Frequency accuracy measurements for the microwave generator used in the Programmable Josephson Voltage Standard at NRC

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2018 Conference on Precision Electromagnetic Measurements (CPEM 2018),

2018-10-22

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Frequency accuracy measurements for the microwave generator used

in the Programmable Josephson Voltage Standard at NRC

Gertsvolf, M.; Granger, G.

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Frequency accuracy measurements for the microwave generator

used in the Programmable Josephson Voltage Standard at NRC

M. Gertsvolf and G. Granger

National Research Council Canada, Ottawa, Ontario, K1A 0R6, Canada

[email protected]

Abstract — Standard frequency and time techniques are used

to characterize the frequency accuracy of the commercial microwave generator used in the Programmable Josephson Voltage Standard at National Research Council Canada. Tests are also performed to verify the frequency resolution of the generator.

Index Terms — Frequency and time, frequency accuracy,

phase offset, frequency resolution, microwave generator, Programmable Josephson Voltage Standard.

I. INTRODUCTION

Recently the National Research Council Canada (NRC) purchased a 10 V Programmable Josephson Voltage Standard (PJVS) system from the National Institute of Standards and Technology (NIST). We estimated the uncertainty budget for voltage calibrations and compared the new system performance with the NRC hysteretic system [1]. The PJVS acts as a frequency-to-voltage converter; therefore, the accuracy of the output voltage is directly tied to the frequency source accuracy. In this paper, we report on high precision measurements of the microwave generator frequency accuracy and on the investigation of the frequency resolution for this generator.

II. FREQUENCY ACCURACY

We use a 10 MHz reference frequency signal derived from the NRC Caesium frequency standard, which has an expanded frequency uncertainty of 10-13

(k = 2), as a time base for the microwave generator (Agilent E8257D). In order to quickly verify the frequency accuracy of the microwave signal (after it is amplified but before it enters the cryoprobe), we connect it (with approximately 30.5 dB attenuation) to a counter (Agilent 53150A) also locked to the same 10 MHz NRC reference frequency signal. For an 18.7 GHz frequency setting on the E8257D, we measure an offset of at most 1 Hz, which corresponds to a standard uncertainty of 0.29 Hz assuming a rectangular distribution. Based on the counter specifications, the accuracy of this instrument is ±1 Hz and the residual stability is ±0.6 Hz (the uncertainty from the NRC reference frequency signal is negligible for this counter). Assuming a rectangular distribution for the accuracy and a normal distribution for the residual stability, we get a combined relative frequency uncertainty of 4.7×10-11

(k = 1) at 18.7 GHz. At an output voltage of 10 V, this results in an uncertainty of 0.47 nV (k = 1).

In order to achieve significantly lower uncertainty, we calibrate the frequency output of the microwave generator with respect to the supplied external reference frequency by using the NRC Frequency and Time Group atomic clock and measurement systems in our test setup. The calibration setup is displayed schematically in Fig. 1(a). The NRC-built hydrogen maser (H4) is used as a source for the reference frequency because of its superior frequency stability at short (seconds) and intermediate (days) time intervals. We use a SpectraDymanics CS-1 synthesizer to generate the reference microwave frequency to be used for this calibration. This synthesizer is specifically designed to be used with primary and secondary Caesium frequency standards and has a frequency uncertainty negligible relative to that of the microwave function generator under test. In addition, we use the following devices: Mini-Circuits power splitter model ZX10-2-98-S+ and mixers models ZX-05-24MH-S+ and ZMX-10G+; MITEQ amplifiers models JS3-08001200-18-5A and AMF-5S-9099-2; and HP mixer model HMXR-5001. A separate measurement was performed to verify that the uncertainty of these components is negligible (not shown).

Fig. 1. Comparison of E8257D with the NRC Hydrogen maser. (a) Schematic of the frequency accuracy and resolution measurement circuit. fH4 = 5 MHz, fCs1 = 9.2 GHz, fDUT = 18.4 GHz + f0, and f0 is

close to 5 MHz. (b) Phase offset x(t) as a function of time where f0 is

set to 5 MHz. (c) Allan deviation from (b). (d) x(t) as a function of time where f0 = (5 + 10

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The signal from H4 at fH4 = 5 MHz is used as an external

reference for the CS-1. The CS-1 10 MHz output is used as the external reference for the E8257D microwave generator set at a test frequency of fDUT = 18.4 GHz + f0, where the value

of 18.4 GHz is chosen to be twice the 9.2 GHz CS-1 synthesizer output and close to the operating 18.7 GHz. The value of f0 is set around 5 MHz to match the standard

frequency used in the Frequency and Time laboratory measurement systems. The DUT phase and frequency noise is part of f0. The CS-1 fCs1 = 9.2 GHz signal is split into two

