US2304134A - Frequency comparator - Google Patents

Description

Dec. 8, 1942. w. H. WIRKLER 2,304,134

v FREQUENCY COMPARATOR Filed May 27, 1941 2 Sheets-Sheet l Qx WWMMQ 8% a:

IN VEN TOR.

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Dec. 8, 1942 w. H. WIRKLE R vFREQUENCY COMPARATOR Filed May 27, 1941 2 Sheets-Sheet 2 INVVENTOR. aware as nira er Edddig FREQUENCY GOMPARATOR Application May 27, 1941-, Serial No. 395,473

12 Claims.

My invention relates broadly to frequency modulation of electrical oscillations and more particularly to a frequency comparator for determining the mean or average frequency of the modulated wave in reference to a fixed frequency, in

order that the center frequency of the modulated wave may be stabilized in a system of the free oscillator type. The frequency comparator of my invention is intended principally for use in conjunction with frequency control means in frequency modulated radio transmission systems but is equally applicable as a mean or average frequency measuring system for a variety of purposes. I

Two methods have been used in the past for determining the mean or average frequency of a frequency modulated wave as required to actuate frequency corrective devices in frequency modulated transmitters of the free oscillator type. The first consists of a crystal controlled oscillator dif- .-fering in frequency from the transmitter fre- 'mean frequency indicator, this device has the disadvantage that its indication depends not only on the frequency of a crystal controlled oscillator but also on the-resonant frequency of its own tuned circuits, which can not well be controlled by piezo-electric crystal elements because they must accommodate a frequency band width determined by audio and deviation frequencies in order to integrate properly over the wholefrequency deviation range.

The second method consists of subdividing the output of the frequency modulated oscillator to such a low carrier frequency that the modulation, considered as phase modulation, amounts to substantially less than ninety degrees phase modulation. The phase of this subdivided wave is then compared with the phase of a constant frequency crystal controlled oscillator in a phase comparing circuit, the integrated output of which actuates either electrical or mechanical frequency correotive means. An interesting characteristic of such an arrangement is that if the mean frequency of the transmitter oscillator differs ever so slightly from the crystal controlled oscillator frequency, a phase difference will eventually appear and the corrective means will be actuated. The main objection to this system is the complexity of the frequency subdividing circuits required.

A third scheme sometimes considered is to compare the frequency of the transmitter oscillator with a crystal frequency differing therefrom by a low audio frequency, and applying the resultant beat note to an audio frequency sensitive network, which can be made much more stable than the intermediate frequency discriminator circuit mentioned first above. This audio network. can, of course, be made operable over the whole deviation frequency range of the transmitter. The chief objection to this scheme is that, in addition to the beat frequency, spurious components dependent on the applied modulation are also present in the audio network and produce faulty op eration.

One of the objects of my invention is to provide an improved frequency comparator which is stable in operation and effective to produce a substantially accurate measur of the mean or average frequency of a frequency modulated wave.

Another object of my invention is to provide a frequency comparator system operative to integrate frequency deviations of the center frequency of a frequency modulated wave over a limited time period and providing a measurement of the net frequency deviation as an indication of the mean or average frequency of the wave at the end of the period.

A further object of my invention is to provide a novel method of frequency comparison employ- .ing'components of a frequency modulated wave and components of an oscillation stabilized atthe center frequency of the modulated wave, the net frequency deviation of the modulated wave with respect to the frequency of the stabilizedoscillation, over a limited time period, being determined to provide a measure of the mean or average frequency of the modulated wave at predetermined intervals,

A still further object of my invention is to provide means for determining the mean or average frequency of a frequency modulated wave in reference to the frequency of a stabilized oscillation at predetermined time intervals, for providing an effective comparison of the average frequency of the modulated wave and the frequency of the stabilized oscillation.

Still another object of my invention is to provide a circuit arrangement employing a stabilized oscillator operative at the desired center frequency of a frequency modulated wave, and means for comparing the frequency of oscillations derived from the oscillator and the frequency of the modulated wave for producing over a limited time a measure of the net deviation of the modulated wave from the frequency of the oscillator, whereby the mean or average frequency of the modulated wave may be adjusted to the frequency of the oscillator.

Other and further objects of my invention reside in the system and circuit arrangement hereinafter described in more detail, with reference to the accompanying drawings, in which:

Figure 1 is a schematic diagram of one embodiment of my invention; Figs. 2 and 3 are theoretical diagrams explanatory of the method employed for frequency comparison in accordance with my invention; and Fig. 4 is a schematic diagram of a modified form of differentiating circuit that may be employed in the arrangement of Fig. 1.

