.

- 4 040762

As the results of the study according to example 2 show, the use of a single method for calculating the border of the operating range allows you to set the frequency of the cosine signal of the adjustable oscillator guaranteed within the operating range, which simplifies and reduces the complexity of choosing the deviation of the frequency of the adjusted signal, and also by synchronizing the PLL within one beat, an increase in reliability and accuracy of the PLL.

The results of the studies described in examples 1 and 2, simulating the specific conditions for the implementation of the claimed method and device, showed the efficiency, reliability and versatility of the invention. The achievement of the technical result became possible also by taking into account the universal dependence of the allowable frequency deviation of the tuned signal on the gain of the DC amplifier and the transfer function coefficients of the low-pass filter and the possibility of using a second-order low-pass filter, which, when testing many models, confirmed the versatility of the claimed method and the stability of the device for the entire allowable range of operating parameters of the classical PLL with reference and adjustable generators that generate harmonic signals, compared with the known prototype method.

The technical and economic efficiency of the claimed invention as a whole consists in optimizing and reducing the complexity in designing a PLL by determining the boundary of the operating range, increasing the stability (stability) of the device by achieving the PLL synchronism mode within one beat, expanding the range of operating parameters of the PLL due to the discovered by the authors universal dependence of the allowable deviation of the frequency of the tuned signal on the gain of the DC amplifier and the coefficients of the transfer function of the low-pass filter, and increasing the reliability (accuracy) of the system by taking into account this pattern.

The claimed invention makes it possible to successfully solve the problems associated with determining the operating range of classical PLLs and modeling the operation of the PLL, with determining the optimal parameters corresponding to the rapid achievement of the synchronous mode and stable operation of the PLL, with the construction of more complex PLLs used in wireless transmission of information, as well as in multi-core and multiprocessor computer architectures.

Information sources used

1. Kudrewicz J., Wasowicz S. Equations of phase-locked loop. Dynamics on circle, torus and cylinder. World Scientific, 2007.

2. Aleksandrov, K. D., Kuznetsov, N. V., Leonov, G. A., Neittaanmaki, P., Yuldashev, M. V., Yuldashev, R. V. Computation of the lock-in ranges of phase-locked loops with PI filter. IFAC-PapersOnLine, 2016.

3. Kudryashova, E. V., Kuznetsov, N. V., Leonov, G. A., Yuldashev, M. V., Yuldashev, R. V. Nonlinear analysis of PLL by the harmonic balance method: limitations of the pull-in range estimation. IFAC-PapersOnLine, 2017.

4. Gardner, F.M. Phaselock Techniques. Wiley, 3rd edition, 2005.

5. Stensby, J.L. Phase Locked Loops: Theory and Applications. Taylor & Francis, 1997.

6. Leonov, G. A., Kuznetsov, N. V., Yuldashev, M. V., Yuldashev, R. V. Hold-in, pull-in, and lock-in ranges of PLL circuits: rigorous mathematical definitions and limitations of classical theory. IEEE Transactions on Circuits and Systems I: Regular Papers, 2015.

7. Leonov, G.A., Reitmann, V., Smirnova, V.B. Non-Local Methods for Pendulum-Like Feedback Systems. Stuttgart: Teubner, 1992.

8. RF patent No. 2 565 526 C1; IPC H03L 7/00.

9. USA Patent No. 0.285.467, Int.Cl. H03L7/103, H03L7/0991, H03L7/087.

10. RF patent No. 2 449 463 Cl; IPC H03D 13/00.

11. RF patent No. 2 625 557 Cl; IPC H03D 13/00, G06F 1/12 (prototype).

Terms used

Two signal multiplier: an electronic device with two inputs and one output that generates a signal (voltage) at the output equal to the product of the signals (voltages) supplied to the two inputs.

Phase detector (PD): In electronics, a device that compares the phases of two input signals. Usually, one of them is generated by a voltage controlled signal generator, and the second is taken from an external source. The PD usually has one output signal that controls the phase-locked loop behind it (the task of the phase-locked loop is to make the phases of the input signals the same), in other words, a phase detector is a device designed to create a signal proportional to the phase difference between the generated signal and the reference signal. (There are various electronic implementations of the FD: for example, a two-signal multiplier, XOR, etc.)

