Space time clock: An on-chip clock with 10-12 instability

Zhendong XU, Yingchun ZHANG, Pengfei LI, Yongsheng WANG,Limin DONG, Guodong XU

School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

KEYWORDS Communication;Embedded processor;Instability;Positioning navigation and timing;Space time clock

Abstract High precision and stable clock is extremely important in communication and navigation. The miniaturization of the clocks is considered to be the trend to satisfy the demand for 5G and the next generation communications. Based on the concept of meter bar and the principle of the constancy of light velocity,we designed a micro clock,Space Time Clock(STC),with the size smaller than 1 mm×1 mm and the power dissipation less than 2 mW.Designed in integrated circuit of 0.18 μm technology, the instability of STC is assessed to be 2.23 × 10-12 and the trend of the instability is reversely proportional to τ.With the potential ability to reach the level of 10-16 instability on chip in the future,the period of the STC’s signal is locked on the delay time defined by the meter bar which keeps the time reference constant.Because of its superior performance,the STC is more suitable for mobile communication, PNT (Positioning, Navigation and Timing), embedded processor and deep space application,and becomes the main payload of the ASRTU satellite scheduled to launch next year and investigate in space environment.

1. Introduction

Over the past two decades,atomic clock and optical clock have reached maturity and defined the SI (the International System of Units) second.1-6As the improvement of accuracy and stability,7-10optical clocks are gradually sensitive to physical phenomena that cause minute alterations in the clock transition frequency and even have the potential ability to detect gravitational waves or dark matter.11,12

The development of atomic clock is toward two directions:precision13and miniaturization.14-16In high precision development, strontium (87Sr) and ytterbium (171Yb) atomic clock have reached stability of 10-17level.17-19The technique such as Magneto-Optical Trap(MOT)20-22and evaporative cooling process23are applied to ensure the precision and stability.For the purpose of applications such as 5G and next generation communications, the other direction is focused on the miniaturization of the atomic clocks.24,25Up to now, the Coherent Population Trapping (CPT) atomic clock26-29is the only atomic clock miniaturized and its stability can be up to 10-10.Due to the effect of temperature shift on the laser wavelength of CPT atomic clock, the medium and long term frequency stability will become worse.30

The second is defined by SI as a standard unit and the meter is defined by the second with light signal.On the contrary,the meter,the international standard unit of length,may define the time interval when light passes through the space interval of a meter.

If the space interval is unchanged, the time interval of the light passing through it will keep constant. If the light signals pass through a constant space interval periodically,a clock can be constructed. By negative feedback mechanism, the time interval is scaled to the space interval,so the signal period will be locked on the time interval defined by the space interval.Inspired by this idea,a clock based on the relationship between space and time is designed and the clock is called Space Time Clock (STC).

We analyzed STC theoretically and setup a mathematical model to simulate the mechanism and performance of STC.The theoretical analysis discovered that the STC possesses a very attractive property.The potential ability to achieve instability better than 10-20level will make STC extremely stable clock.The simulation shows that the STC behaves an excellent performance both in accuracy and stability. So we designed and made a prototype of STC in 0.18 μm integrated circuit technology to verify the STC theory and its performance.

2. Theory and method

2.1. Principle of space time clock

A stable time reference is the key element to build a stable clock.Because of the quantum characteristics of a stable transition between the two levels of atoms,the clock is designed by scientists with atomic time reference. A Voltage Controlled Oscillator(VCO)is used in Phase Locked Loop(PLL)to generate a frequency signal that is locked on the transition periods of the atoms.The atomic clocks are considered to be the most accurate clocks. However, the atomic clocks are the most sophisticated device. High technical requirements limit the extensive application of atomic clocks.

The most common time reference is crystal oscillator which merges in mobile phones, computers and other electronic devices. The only defect of the crystal oscillator is that its frequency instability is much worse than that of atomic clocks.Therefore, the frequency of crystal oscillator must be tamed by GPS in some applications.

Any source that provides stable period can be used as a clock. In the study of space-time, we have known that the space interval can be expressed as Δl = cΔt, where c is speed of light, Δl is space interval and Δt is time interval that light signal passes through Δl. This indicates that if Δt is a determined value, Δl will be fixed. On the contrary, if Δl is a determined value, Δt will be fixed. Therefore, we expect to build a time reference with meter bar(Δl).As long as a time reference is set up,a clock can be built.If the time reference is constant,the clock will have a stable property. Because the stable property relies on the time reference, we will focus on the methods to keep meter bar (Δl) stable.