The operation of the frequency comparator of my invention will be explained in terms of a somewhat different conception of a frequency modulated wave. It is well known that a wave of constant amplitude can be represented by a vector rotating at a velocity, in revolutions per second, equal to the instantaneous frequency of the wave in cycles per second. If the wave is frequency modulated, the vector is considered rotating at non-uniform angular velocity. The wave then can not be expressed mathematically as a single frequency, but can be represented as a group of sideband and carrier frequencies, best evaluated by means of Bessels functions. An amplitude modulated wave is considered as a rotating vector of constant angular velocity and 'of varying amplitude; this wave cannot be expressed mathematically as; single frequency either, but can also be represented as a group of sideband and carrier frequencies.

A well-known illustration of an amplitude modulated wave is obtained by considering the observer as rotating in synchronism with the rotating vector, giving the impression of a stationary vector of changing amplitude. Similarly,

' if the observer be considered as rotating in syn chronism with a wave of constant frequency, such as that from an oscillator operating at the mean frequency in a frequency modulation system, the impression will be that of a stationary vector of constant amplitude. At a moment when the frequency modulated oscillator is operating at a frequency diiferent from the mean oscillator frequency, corresponding to a modulated condition, the impression will be that of a vector rotating at a rate, in revolutions per second, equal to the deviation from the mean frequency in cycles per second. In conventional representation, the vector apparently will be rotating clockwise when the wave under observation is of a frequency lower than the mean frequency, and counterclockwise when of higher frequency.

The point of importance here is that this is an illustration of a frequency modulated wave just as completely and uniquely as the stationary vec= tor of changing amplitude is an illustration of an amplitude modulated wave. The Fourier representation of either wave in terms of sideband frequencies is useful for predicting its effect on frequency selective circuits, such as in receiving sets tuned to adjacent channels, but is by no means necessary for a complete representation of the wave and for an analysis of the mechanism by which its average frequency may be determined. Considering this rotating vector corresponding to a frequency modulated wave as seen from a platform rotating at mean oscillator'frequency, so to speak, it is obvious that its instantaneous velocity (hereinafter taken to mean its angular velocity in revolutions per second) is equal to its frequency deviation (taken to mean the difference between its instantaneous frequency and the mean frequency) and the direction of rotation is equal to the sense or direction of its frequency deviation. The frequency deviation can then be said to be equal to the rate of change of phase angle.

For comparison of the actual mean frequency of the frequency modulated wave with th desired mean frequency, a stabilized oscillation of the desired mean frequency is adopted as a reference, and the frequency deviation is measured with respect to the stabilized oscillation. If the mean frequency of the modulated wave remains at the desired value, the deviation with respect thereto will be the same as with respect to the stabilized oscillation, but if the mean frequency varies, the deviation with respect to the stabilized oscillation will be greater or less by the amount of the variance of the mean frequency of the modulated wave, which variance is the factor to be determined.

The average frequency deviation with respect to the desired mean frequency for a time period of one second, for example, will be numerically equal to the net number of apparent revolutions of the vector, observed as above described. Thus, if the average frequency deviation is zero, the vector may, with modulation, rotate for a time in one direction and then in the other but will not make any net progress in one direction over the assumed period of time. If the average frequency deviation is, say 100 cycles per second high, the vector will, at the end of the one second, have rotated counterclockwise one hundred revolutions more than clockwise.

The frequency comparator circuit of my invention was devised especially to indicate the average frequency deviation over a limited time period, and not the instantaneous frequency deviationas doesthe discriminator" in a frequency modulated receiver. Accordingly, it operates only to sum up or "keep score on the net apparent revolutions of the vector over the prescribed period of time. A preferred form of circuit for accomplishthis function is shown schematically in Fig. 1, wherein the frequency modulated wave is applied at terminals i to the grids of detector tubes 2 and S. A constant frequency, crystal controlled oscillator is provided at 4, operating at a frequency equal to' the desired mean or average frequency of the wave applied at l. The output of oscillator i is applied directly to a second grid of detector tube 2 and through a degree phase shifting network 5 to a second grid of detector tube 3. The output of tube 3 passes through amplifier i, differentiating circuit l0, amplifier 8, and transformer II to the input of a balanced rectifier 9. The output of tube 2 passes through amplifier 6 and transformer l2 to the second pair of input terminals on balanced rectifier The output of rectifier 9 passes through resistor l3 to an integrating'condenser id, and to the output terminals I5 which are connected across condenser l4;

Referring to Fig. 2, a and I) represent vectorially t e oscillator frequency voltages applied in I v plied to the With vector V in phase quadrature to the grids of detector tubes 3 and 2, respectively. V indicates the rotating vector representing the frequency modulated wave. X represents the low frequency output from detector tube 3 and Y the low frequency output from detector tube 2. The construction of Fig. 2 is justified from the well-known theory of demodulation in that if the applied constant frequency voltage, such as a and b, is large com- The balanced rectifier 8 serves essentially as a reversing switch so that when the voltage Y obtained from detector tube 2 through amplifier '5, and transformer i2, is positive, the output of transformer H is, in effect, connected to integrating circuit i3|4 in one sense, and when Y is negative it is applied in the opposite sense.

