WO2014189366A1

WO2014189366A1 - Method and system for measuring a frequency ratio

Info

Publication number: WO2014189366A1
Application number: PCT/NL2014/050257
Authority: WO
Inventors: Antonius Johannes Maria Montagne
Original assignee: Frapinventions B.V.
Priority date: 2013-04-24
Filing date: 2014-04-22
Publication date: 2014-11-27
Also published as: NL2010698C2

Abstract

The present invention relates to a method for determination, with a reduced quantization error, a ratio of the frequencies of two periodic signals, comprising the steps of receiving two periodic signals x 1 (101) and X₂, having frequencies f ₁ and f₂ respectively; adjusting a measurement time interval of length T_m that equals a natural number m times the period 1/f₁; deriving a periodic signal x_s (106) with a frequency f ₅, from X₂ in such a way that f ₅= (mn+ 1)/T _m, in which n is also a natural number; determining the average phase of the signal x₅ with respect to the average phase of the signal X₁, over a first time interval of the length T _m by counting the number of periods of x₅ that elapsed since the start of the first time interval, and determining the ratio of the sum of those count numbers that follow either the positive or the negative transitions of the signal X₁, and the number of transitions of x ₁ over the first time interval; determining the average phase of the signal x₅ with respect to the average phase of the signal x ₁, over a second time interval of the length T subsequent to the first time interval; determining the frequency ratio f ₁ /f ₅and dividing this by the average number of periods of x₁ found over the two subsequent time intervals.

Description

METHOD AND SYSTEM FOR MEASURING A FREQUENCY RATIO

SmartXtals are high-stability clock signal generators built from a piezoelectric resonator (crystal) and an integrated circuit (IC). The IC of the smartXtal incorporates solutions for compensation of changes in the resonance frequencies of the crystal due to state dependent behavior.

One method for finding the state of the crystal uses a multiple mode crystal oscillator. Such an oscillator generates multiple frequencies that are accurately linked to resonance modes of the crystal, which in turn, depend on the state of the crystal. For compensation of this state dependent behaviour, high resolution determination of the ratios of the oscillation frequencies is of outmost importance. Various measurement techniques are known in the art. The most simple technique for frequency measurement is illustrated in figure 1.1 below. There, the number of cycles of an incoming signal with unknown frequency fi is counted during a time interval T_m. In this way fi is found as: ^ ⁼

If the start of this measurement interval is synchronized with a zero crossing

of the input signal, the number of counts equals

Hence, the frequency quantization error e_q equals:

1

¾ =—

This figure can be taken as a figure of merit for a frequency measurement system. A much higher resolution can be obtained using the so-called reciprocal counting method. This method is illustrated in figure 1.2 below. In the reciprocal counting method, both the start and stop time of the measurement interval are synchronized to the period of the measurement signal. This synchronization is performed using a high- frequency sample clock with period T_s. The frequency of the measurement signal is again found as the ratio of the number of cycles and the measurement time: :— m† _{c ^} Due to the synchronization at the beginning and at the end of the measurement cycle, the count number equals

Hence the frequency quantization error equals: =

One known technique to further improve the reduction of quantisation errors is so called integration of rest terms. However, this is an analogue method, which does not allow to obtain a quality of 0,01 parts per billion within a measurement interval of 1 millisecond. EP 1 199 574 discloses a method according to the preamble of claim 1.

However, still, there is a desire for a better and more accurate technique for

measurement and reduction of quantisation errors. The present invention provides such technique which comprises a frequency measurement by distributed phase sampling.

Further decrease of the quantization error is achieved by distributing the time quantization error t_q uniform between 0 and its maximum value T_s over the

measurement interval, and then evaluating the frequency ratio fi/f_s from the average relative phase change of the input signal and the sample clock, over two subsequent time intervals.