As the length of the meter bar varies with ambient temperature, the time reference defined by the meter bar will vary with the ambient temperature. Therefore, the key to attain a stable time reference is to keep the ambient temperature unchanged or make the time reference insensitive to temperature changes. There are various methods to keep the ambient temperature stable, but it is difficult to keep it constant. It is similar to circumstances that encountered in the atomic clocks

where the most advanced temperature control methods are used to prevent from disturbance of temperature variations.The methods include magneto-optical trap and evaporated cooling process which limit the temperature to a narrow range,but meanwhile the clock becomes sophisticated and sensitive to environment variations.

There are numerous methods to deal with temperature changes. A complementary structure or differential method are common choice in integrated circuits. In this paper, we design a stable time reference with meter bar according to complementary variation of materials. It is known that some materials have Positive Coefficient of Thermal Expansion(PCTE) and some have Negative Coefficient of Thermal Expansion (NCTE). These characteristics can be used to design a constant length of meter bar which may build a stable time reference.

The initial idea is to combine a meter bar of PCTE and a meter bar of NCTE to a complementary meter bar, one part of which expands while the other part compresses with temperature variations. By detail design, a fixed length of the meter bar can be attained so that a constant time reference is expectable.However,it is difficult to have NCTE material to design a complementary meter bar.Only a few of invar alloy has NCTE characteristics. Therefore, a simulated NCTE meter bar is adopted instead of a real NCTE material. The simulated NCTE meter bar is a time delay line with negative property that delay time decreases with temperature increases. In integrated circuit,the CMOS gate can be designed to have positive or negative time delay characteristics,so we adopt CMOS gate to simulate NCTE meter bars.

NOT gate is the basic CMOS circuit which simulates NCTE meter bar to compensate the temperature variations in order to build a constant time reference.Define temperature coefficient as αn, so the time delay of the NOT gate can be expressed as

where tn0is the time delay of the NOT gate at ambient temperature T0,and ΔT is the temperature difference around T0.Since αnis designed as a negative value, tnwill exhibit NCTE characteristics.

A PCTE meter bar, a length of micro strip, is used as the main part of time reference that combines with NCTE meter bar to provide a Stable Time Interval (STI) for comparison.The period of the signal generated by VCO is compared to STI in Phase Detector (PD). If there is any time difference between the two inputs,the negative feedback mechanism will force the period of the VCO signal to approach STI.Since the STI is stable,the period of VCO signal will be stable.Based on this principle, a clock with high frequency instability is achieved.

Suppose the length of PCTE meter bar is lp,the time of the electromagnetic signals passing through PCTE meter bar will be

where tr0=tp0+tn0.In Eq.(3),if tp0αp+tn0αnis designed to zero,the time reference trwill be a constant value which makes the clock very stable. The clock designed in this principle is shown in Fig. 1. Since it uses space interval to generate time interval, the clock is called Space-Time Clock (STC).

The STC consists of a Voltage Controlled Oscillator(VCO), a Phase Detector (PD), a Low Pass Filter (LPF) and a meter bar as shown in Fig. 1. Foscdenotes frequency signal of STC, fsysdenotes frequency foscdivided by 2, # fsysdenotes inversion of fsys, and Vcois control voltage. Constant current source,denoted by I in Fig.1(b),is controlled by up and down signals which switch on and off according to the phases detected by two D flip-flops. In the STC, the meter bar is a delay line which acts as a time reference. When the frequency signal from VCO passes through the meter bar, the signal is delayed.The design of meter bar makes the delayed time equal to the nominal period of the signal. When the period of VCO output signal is the same as delayed time of the meter bar, no time difference can be detected by the phase detector and the period of VCO output signal keeps constant.If the time difference is detected,the phase detector will output the control signal to regulate the VCO to decrease the time difference to zero by negative feedback mechanism. As a result, the STC works at the constant period defined by the meter bar.