I The voltage dt I through amplifier 8 and transformer ii, subject to the. reversing action ofrectifier 5,. controls the rate ofcharge (or discharge) of condenser Hi, through resistor i3 so that the voltage across condenser It is substantially the integrated value which may be written as da: ad!

orfdx for short. The j'dx is substantially proportional in magnitude to X, but its sign is determined by whether is positive or negative, and, on the reversing action of rectifier 9, determined by whether Y is positive or negative.

Figure 3 shows how the voltage at terminals l5 becomes proportional in magnitude and sense to the net number of revolutions of vector V. one of the upper quadrants of the figure as shown and with vector V, rotating counterclockwise, the rate of change of X is toward the negative and i2 n dt is negative. Since Y is positive,

is applied in reversed sense to the circuit 13-46 and the accumulated condenser it is considered is shown by the arrow to be increasing when vector V rotates counterclockwise. When vector integrating charge in positive. ,I-Ience j'dx V is in one of the lower quadrants, it is seen that a counterclockwise rotation of the vector produces a positive value of and since if is negative, rectifier 9 applies this directly to the integrating circuit rather than in reversed sense. to show Ida still increasing with counterclockwise rotation. Conversely, the fdx will be found to be decreasing with clockwise rotation of vector V.

It thus becomes evident that no matter what the angular movement of the vector, whether it be uniform rotation, reciprocation, or non-uni-' form rotation in one direction, as long as it remains of constant amplitude and as long as its instantaneous velocity is not so great that the circuit of Fig. 1 can not pass faithfully the resulting fluctuations in Y and X, and; if the dif-- :ferentiating and integrating circuits perform faithfully, each net revolution counterclockwise will resultin a certain increase in charge on condenser it and each revolution clockwise will result in an equal decrease in charge. Hence the charge on condenser it at the end of a specified period of time will be proportional to the total number of net revolutions of the vector V.

In practice, it is necessary that the circuits of Fig. 1 pass audio components equal to the highest instantaneous deviation frequency encountered with frequency modulation in order that the components Y and b faithfully reproduced at the input terminals of rectifier 8. If the audio frequency is higher than the deviation frequency, the vector V never accomplishes a complete phase revolution but merely oscillates. Since this oscillating component is of no interest in determining the net phase turnover or revolutions of the vector, it is not necessary that the circuit be capable of passing the highest audio frequency if this is higher than the highestdeviation frequency.

It is, of course, necessary that the differentiatin g circuit it perform substantially perfectly up to the highest deviation frequency so that its output voltag is always proportional to l dt However, it is neither necessary nor desirable that the integrating circuit iii-4 c be perfect. If it were, and the average frequency deviation were other than zero, the charge on condenser it would continue to increase indefinitely. In practice, the

resistance of rectifier 9 is comparatively low and the charge-will leak back through the rectifier and the circuit i3-ld is not, therefore, a perfect inmrator. All that is required of it, however,

is that it integrate approximately correctly for relatively short periods of time such as one second or less. Under these conditions, the voltage across terminals it will be substantially proportional to the mean frequency deviation over the preceding short period of time, and poled according to' whether this frequency deviation is positive or negative. Hence this output voltage may be used to actuate frequency corrective means such as a frequency control tube connected to the oscillator Hence, the arrow is drawn circuit of the transmitter, or adapted to any other of a variety of purposes.

The use of transformer coupling between tubes 6 and 8 and the rectifier circuit 9 as shown is preferred because the D. C. voltage at terminals i5 is thereby isolated from the remainder of the circuit, which permits this voltage to be used directly or with a. conventional D. C. amplifier to actuate a frequency control device. The two transformers H and i2 should have uniform frequency response and identical delay factors up to the highest deviation frequency. For example, if the transmitter oscillator operates at 5 mo, and the output frequency is 45 mo., obtained from the oscillator through two tripler stages, a desired output frequency modulation capability might be i100 kc., corresponding to at the oscillator. The audio transformers would therefore be required to handle a maximum frequency of 11 kc. If the lowest frequency the transformer can handle is 20 C. P. 8., a mean oscillator frequency deviation of 20 C. P. S., corresponding to an output frequency deviation. of 180 C. P. 8., might escape uncorrected; however, this is well within the present requirements of the art.