This can be done by recording the number of elapsed clock cycles since the start of the measurement, at the clock transient that follows either a positive or negative transition of the input signal. The average of these numbers, over the m values, obtained during Tm, represents the average relative phase of the input signal with respect to the sample clock. This average relative phase is thus obtained with a time resolution of l/(m *f_s). The difference between two subsequently obtained values will then yield the average relative phase change over the measurement interval. The ratio of that average relative phase change and T_m then yields the average frequency ratio///; during T_m. Uniform distribution of the quantization error between 0 and T_s, over the measurement time, can be achieved in several ways. Figure 1.3 shows a situation in which the ratio R between the frequency/, of the sample clock and the frequency of the measurement signal/ is set to:

In which m and n are positive nonzero natural numbers, from now on referred to as natural numbers. Such a relation between/ and/ can be established with a

programmable fractional synthesizer. One can decide whether to adjust either the input frequency or the sample clock frequency with this synthesizer. The measurement time interval T_m is set to:

T_m = Ts (tnn -f t) = m -

We then measure a natural number of m periods of the input signal and a natural number of mn + 1 sample clock periods T_s over T_m, while the time delays between the rising edges of the measurement signal and the rising edges of the clock signal are uniformly distributed between 0 and Ts over the m samples. Hence, the quantization error fi_q in the measured phase difference amounts to:

_ r, The frequency quantization error is now found as:

Φα T_s 1 1

T_m mT m (mn 4- 1} m²n

Hence, this system gives a factor 2m² improvement with respect to the reciprocal counting technique.

In general, the method according to the invention for determination, with a reduced quantization error, a ratio of the frequencies of two periodic signals, comprises the steps of:

(a) Receiving two periodic signals xi and X2, having frequencies/; and/2 respectively; (b) Adjusting a measurement time interval T_m that equals an natural number m times the period 1/ Ί; (c) Deriving a periodic signal x_s with a frequency/,, from xi in such a way that/, = (mn+1) I T_m , in which n is also a natural number; (d) Determining the average phase of the signal x_s with respect to the average phase of the signal xi, over the time interval T_m by counting the number of periods of x_s that elapsed since the start of the measurement time interval, and determining the ratio of the sum of those count numbers that follow either a positive or a negative transition of the signal xi, and the number of transitions of xi over the measurement time interval T_m; (e) Determining the average phase of the signal x_s with respect to the average phase of the signal xi, as described under (d), over a second measured time interval T_m; (f) Determining the frequency ratio filfs by subtracting the result of step (d) from the result of step (e) and dividing this result by the average number of periods of xi found over the two subsequent time intervals T_m. The key of this method is the uniform distribution of the phase quantization error of the input signal, between 0 and T_s = 1//, over the measurement time interval T_m. This can for example be achieved in the following ways.

In particular step (c) comprises choosing the highest frequency for x_s that is possible within the technology used.

In a practical embodiment, one of the signals, for instance xi is a signal that can be generated and modified. As a first step, this signal is used as the first input signal. An indicative first frequency measurement of a second input signal X2 offered on is performed with a method according to the state of the art. Then a ratio between the signals is determined, which may as an example be 1: 100.4.

As a second step, a desired ratio between the first input signal and the second input signal is determined. This may for instance be 1: 100.00001 or 1: 100.99999.

As a third step, the first signal xi is altered, to a value that is (the measured ratio/the desired ratio) times the value X2 had before. Steps two and three are repeated until the desired ratio is obtained with an acceptable margin.

In an embodiment, at least one of the periodic signals, xi and/or xi is replaced by a signal Xi and/or xj whose frequency fi is accurately related to that of xi or X2, respectively

Herein, p and/or q may be real numbers that can be varied, but this is not a requirement. In general, the set point for p and/or q may be based upon the evaluation of the difference between the measured frequency ratio and the expected ratio fi /f_s= m/(mn+l).

The first method comprises a fractional frequency synthesizer that relates either the sample clock frequency to the input frequency, or the input frequency to the sample clock frequency, in such a way that the sample clock frequency has a small offset with respect to an natural number multiple of the frequency of the input signal. The measurement time is set to an natural number multiple of the reciprocal value of this frequency offset.

In theory, the natural numbers m and n and the set point of the fractional synthesizer can be fixed after they have been determined at the start of the measurement cycle.

However, in practice, the actual relation between the frequency of the sampling clock and that of the input signal may vary. This may then result in a non-uniform distribution of the quantization error over the measurement time, which is detrimental to the linearity and the effective resolution of the frequency measurement system. For this reason, practical implementation of this principle requires negative feedback control of the synthesizer parameters.

