DESIGN PRINCIPLES FOR DIGITAL A.

OF F R E Q U E N C Y

FREQUENCY-MEASURING

M. M a r g o l i n

MULTIPLIERS INSTRUMENTS UDC621.374.4.

The greater part of frequency-muhiplier research amounts to an analysis of the circuits based on a nonlinear conversion of the input signal with a subsequent picking out of the required harmonic [1]. Multipliers of that type are widely used in various radiotechnical devices which operate at a fixed frequency; however, they are not suitable for application over a wide frequency range. The basic characteristic of frequency multipliers which are suitable for digital frequency-measuring instruments consists of their output signal processing being reduced to the measurement of the multiplied frequency by counting the number of periods over a reference time interval. Therefore, the requirements of a pure output-signal wave form which is characteristic for radiotechnical frequency multipliers does not apply to the multipliers of the above type. The wide-band frequency multipliers are examined in the literature only from the point of view of their electrical circuitry, whereas their principles of muhiplication are not described. In order to simplify the study of a whole number of such multiplier circuit designs, evaluate to a certain extent the applicability boundaries of each design and facilitate the selection of the multiplier-design principles we suggest their classification according to the basic principles of their frequency multiplication. Taking into consideration that all electronic devices react in the long run to an instantaneous input signal, it is convenient to take as a starting point for their classification the waveform of the multiplied frequency signal. The most frequently used signals have either a sinusoidal, sawtooth, or pulse waveform. Such a classification of the frequency-multiplication principles is shown in the table, in which the minus sign means that it is impossible to use a certain operation with the given waveform. The division of multipliers into groups shown in the table serves not only to underline the existence of different principles for frequency multiplication, but also to find an adequate mathematical apparatus for their description, and to predict correctly in experimental investigations the most important characteristics of multiplying devices. Below we examine certain multiplication principles which have been hardly mentioned in print. Frequency Multipliers with Level Quantization. In digital frequency-measuring instruments the amplitude discriminator which shapes the counting pulses uses, as a rule, the information only about a single point on the input-signal curve, for instance, the point of its transition through zero in one direction. In the case of a continuous signal it is possible to form several counting pulses over one period at the instants when the input signal attains each of its preselected values, i.e., it is possible to use level quantization (Fig. 1).* The multiplied frequency signal can be represented not only by a voltage, but also in the form of a spatial displacement (circular scanning, rotating magnetic field). Multipliers of this type can use quantizing devices consisting of amplitude discriminators and masks [2-5]. The simplest block schematic of a level-quantization multiplier with the signals indicated at various points of the circuit is shown in Figs. 2a and 2b (where AD is an amplitude discriminator).

Fig. 1.

* Figures 1 and 2b represent in an idealized form a sawtooth voltage (the sawtooth flyback time is eliminated).

Translated from Izmeritel'naya Tekhnika, No. 1, pp. 52-55, January, 1967. Original article submitted July 14, 1965.

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~f

iOutput

I !

Fig. 3. Fig. 2a. X i n ( ft i ~n ,' ~

~

V _ ~ f o u = Kfi n

C

Input ba /

2

-~t

N

Fig, 4,

I

A4

--~t

B

--~t

Level quantization should obviously be regarded as an ideal multiplication method. Its practical value is reduced by the requirement for a constant amplitude and waveform of the multiplied frequency.

|

C {~___J

~ D [-71_ILl

t

P_hase-Shift

ii

Frequency

Multipliers.

Let

=t

us examine a device consisting of k phase-shifting circuits (PSC) and k shapers (~I,), each of which generates a pulse E =t when the signal fed to it crosses a given level (for instance, zero). The pulses are fed from the shapers to a collecting Fig. 2b. circuit (Fig. 3). If all the phase-shifting circuits are fed at the same time with a sinusoidal signal of frequencyf, the output pulses will have a uniform repetition and a frequency k f . Moreover, each of the phase-shifting circuits must provide an input-signal phase shift of I

Aq)i--

k

( i = 0 ; 1; . . . ; k - - l ) .

The above device is a frequency multiplier based on shifting the phase of the multiplied-frequency signal. The phase shifting of pulsed signals whose frequency changes but little with time can be replaced by their shifting with respect to time. In such a case the pulse-repetition frequency multiplier should consist of delay lines, each of which produces a delay of ~i=

r2ta_. k -(i=0;

1; . . . ; k - - l ) .