9.2 GHz reference signals (fCs11 and fCs12) using the

Mini-Circuits power splitter. We then mix the test signal fDUT at

18.4 GHz + f0 with the fCs11 reference signal to obtain an

fB = 9.2 GHz + f0 beat signal. We amplify both fCs12 and fB and

mix them together to produce the test signal fT = f0. The signal

at fT is amplified and then compared to H4 using the

NRC-built phase comparator system, which provides a continuous phase offset measurement, x(t), between any test 5 MHz signal and a 5 MHz reference derived from H4. This phase measurement closes the loop between fH4 and H4. The noise

characteristics of this measurement combine the noise of all test and measurement equipment used in the setup and provide the upper limit on the frequency stability of the PJVS microwave generator.

The phase comparator acquires one measurement of x(t) every second, and these results are analyzed to derive the phase and frequency noise and the fractional frequency offset (FFO) (f0 - fH4)/fH4 (calculated from the first differences of the

phase data). We use the two-sample overlapping Allan deviation [2] to analyze the noise performance at averaging interval ta. The stability of f0 is evaluated in order to check the

test device for frequency accuracy. Results are shown graphically in Figs. 1(b) and (c) and are summarized in the first line in Table 1. Namely, the frequency offset of f0 relative

to fH4 is (0 ± 2)×10 -11

, where the standard uncertainty (k = 1) is derived from the Allan deviation results at ta = 20 s [see

Fig. 1(c)].

The calibration method outlined here is repeated three years later, showing frequency stability and uncertainty for the E8257D similar to the results presented in this paper. The microwave generator is, therefore, stable on long time scales and locks properly to its external reference.

III. FREQUENCY RESOLUTION

The PJVS system allows for up to a 10 MHz frequency change away from the frequency used to get the margins required in order to produce voltages with a specific numerical value. In order to verify that the E8257D microwave generator achieves the 1 mHz resolution assumed by the fine tuning of the PJVS, we change the set frequency fDUT by up to 10 mHz.

Again, we look at the phase offset between the new signal at fT

and fH4. For the case where the set change in f0 is only 1 mHz

(i.e. the highest resolution of the generator), the phase offset

and Allan deviation as a function of time are shown in Figs. 1(d) and (e). The results for different frequency settings are tabulated in Table 1, where the calculated values are compared to the measured values and the standard uncertainty at 5 MHz, u5MHz, (k = 1) comes from the Allan deviation results

at ta = 20 s.

Table 1. Measured fractional frequency offset (FFO) relative to the NRC 5 MHz reference from the hydrogen maser for different test frequencies around 18.405 GHz. fDUT (GHz) Calc. FFO (10-11) Meas. FFO (10-11) u5MHz (10-11) 18.405 0 0 2 18.405+10-12 20 19 2 18.405 - 10-12 -20 -21 2 18.405+10-11 200 201 2

From the results in Table 1, we can calculate the upper limit for the absolute frequency noise of f0, simply by multiplying

2×10-11 by 5 MHz, to get 10-4 Hz. We get to the relative frequency offset at 18.4 GHz by a simple division to get a standard relative frequency uncertainty of 6×10-15 (k = 1). Therefore, the microwave synthesis process does not add a significant uncertainty to the already known offset of the reference frequency signal from the SI second proper time frequency, which is (0 ± 10-13) (k = 2). For a 10 V PJVS output, this converts into a 1 pV type B uncertainty (k = 2) in the uncertainty budget.

IV. CONCLUSION

We have measured the fractional frequency offset of our PJVS microwave generator using standard frequency and time techniques. The offset with respect to the Frequency and Time Group frequency reference is (0 ± 6×10-15) at k = 1. Therefore, the accuracy of the frequency is dominated by that of the reference frequency signal itself, which is (0±10-13) at k = 2. The 1 mHz resolution for this generator as well as its long-term stability were also confirmed using the same setup.

ACKNOWLEDGEMENT

We thank D. Patel and W. Pakulski for technical help. REFERENCES

[1] G. Granger and B. M. Wood, "Preliminary comparison of a 10 V programmable Josephson voltage standard and a hysteretic Josephson voltage standard," 29th Conference on Precision Electromagnetic Measurements (CPEM 2014), Rio de Janeiro, pp. 530-531, 2014.

[2] D. W. Allan, “Statistics of atomic frequency standards,” Proceedings of the IEEE, vol. 54 no. 2, pp. 221-230, February 1966.