Another method for generating a uniform distribution of the quantization error over the time interval uses randomizing of either the sample clock phase, or the input signal phase. This can be achieved through application of phase modulation in the fractional synthesizer with quasi random noise that has a uniform distribution function. The initial settings of the fractional synthesizer and the measurement time can be determined at the start of the measurement and then be fixed during the measurement. Since the noise is quasi random, the phase samples of the input signal can be corrected for it. Hence, using this so-called subtractive phase dithering technique, the quantization error is reduced as in the previous case, while no noise is added to the result of the frequency measurement.

In an embodiment of the present invention, the modified frequency fi is determined iteratively, wherein a first value fi' is p *fi, wherein p = (f fi) * (Ι/η').

After initialization, a negative feedback system measures fi I f_s and maintains its value n + 1/m by controlling the set point p of the frequency synthesizer. The frequency fi is then found as:

m

·^'"^■ p (nm ÷ 1) of which/, is the reference frequency, m and n are set during initialization. During normal operation, p is controlled by negative feedback such that the relation between fi and fs is maintained even if i or/_s changes. The method according to the present invention thus comprises determining fi by calculating f_s (ml p(nm + 1))).

Measurement of fi I f_s may then be performed by measuring the average phase change of the sample clock with respect to that of the synthesized input signal over the average time interval T_m, and dividing it by the time interval. The measurement technique is illustrated in figure 2.3.

1. The average phase of the sample clock with respect to that of the synthesized input signal is found by adding the sample clock cycle numbers at which a transition of the synthesized input signal is found, and dividing it by the number of transitions found. In figure 2.3, this number is A/C over the first measurement period and B/D over the second measurement period.

11. The frequency ratio is now found as the phase change over the two periods divided by the average duration of the measurement period, which is (C + D) 12 in figure 2.3. Control is performed by feeding the difference between the measurement result and the desired value of the frequency ratio, as determined during initialization, to a digital PID controller which output provides the set point p for the synthesizer. As shown above, the distributed phase sampling method, in the absence of noise, is capable of providing measurement results with a very high resolution. In practice, however, this resolution will be limited by phase noise of the sample clock and of the input signal. In the following sections, the effect of noise and interference on the effective resolution of the distributed phase sampling frequency measurement system is shown. The RMS number of detection errors per interval T_m = T_mi = _m2 due to phase noise is evaluated. If this number equals N, the RMS value of the relative frequency measurement error e_Si_gma becomes: m-n

The method according to the present invention may further comprise determining the average phase frequency by dividing the sum of the ranking number of periods T_s during T_m in which fi' has a transition by the total number of transitions in the measurement interval. Three situations are distinguished:

1. Random phase noise with a normal distribution added to the input signal.

2. Random phase noise with a uniform distribution added to the input signal.

3. Single frequency phase modulation of the input signal. Single frequency phase modulation is of special interest in dual mode and multiple mode and oscillators. Due to mixing of oscillation modi, the (spurious) beat frequency is found in the two outputs of such oscillators.

Spurious frequency components also appear in the output signal of PLL systems.

Fortunately, the distributed phase sampling measurement system can be designed in such a way that it becomes highly insensitive to specific spurious signals added to the sampling clock or to the input signal.

In the distributed phase sampling frequency measurement system, the input frequency is sampled with a high frequency clock. In order to comply with Nyquist' s sampling criterion, the frequency of the sampling clock should be more than twice that of the input signal. The measurement result is obtained after low-pass filtering and down sampling of the output signal of the sampler. If both the sampling frequency and the input frequency are obtained from a multi-mode oscillator, they exhibit phase modulation due to cross modulation of modi in the multi- mode oscillator. In other words, spurious frequencies, equal to the beat frequencies are found in the phase of both signals. The distributed phase sampling measurement system can be made highly insensitive to spurious noise with known frequencies. Since the sampler can be viewed upon as a phase detector, its output signal comprises beat frequency components. The transfer of the output signal of the sampler to the output of the measurement system is governed by the decimator. This subsystem reduces the update frequency from/, to \IT_m. Hence if l/Tm is made equal to the lowest beat frequency, this frequency is suppressed. Higher beat frequencies can be suppressed by using higher order decimators that have transmission zeroes (notches) in the low-pass filter sections of the decimator.