In addition to delay lines a shock-excited generator can also be used which provides constant-frequency oscillations between pulses with the input repetition frequency [6]. It can be easily be seen that frequency multiplication with a time shift amounts to dividing the period of the input signal. In a general case, when the multiplied frequency is not known in advance, the multiplication process can begin only at the end of a period. Frequency Multipliers with Balancing. These are automatic control systems.* The controlled members in a generator whose periodic oscillations have an arbitrary shape. The simplest frequency-multipIier circuit of this type (Fig. 4) consists of a comparison element 1, controlled generator 2,and frequency divider 3 connected in the feedback circuit. The generator is controlled by the unbalance signal and adjusted in such a manner that the divider's output signal frequency is equal to the multiplied frequency. The multiplication factor is equal to a division factor of the feedback divider. * In radiotechnology such circuits are known as automatic frequency-trimming systems with a divider in the feedback circuit. 73

Input signal type No,

I

II

Output signal type

[Continuous

Pulsed

Operation

4Ill

Functional conversion with ' filters* iLevel quantization

-

[3,4]

l

Phase or time Ishifting Ill

+ [2,51

+

+

~j

+ [71

[lOl

Continuous!Balancing or pulsed ]

[~ + [gJ

* The use of such a frequency-multiplication signal conversion as, for instance, ideal linear or square-law detection requires only the separation of the dc compo!nent in the output signal. In the remaining cases passband or tuned filters are required. i

The comparison element may consist of a circuit whose output signal is proportional to the difference between the frequencies or phases of the multiplied-frequency and feedback signals. In the first instance the frequency multiplier is a static control system, and in the second it is an astatic system. In practice only astatic systems are used. The implementation of the comparison element depends on the shape of the input signal. Thus, in the frequency multiplier designed by Burne and Goldstein [7] a phase comparator with a sawtooth characteristic is used, whereas in the multiplier of V. O. Brooks [8] a sinusoidal comparator is used. A reversible counter can be used as a comparison element for a pulsed input signal [9]. Multipliers with phase comparators are useful when it is necessary to obtain a high phase stability of the output signal. It is advisable to use multipliers with reversible counters in the case of input signals with a stray frequency modulation. CONCLUSIONS

It will be seen from this review of various methods for multiplying frequency that, in addition to the generally known multipliers which use functional conversion of the input signal, there can also be designed multiplying devices based on level quantization, on shifting of signals with respect to their phase or time, and on balancing. It should be noted that the output signal of the first group of multipliers has the same shape as their output signal. The frequency multiplication process in devices of the second and third groups can be accompanied by a transformation of the signal shape. The application of a given type of multiplier in digital frequency-measuring instruments depends basically on the maximum permissible variation of the transducer's output frequency. Thus, in transducers with a small deviation it is, probably, advisable to use frequency multipliers of the first group. It is obvious that balancing multipliers whose comparison element consists of a reversible counter are predominantly suitable for transducers with a large frequency deviation. The problem of obtaining the required frequency multiplier characteristics, consisting of their speed of operation and precision, requires a detailed investigation. LITERATURE 1.

74

CITED

M.E. Zhabotinskii and Yu. L. Sverdlov, Foundations of the Theory and Technology of Frequency Multiplication [in Russian], Izd. "Sovetskoe radio," Moscow (1964).

2, 3, 4. 5. 6. 7. 8. 9. 10.

A, Ya, Rotshtein, Author's Certificate No, 124004 (1958); Bulletin of Inventions No, 22 (1959), A. G, Pinchuk, Author's Certificate No. 67166 (1946); Bulletin of Inventions No, 9 (1946), A . K . Zavolokin and Yu, E. Rabkin, Author's Certificates Nos, 119718, 123243 (1958); Bulletins of Inventions Nos, 9 and 20 (1959), G. A, Kondrashkova, Scientific Notes of Graduate Students and Candidates of the M, I, Kalinin Leningrad Polytechnic Institute (1964), Mak-Alir, Zarubezhnaya radio41ektronika (Foreign Radio Electronics), No. 4 (1960), Burneand Goldstein, Bell Technical Journal, 41, No. 2 (March, 1962), Brooks, Electronics, 32 (July 17, 1959). V.G. Knorring. Izmerit. tekhn., No. 7 (1964). Ya. V. Novosel'tsev, E. E. Afanas'ev, N. A. Smirnov, and E. P. Ugryumov. "Semiconductor frequency meter for nuclear-resonance magnetometers," in the collection: Geophysical Instrument Making,6th Issue [in Russian], Izd. "Nedra," Leningrad (1960).

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