2.2. Experiment system

To evaluate the stability of STC, an experiment system has been designed as shown in Fig. 2. The system consists of two independent STCs on a single PCB. The frequency of each STC is recorded by a counter, and two counters are latched simultaneously by a periodic pulse signal generated by a processor. The processor reads the counter 25 times per second and the counts read is used to calculate the frequency of each STC. The simultaneous latch-up operation of two counters ensures that the timing instability of the processor is eliminated from the measurement of frequency stability.

In Fig. 2(a), a system for STC test is set up and the system consists of a PCB and a computer. In Fig. 2(b), the PCB is designed to test the STC and the counts of the frequency signal is measured by a C8051F041 SoC processor. The data of the counts are transmitted to a computer through UART and the frequency instability is assessed.The meter bar is explicitly marked on the PCB, since it is covered by the copper ground and is shielded in the PCB. In Fig. 2(c), the IC layout of STC is shown and only a 1 mm2area is used to integrate STC which is packaged in DIP16. Fig. 2(d) is STC Bonding and Fig. 2(e) is STC DIP16 packages. In Fig. 2, STCs output the period signal defined by a meter bar. As the meter bar is designed with the length of 0.993 m long in the PCB and the relative dielectric is 4.2, the effective length of the meter bar is 2.035 m long (half wave length), leading to 73.6 MHz frequency output. The frequency of the STC output is divided 16 times by the counter,which converts into 4.6 MHz nominal frequency to the processor. In the processor, a 16 bits embedded counter is used to count the frequency of the signal,and a timer in the processor generates a latch-up signal periodically.When the latch-up signal appears, the counts is recorded and the frequency is calculated. The STC is packaged in standard DIP16 and the maximum power dissipation is about 2 mW with peak-to-peak output of 1.8 V.

STC is constructed as a frequency signal source, which is based on the concept of meter bar and the principle of constancy of light velocity. The meter bar is a standard length and is converted to a standard time period. The time period is used to set up a time reference. After the time reference sets up, it is applied to regulate the period of VCO output signal and to keep the period constant.By negative feedback,the signal period is locked on the time reference defined by the meter bar.

2.3. Instability analysis

The meter bar is mainly affected by the ambient temperature.The length of the meter bar varies with the temperature because of material thermal characteristic. The period of the VCO output signal is the function of the length of the meter bar when VCO is locked on. In this condition, the variation of the length will introduce instability of the VCO output period. The instability is given by

where αeis the equivalent coefficient of thermal expansion,ΔTmaxis the maximal temperature differential around T0which is the average ambient temperature,and τ is the average time.

According to Eq.(4),the instability mainly relates to αeand ΔTmax. The equivalent coefficient of thermal expansion is a function of material property and machine precision. The equivalent coefficient of thermal expansion is fixed at a specified temperature after the meter bar is made, so it affects the instability negligibly. The temperature change dominates the instability and the temperature control is the key factor to keep the meter bar length stable. Compared with keeping the temperature constant or controlling ΔTmaxto zero, it is feasible to keep the temperature within a certain range.In case of temperature being limited in a narrow range,the instability can be limited to the level expected.

It is ideal for αeto be zero which gives zero instability caused by temperature changes. In state-of-the-art technology of micro-nano machining, the accuracy approaches to nanometers, or even reaches atom scales. The meter bar can be machined in atoms one by one. Therefore, the machining accuracy is expected to be in 10-10m level which makes αein the order of 10-16/K with the common materials.The overall instability is expected to be 10-19level if the temperature is limited within the range of 1 mK.

The stability of STCs is limited by noises including thermal noise,shot noise and flicker noise.The noise is reflected in the period of the VCO output and called phase noise. The phase noise perturbs the frequency of the VCO output directly and makes contributions to the instability. The instability introduced by noises is as follow

where βeis VCO control ratio constant, k is Boltzmann constant,T is ambient temperature,C is capacitor of the Low Pass Filter (LPF), Vgis the threshold of the inverter in VCO, and Vcois VCO control voltage.

By optimization of the parameters and simulation of the electronic systems, the phase noise is limited to 10-15level.Since all electronics component is integrated on a single chip,the consistency of the functional blocks,such as flip-flops used in phase detector,are guaranteed.As a consequence,the instability is suppressed, and the period of a well-designed STC is typically locked on the standard time reference provided by the meter bar.

For high stability clock, it is necessary to design the Electromagnetic Compatibility (EMC) in detail. The meter bar must be shielded to prevent it from interference and noise.The meter bar is designed in micro-strip circuit on PCB and is coated with copper cover grounded. As a result, the meter bar is less influenced by the interference and noise, and the instability contributed by artificial noise is eliminated.