The invention further relates to a system for measuring with a reduced quantisation error, a frequency of oscillation of an input signal i from an piezoelectric resonator circuit, comprising: a first input for receiving the input signal i, a second input for receiving a sample clock signal s with a frequency/,, a sampler for sampling the first input signal at each pulse of the sample clock signal s, an accumulator, for adding up the ranking numbers of the samples in which a positive transition of the input signal takes place, a calculator, for calculating p times the ratio between and/.

The system may further comprise a fractional synthesizer, for multiplying the frequency of the input signal i with a factor p; and a controller, for calculating p on the basis of the measured ratio of / and/. The controller may be configured for calculating p based on the calculator output.

The system may further be configured for adding random phase noise to the input signal i, and comprise a generator for the sample clock signal, wherein the generator increases the sample clock phase from 0 to 2 π (mn + 2) during a measurement period T_m. Measurement of fi /f_s may then be performed by measuring the average phase change of the sample clock with respect to that of the synthesized input signal over the average time interval Tm, and dividing it by the time interval.

The invention was and will be elucidated into more detail with reference to the figures: figure 1.1 shows a technique for frequency measurement according to the art; figure 1.2 shows another technique according to the art wherein a much higher resolution can be obtained using the so-called reciprocal counting method;

- figure 1.3 shows a graph of a measurement technique according to the invention; figure 2.1 shows the modeling of jitter of the input signal to the sampling clock; figure 2.2 shows a simplified block diagram of a system according to the present invention, and;

Figure 2.3 shows a timing diagram of the operation of the system from figure 2.2.

Figure 2.2 below shows a simplified block diagram of the distributed phase sampling frequency measurement system. The system measures the frequency f, with respect to/,. To do so, a controller sets the positive rational frequency scaling factor p of a fractional synthesizer such that: r .. , * ,

Under this condition, the measured positive real/, // measured at the system's output, equals the desired set point n + lm at the input of the controller. The output update rate equals T_m.

The operation of the system can be summarized as follows. The frequency of the input signal is accurately determined by measuring the change of its average phase with respect to that of the sample clock, over two subsequent time intervals. This change, divided by the time average of the two subsequent measurement time intervals gives a first-order approximation

for///. During a measurement period T_m the phase of the sample clock signal increases from 0 to 2p(mn + 1), while that of the input signal increases from 0 to 2pm. A counter in the acquisition and control part, indexes each clock cycle of the sampling clock. At each positive edge of the measurement signal, the corresponding index is added in the accumulator. At the end of one measurement cycle, this accumulated value as well as the number of transitions found are transferred to the calculation block and the latch. The ratio of these two numbers expresses the average phase of the input signal over the measurement interval in number of sample clock cycles. After this transfer, the accumulator and transition counter are reset. The calculation block calculates the change of this average phase over two subsequent time intervals.

The result is a measure for the ratio of the sample clock frequency and the frequency of the measurement signal. The average phase of the input signal, relative to that of the sample clock and over the time interval T_m, is thus obtained by dividing the sum of the sample clock cycles that correspond with a zero crossing of the input signal, by the number of zero crossings of the input signal over this time interval. In the absence of noise and errors, this number will be m. The time average of the two subsequent measurement time intervals is then obtained as the average number of zero transitions found over the two time intervals. In the absence of noise, this number will also be m. Figure 2.3 illustrates the procedure for m = 3 and n = 2.

During the two subsequent measurement intervals T_m\ and r_m2, we have exactly mn + 1 cycles of the sample clock against m cycles of the input signal. The sample clock cycles have been numbered from 1 to 2(mn + 1); so they range from 1 ... 14. The periods of the input signal during each time interval range from 1 ... 3. In order to find the average phase of the input signal expressed in ample clock cycles, we determine the sum of the sample clock cycles in which positive edges of the input signal are found. For the first measurement period T_mi these numbers can be read from the figure: we have 2, 4 and 6. Their running sum equals 2, 6 and 12, and the average phase over three cycles of the input signal is thus found as 12/3 = 4. During the following time interval Tm2, we find positive edges of the input signal during the sample clock periods 9, 11 and 13. Hence, the average phase is found as 33/3 = 11. The average number of cycles of the input signal per time interval equals (3 + 3)/2 = 3. Hence, the frequency ratio fjfi is found as (11 - 4) /3 = 7/3. This exactly corresponds with n + 1/m and we obtain: 9 3 ,

With the aid of this figure, we will also show that the relative quantization error equals 1/ (m(mn + 1)). To do so, let us assume one count error, which means that a transition during one measurement cycle is detected either one sample clock cycle too early, or one sample clock cycle too late.