To improve the low frequency response, it is possible to substitute resistance coupling with a. phase inverter stage for the transformer coupling shown. This would not permit the output D. C. voltage tobe isolated from ground, however. The other limitation of the circuit of Fig. 1 is the performanc of the differentiating circuit. A circuit as shown at it, Fig. 1, can differentiate perfectly only if the resistance of the circuit feeding the inductor is infinite and if the inductor has zero resistance. This can not be achieved in practice, and, if it were, the attenuation would also be infinite, although fairly good differentiating action can be obtained if the resistance is such that a loss of 20 db. occurs in the circuit.-

An improved differentiating circuit is shown in Fig. 4, in which condenser it and resistor i! form the differentiating circuit, with a feedback. connection from th output of this circuit to the grid of detector tube 3. Without the feedback connection, perfect differentiating action would be obtained only if the plate resistance and the re-= sistance of th plate circuit of amplifier i were zero. With the feedback connection, resistor it can be adjusted so that the alternating current through resistor ii is the same as it would be if no resistanc were present. That is, the back voltage across resistor ii, acting through resistor i 8, tube 3, and amplifier T produces, in effect, a forward voltage on the resistor il equal to the sum of the voltage drops across the plate resistance of the tube, the equivalent series resistance of condenser it; and the resistor ii. Actually, of course, the feedback would be adjusted so that the net circuit resistanc has a small positive value. The tendency to oscillat can be made relatively small, however, if condenser 16 has rather high reactance. The A. C. current will then he, in effect, determined by a finite voltage and a finite capacitative reactance, with little or no positive or negative resistance. The charging current of condenser i6, and therefore, the voltage across resistor ii, is proportional to the rate of change of the grid votlage X within very close limits. The more accurately resistor it is adjusted, the higher the permissible value of resistor I1 and the higher is the output voltage,

da: W

produced across it.

It can be seen that if the adjustment of phase shift network 5, Fig. 1, is not quite correct, the timing relativ to X of voltage Y, which acts to control the reversing switch action of rectifier 9, will not be as shown in Fig. 3. That is, the switch over points, instead of being at M and N, Fig. 3, might be at P and Q, for example. However, the net increase in fda: for one revolution of V in the counterclockwise direction will still, be the same as the net decrease for one revolution in the clockwise direction, and the performance of the circuit will be substantially unimpaired.

The circuit shown in Fig. 1, with the alternative arrangement of Fig. 4, provides a positive comparison between the mean frequency of a frequency modulated wave and the frequency of a constant oscillator, independent of the resonant frequency of tuned circuits, without critical adjustments, and with tubes of conventional detector and class A audio frequency amplifier and diode rectifier functions.

While I have described my invention in certain preferred embodiments, I desire it understood that modifications may be made, and that no limitations upon my invention are intended except as may be imposed by the scope of the appended claims.

What I claim as new Letters Patent of the lows: 1

1. The method of frequency comparison which comprises relating an oscillation of fixed frequency to a wave, the frequency of which is sub- Ject to variation, producing a first heterodyne voltage of frequency equal to the difference between the frequency of said oscillation and the frequency of said wave, producing a second heterodyne voltage in phase quadrature with said first heterodyne voltage, producing a differential voltage substantially proportional to the rate of change of said second heterodyne voltage, and measuring the intensity of said differential voltage and its phase relation with respect to said first heterodyne voltage, said intensity being a measure of the frequency variation of said wave from said fixed frequency and said phase relation indicating the direction of said frequency variation. 1

2. The method of frequency comparison which comprises relating a frequency modulated wave; the center frequency of which is subject to variation, to an oscillation of fixed frequency equal to the desired center frequency of said modulated wave, producing a first heterodyne voltage of frequency equal to the difference between the frequency of said oscillation and the frequency of said wave, producing a second heterodyne voltage in phase quadrature with said first heterodyne voltage, producing a differential voltage substantially proportional to the rate of change of said second heterodyne voltage, and measuring the intensity of said differential voltage and its phase relation with respect to said first heterodyne voltage, said intensity being a measure of the freand desire to secure by United States is as folquency variation of said wave from said fixed frequency and said phase relation indicating the direction of said frequency variation.