Transfer function: one of the ways of mathematical description of a dynamic system. Mainly used in control theory, communications and digital signal processing. Represents

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Claims (2)

differential operator expressing the relationship between the input and output of a linear stationary system. Knowing the input signal of the system and the transfer function, it is possible to recover the output signal. Low pass filter: An electronic or any other filter that effectively passes the frequency spectrum of a signal below a certain frequency (cutoff frequency) and reduces (suppresses) the signal frequencies above that frequency. The degree of suppression of each frequency depends on the type of filter. CLAIM 1. A device for determining the boundaries of the operating range of phase-locked loop systems, made in a housing and containing a reference generator of a highly stable oscillation in frequency, the output of which is connected to the first input of the phase detector, which is made in the form of a multiplier of two signals, the output of the phase detector is connected to the first input of the low-frequency filter frequencies of the second order, the transfer function of which is given by the relation: „Z _λ bcs+c , s(s+a) where H(s) is the transfer function of the low-pass filter, s is a complex variable, a>0, b>0 and c>0 are the first, second and third coefficients of the transfer function low-pass filters satisfying the relations: a(a+b)>1, aYM, the output of the low-pass filter is connected to the first input of the DC amplifier, the output of the DC amplifier is connected to the control input of the adjustable oscillator of highly stable oscillation frequency, the output of the adjustable oscillator is connected to the second input of the phase detector, the detection unit boundaries of the operating range, made in the form of an arithmetic controller with calculation accuracy of at least four decimal places, which determines the permissible deviation of the frequency ωι of the signal of the adjustable generator from the frequency of the signal of the reference generator according to the formula: where K is the gain of the DC amplifier, the output of the block for determining the boundaries of the operating range is connected to the recorder, which fixes the boundaries of the operating range of the phase-locked loop system, the block for setting the gain of the DC amplifier, the first output of which is connected to the second input of the DC amplifier, the second output of the block for setting the gain of the DC amplifier is connected to the first input of the block for determining the boundaries of the operating range, characterized in that the device additionally contains a block for setting the first coefficient of the low-pass filter transfer function, the first output of which is connected to the second input of the low-pass filter, and the second output of the setting block the first coefficient of the transfer function of the low-pass filter is connected to the second input of the block for determining the boundaries of the operating range, the block for setting the second coefficient of the transfer function of the low-pass filter, the first output of which is connected to the third input low-pass filter, the second output of the block for setting the second coefficient of the low-pass filter transfer function is connected to the third input of the block for determining the boundaries of the operating range, the block for setting the third coefficient of the low-pass filter transfer function, the first output of which is connected to the fourth input of the low-pass filter, the second output of the block setting the third coefficient of the transfer function of the low-pass filter is connected to the fourth input of the unit for determining the boundaries of the operating range. 2. A method for determining the boundaries of the operating range of phase locked loop systems according to claim 1, which consists in setting two highly stable signal oscillations in frequency, one of which is chosen as a reference, and the second is chosen as adjustable, and their frequency range is chosen from 20 kHz to 20 GHz, after which, according to the ratio of these two signals, an additional signal is set, which is filtered using a low-pass filter, and the additional signal is used as a control signal, characterized in that the forms of the reference and adjustable signals are chosen sinusoidal and cosine, respectively, as a low-pass filter. frequencies, a second-order low-pass filter is selected with a transfer function of the form: _λbcs +c H(s) = ----- + C, s(s+a) ' where H(s) is the low-pass filter transfer function, s is a complex variable, a>0, b>0 and c>0 is the first, the second and third coefficients of the transfer function of the low-pass filter, satisfying the relations: a(a+b)>l, ab^l, and the frequency of the tuned signal is chosen in such a way that the absolute value of the frequency difference between the reference and tuned signals is less than or equal to the permissible deviation h-6-