If a rising edge of the input signal is detected one sample clock cycle too late, during the first measurement interval Tml or one sample clock cycle too early during Τπΰ,, we would obtain:

9

Λ ⁼ 22-^

The relative error e⁺ in fi then becomes:

^■Ύ~)

fi h

If a rising edge of the input signal is detected one sample clock cycle too

early, during the first measurement interval T_m\ or one sample clock cycle

too late during r_m2, we would obtain:

if

Relative error e in fi then becomes:

Hence, this can be approximated by:

, 1 1 1. 1

¾ ±— = ±

20 ^' 21 m(mR + l) Hence, for mn » 1, the relative quantization error e^q equals:

1 1

£,5

m imn + 1 s -mHi

which is significantly lower than the quantisation achieved with the state of the art measurement techniques.

Claims

1. Method for determination, with a reduced quantization error, a ratio of the frequencies of two periodic signals, comprising the steps of:

(a) Receiving two periodic signals xi and X2, having frequencies/; and/2 respectively; (b) Adjusting a known measurement time interval T_m that equals an natural number m times the period 1/fi;

(d) Determining the average phase of the signal x_s with respect to the average phase of the signal xi, over the time interval T_m by counting the number of periods of x_s that elapsed since the start of the measurement time interval, and determining the ratio of the sum of those count numbers that follow either a positive or a negative transition of the signal xi, and the number of transitions of xi over the measurement time interval T_m;

(e) Determining the average phase of the signal x_s with respect to the average phase of the signal xi, as described under (d), over a second measured time interval T_m;

(f) Determining the frequency ratio fi/f_s by subtracting the result of step (d) from the result of step (e) and dividing this result by the average number of periods of xi found over the two subsequent time intervals T_m

characterised by (c) Deriving a periodic signal x_s with a frequency/, from X2 in such a way that/ = (mn+1 ) I T_m , in which n is also a natural number.

2. Method according to claim 1, wherein step c comprises choosing the highest frequency for x_s that is possible within the technology used.

3. Method according to claim 1 or 2, in which at least one of the periodic signals, xi and/or x₂ is replaced by a signal Xi and/or Xj whose frequency fi is accurately related to that of xi or x₂, respectively by/ = pfi, or fj = qfi.

4. Method according to claim 3, in which p and/or q is a real number that can be varied.

5. Method according to claim 4, in which the set point for p and/or q is based upon the evaluation of the difference between the measured frequency ratio and the expected ratio /;//= m/(mn+l).

6. Method according to any of claims 3-5, in which p and q are a real numbers that can be varied.

7. Method according to claim 6, in which a set point for either p or q, is based upon the evaluation of the difference between the measured frequency ratio and the expected ratio fi/fs = m/( mn +1).

8. System for performing a method according to any of the preceding claims, comprising:

- a first input for receiving the input signal z;

- a second input for receiving a sample clock signal s with a frequency/,;

- a sampler for sampling the first input signal at each pulse of the sample clock signal s;

- an accumulator, for adding up the ranking numbers of the samples in which a positive transition of the input signal takes place;

- a calculator, for calculating p times the ratio between fi and/.

9. System according to claim 8 according to claim 3, further comprising:

- a fractional synthesizer, for multiplying the frequency of the input signal i with a factor p; and

- a controller, for calculating p on the basis of the measured ratio of and/.

10. System according to claim 8 or 9, wherein the controller is configured for calculating p based on the calculator output.

11. System according to any of the preceding claims 8-10, configured for adding random phase noise to the input signal i.

12. System according to any of the preceding claims 8-11, comprising a generator for the sample clock signal, wherein the generator increases the sample clock phase from 0 to 2 π (mn + 2) during a measurement period T_m.