3. The method of frequency comparison which comprises relating an oscillation of fixed frequency to a wave, the frequency of which is sub- Ject to variations above and below the fixed frequency of said oscillation, producing a first heterodyne voltage of frequency equal to the difference between the frequency of said oscillation first heterodyne voltage, said intensity being a measure of the frequency variation of said wave from said fixed frequency and said-phase relation indicating the direction of said frequency variation.

4. The method of frequency comparison which comprises relating an electrical oscillation of fixed frequency to an electrical wave the frequency of which is subject to variations above and below the fixed frequency of said oscillation, producing a first heterodyne voltage of frequency equal to the difference between the frequency of said oscillation and the frequency of said wave, producing a second heterodyne voltage in phase quadrature with said first heterodyne voltage, producing a differential voltage substantially proportional to the rate of change of said second heterodyne voltage, deriving from said second heterodyne voltage and said differential voltage electrical charges substantially proportional to the intensity of said differential voltage and of polarity depending on the phase relation between said first heterodyne voltage and said differential voltage, integrating said charges over a given time period, and measuring the net charge at the termination of said time period, the magnitudeand polarity of said net charge indicating the average frequency relation of said oscillation and said wave over said time period.

5. The method of frequency comparison which comprises relating an electrical frequency modulated wave, the center frequency of which is subject to variation, to an electrical oscillation of fixed frequency equal to the desired center fre-- 'quency of said modulated wave, producing a first heterodyne voltage of frequency equal to the difference between the frequency of said oscillation and the frequency of said wave, producing a second heterodyne voltage in phase quadrature with said first heterodyne voltage, producing a differential voltage substantially proportional to the rate of change of said second heterodyne voltage, deriving from said second heterodyne voltage and said differential voltage electrical charges substantially proportional to the intensity of said differ ential voltage and of polarity depending on the phase relation between said first heterodyne voltage and said differential voltage, integrating said charges over a given time period, and measuring the net charge at the termination of said time period, the magnitude and polarity of said net balanced detector means energized from the last said means and from the other of said detectors, and a condenser connected in the output of said balanced detector means, the net charge on said condenser integrated over a given time period being substantially proportional to the average difference between the fixed frequency of the oscillations from said source and the center frequency of said frequency modulated energy at the termination of said time period.

7. A frequency comparator as set forth in claim 6 wherein said detectors each comprise an electron tube having an anode, a cathode and a plurality of grid electrodes, with said oscillations and said modulated energy being applied toseparate grid electrodes in each of said detectors.

8. A frequency comparator as set forth in claim 6 wherein said frequency differentiating circuit comprises a resistanceand an inductance connected in series, with output connections across said inductance and said resistance providing a relatively high proportion of the impedance of the circuit.

9. A frequency comparator as set forth in claim 6 wherein said frequency differentiating circuit comprises a capacitance and a resistance connected in series, with output connections across said resistance and said capacitance providing a relatively high proportion of the impedance of the circuit.

10. A frequency comparator as set forth in claim 6 ,wherein said frequency differentiating circuit comprises a capacitance and a resistance conected in series, with output connections across said resistance, and a feedback circuit from said resistance to the input of the detector with which said differentiating circuit is connected, whereby said capacitance provides, a relatively high profrequency of which is subject to variation, an

charge indicating the average frequency relation of said oscillation and said wave over said time period.

6. A frequency comparator comprising a source of oscillations of fixed frequency, a pair of de-- tectors, means for applying oscillations from said source in phase quadrature and frequency modulated energy in like phase to each of said detectors, frequency differentiating means consaid detectors,

nected with the output of one of portion of the impedance of the circuit and said feedback connection substantially balances the effect of said resistance in the circuit.

11. A frequency comparator. comprising a source of oscillations of fixed frequency, means for relating oscillations from said source directly to a wave the frequency of which is subject to variation, means for relating oscillations from said source in phase quadrature to said wave the impedance network connected in the output circuit of one of said means and means energized from both one of the aforesaid means and from said impedance work for determining the net angular displacement of said wave with respect to the oscillation of fixed frequency over a given time period.

12. A frequency comparator comprising a source of oscillations of fixed frequency, a detector energized from said source of oscillations and directly from a wave the frequency of which is subject to variation, a separate detector energized from said source of oscillations of fixed frequency in phase quadrature with respect to the first mentioned detector and directly from said wave the frequency of which is subject to variation, differentiating means for producing a voltage substantially proportional to the rate of change of the output of one of said detectors, balanced rectifier. means energized by said differentiating means and by the other. of said detectors, and integrating means connected to the output of said rectifier.

WALTER H. WIRKLER.

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