3. Frequency instability measurement

The instability is measured with the system shown in Fig. 2.Two embedded counters in the processor are used to count the frequencies of the STC1 and STC2 respectively. The average frequency of both STCs is 4,485,419 Hz. The counts are logged and a comparison is made per second. The instability is computed by ratio of the accumulated error counts and the total accumulated counts of STCs.The measurement index of the STC is equivalent to the frequency instability measurement (see Refs.13,31). The measurement results are shown in Fig. 3.

It is observed that the frequencies of two STCs are almost the same during the statistical periods. The accumulated counts, which are equivalent to the phases of frequency signals, increase linearly with time. This characteristic means the frequency of the STC is very stable.The accumulated error counts between the two STCs are almost invariable which indicates the frequency difference between two STCs approaches zero at the sample time. Because the assessment is continuously evaluated per second, the zero frequency difference between two STCs demonstrates that the instability of the STC is zero. Though the frequency instability in Fig. 3 shows the value assessed to be about 10-12level, the real frequency instability is better than the assessed value.

Through the observation of accumulated error counts, it is noticed that the frequencies of two STCs are nearly the same in the successive samples per second. The zero frequency difference shows that the short term frequency instability of the STC is so excellent that the observation time must be lengthened to distinguish the tiny frequency variations. Therefore,the long term frequency instability assessment is done in 10,000 s and even in 100,000 s. By analyzing the frequency instability,it is found that the frequency instability is reversely proportional to the averaging time τ, which shows that the STC has a very stable behavior both in short term and in long term frequency instability.

The occasional jump from 0 to 1 or 1 to 0 of the accumulated error counts in Fig. 3 indicates that the time reference based on meter bar meets expectation.If there is any deviation from time reference defined by meter bar, the negative feedback mechanism will force the deviation to zero. The STC measures time intervals many times per second with the meter bar.The time intervals are accumulated each time and the total accumulated counts are elapsed time while the error is also accumulated that exhibits as the deviation. This random jump feature can be improved by precisely designing meter bar with complementary materials or complementary structure. As the accumulation goes on, the deviation will decrease. The accuracy of the STC will be improved with the increase of measurement time, which is the reason why the STC has an excellent frequency instability both in short term and in long term. As shown in Fig. 3, in the total counts of 44827340000, only one count difference is recorded corresponding to one cycle(about 223 ns) instability in 10,000 s. Since the count takes an integer value,it can be deduced that the instability is better than assessment value in the paper.The result of assessment in 100,000 s in Fig. 3(c) and (d) verifies our deduction.

The assessment of frequency instability in the paper is a real-time measurement of two STCs output frequency. To eliminate the instability of the processor timing,the assessment method is specially designed.Suppose frequency of STC1 be f1,and frequency of STC2 be f2, a relative frequency stability is defined to assess the instability of both STCs as follow

Since the relation between the single STC instability and two STCs instability is only scaled to a constant coefficient,the Eq. (8) is used to assess the instability. It is noticed that the count number N1and N2can be represented by N1=f1τ and N2=f2τ respectively, while the frequency instability is a relative value of the frequencies, so the frequency instability given by Eq.(7)can also be depicted by the accumulated error counts over the total accumulated counts.

The frequency instability of STC is insensitive to temperature variations due to the complementary design of the meter bar. The positive and the negative temperature properties of the meter bar compensate the time delays each other which makes the time reference vary stable. The experiment verifies this point and the result is shown in Fig. 4.

4. Conclusions

The STCs represent an innovative and remarkable achievement in high stability and miniaturization of the clock on chip.Considering the effect of noise in electronics system,the stability may be limited 10-15level estimated by the current design.The STC is less than 1 mm×1 mm in size,which is suitable to be integrated into the embedded processor used in mobile phones and other electronic devices. The frequency instability of STC reaches to 10-12level that makes it attractive in 5G and the next generation communications. It can be used as intellectual property in many applications.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No.11973021), Harbin Institute of Technology, Research Centre of Satellite Technology and Department of Microelectronics Science and Technology. All authors are supported by the ASRTU satellite project. The authors thank H. Zhao and W. J. Han for careful simulation of electronics.