^{1,a)}and D. S. Ricketts

^{2}

### Abstract

This work presents a technique for measuring ultra-low power oscillator signals using an adaptive drift cancellation method. We demonstrate this technique through spectrum measurements of a sub-pW nano-magnet spin torque oscillator (STO). We first present a detailed noise analysis of the standard STO characterization apparatus to estimate the background noise level, then compare these results to the noise level of three measurement configurations. The first and second share the standard configuration but use different spectrum analyzers (SA), an older model and a state-of-the-art model, respectively. The third is the technique proposed in this work using the same old SA as for the first. Our results show that the first and second configurations suffer from a large drift that requires ∼30 min to stabilize each time the SA changes the frequency band, even though the SA has been powered on for longer than 24 h. The third configuration introduced in this work, however, shows absolutely no drift as the SA changes frequency band, and nearly the same noise performance as with a state-of-the-art SA, thus providing a reliable method for measuring very low power signals for a wide variety of applications.

This work was supported by the NSF grant (Grant No. ECCS-1055279).

I. INTRODUCTION

II. CALCULATION OF THE BACKGROUND NOISE

III. MEASUREMENT OF BACKGROUND NOISE FOR THREE CONFIGURATIONS

A. Config. I: Standard STO apparatus with Advantest R3271A Spectrum Analyzer

B. Config. II: Standard STO apparatus with Agilent E4440A Spectrum Analyzer

C. Config. III: Proposed new STO characterization apparatus

IV. STO OSCILLATIONMEASUREMENT: A COMPARISON OF THREE CONFIGURATIONS

V. CONCLUSION

### Key Topics

- Position sensitive detectors
- 25.0
- Thermal noise
- 15.0
- Oscillators
- 9.0
- Machinery noise
- 7.0
- Amplifiers
- 5.0

##### B82B1/00

##### G01L

##### G01L3/00

##### G01R21/00

##### G01R23/16

##### H03B

## Figures

Block diagram of the standard STO characterization apparatus considered in this work.

Block diagram of the standard STO characterization apparatus considered in this work.

VSD of the SC output, , for different VBWs. The plot was produced through a numerical experiment, by generating random values for the real and imaginary parts of the SA input and applying the corresponding RBW and VBW filtering, rectifying by an envelope detector and squaring the signal to produce the final normalized VSD plot. The frequency and VBW are normalized by RBW. The VSD plots are normalized by the intersection point of the VSD plot for VBW/RBW = ∞ with the y axis.

VSD of the SC output, , for different VBWs. The plot was produced through a numerical experiment, by generating random values for the real and imaginary parts of the SA input and applying the corresponding RBW and VBW filtering, rectifying by an envelope detector and squaring the signal to produce the final normalized VSD plot. The frequency and VBW are normalized by RBW. The VSD plots are normalized by the intersection point of the VSD plot for VBW/RBW = ∞ with the y axis.

(a) RMS of the difference between the nth and 50th PSDs measured by the old SA (Advantest R3271A). These RMS plots are normalized by the total gain to be referred to the input. The sweep parameters are given in the text. The SA performs 5 sequences of PSD measurements, centered at 4, 9, 14, 19, and 24 GHz, as shown by the sequence number on the plot. The arrow in sweep sequence 1 shows that the entire 50 PSD measurements for sweep sequence 1 are completed before sweep sequence 2 begins. The 50th PSD is used as the base line noise subtracted from the nth PSD (1 ⩽ n ⩽ 49), thus 49 lines are plotted in the figure. (b) blue line is the RMS of the difference between 49th and 50th PSDs, and the red line is the STD of the input referred PSD calculated from . Note that σ49 corresponds to the interval of 1 between two sweeps in (a).

(a) RMS of the difference between the nth and 50th PSDs measured by the old SA (Advantest R3271A). These RMS plots are normalized by the total gain to be referred to the input. The sweep parameters are given in the text. The SA performs 5 sequences of PSD measurements, centered at 4, 9, 14, 19, and 24 GHz, as shown by the sequence number on the plot. The arrow in sweep sequence 1 shows that the entire 50 PSD measurements for sweep sequence 1 are completed before sweep sequence 2 begins. The 50th PSD is used as the base line noise subtracted from the nth PSD (1 ⩽ n ⩽ 49), thus 49 lines are plotted in the figure. (b) blue line is the RMS of the difference between 49th and 50th PSDs, and the red line is the STD of the input referred PSD calculated from . Note that σ49 corresponds to the interval of 1 between two sweeps in (a).

(a) RMS of the difference between the nth and 50th PSDs measured by the modern SA (Agilent E4440A). These RMS plots are normalized by the total gain to be referred to the input. The sweep parameters are given in the text. (b) blue line is the RMS of the difference between 49th and 50th PSDs, and the red line is the STD of the input referred PSD calculated from . Note that σ49 corresponds to the interval of 1 between two sweeps in (a).

(a) RMS of the difference between the nth and 50th PSDs measured by the modern SA (Agilent E4440A). These RMS plots are normalized by the total gain to be referred to the input. The sweep parameters are given in the text. (b) blue line is the RMS of the difference between 49th and 50th PSDs, and the red line is the STD of the input referred PSD calculated from . Note that σ49 corresponds to the interval of 1 between two sweeps in (a).

(a) Block diagram of the STO characterization apparatus with the adaptive drift cancellation technique. (b) STD of the nth sweep obtained by this technique. The sweep parameters are given in the text. (c) blue line is the STD of the 50th sweeps obtained by this technique, red line is the STD of the input referred PSD calculated from , and black line is the RMS of the difference between 49th and 50th PSDs obtained by the standard baseline noise subtraction algorithm with the same SA (blue line in Fig. 3(b) ).

(a) Block diagram of the STO characterization apparatus with the adaptive drift cancellation technique. (b) STD of the nth sweep obtained by this technique. The sweep parameters are given in the text. (c) blue line is the STD of the 50th sweeps obtained by this technique, red line is the STD of the input referred PSD calculated from , and black line is the RMS of the difference between 49th and 50th PSDs obtained by the standard baseline noise subtraction algorithm with the same SA (blue line in Fig. 3(b) ).

Comparison of the STO signal obtained by the three different configurations. From top to bottom, the blue, red and black lines are obtained by the standard baseline subtraction technique with an old SA, the same technique but with a modern SA and by the adaptive drift cancellation technique with the old SA introduced in this work, respectively.

Comparison of the STO signal obtained by the three different configurations. From top to bottom, the blue, red and black lines are obtained by the standard baseline subtraction technique with an old SA, the same technique but with a modern SA and by the adaptive drift cancellation technique with the old SA introduced in this work, respectively.

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