# Zurich Instruments Newsletter - Edition Q3/2011

## Content

• Interview Alexander Trusov, University of California, Irvine: Gyros in Space
• Reducing Lab Complexity: About pentodes and lock-in amplifiers (a historical research)
• Detailed Application Know-How: Coupling of light to macroscopic mechanical resonators
• Premium Customer Support: Zurich Instruments Blogs
• Premium Customer Support: Scientists for world-wide customer support
• Tips & Tricks: How does one set the sampling rate in a lock-in amplifier?
• Company Agenda

## Interview Alexander Trusov, University of California, Irvine

Dr. Alexander Trusov

Silicon MEMS Quadruple Mass Gyroscope (QMG) with measured Q-factor above 1 million and sub-deg/h performance. (Courtesy of Dr. Alexander Trusov, UC Irvine MicroSystems Lab)

### Gyros in Space

Hello Stephan, thank you for this opportunity. Our field of research at the UC Irvine MicroSystems Lab is sensors and actuators, which in this day and age automatically implies relying on MEMS and microtechnology as the main vehicles of innovation. More specifically, we are developing next generation inertial microsystems based on new architectures for MEMS accelerometers and gyroscopes. These high performance miniature sensor systems are desired for many applications ranging from personal navigation with consumer electronics devices to guidance and control of various weapon platforms. Also, civilian and military users of GPS navigation are becoming increasingly concerned about the vulnerability of GPS to GPS-denied environments (forests, urban canyons, buildings) and potential jamming of GPS signals.

There are two main applications, rate and angle measurements. Can you please explain these two applications in simple words?

All gyroscopes can be divided into two main categories, depending on whether the angular velocity or orientation is being measured. Rate gyroscopes measure the angular velocity, or the rate of rotation of an object. Angle gyroscopes, also called whole angle or rate integrating gyroscopes, measure the angular position or orientation of an object directly. Essentially all existing Micro-Electro-Mechanical-Systems (MEMS) gyroscopes are of the rate measuring type and are typically employed for motion detection (for example, in consumer electronics and automotive safety devices) and motion stabilization and control (for example, in smart automotive steering and antenna/camera stabilization systems). True inertial navigation relies on the continuous tracking of the object's orientation. Measurement of the angular position can be accomplished either by numerical integration of a rate gyroscope's output, or by using an angle gyroscope which effectively integrates the rotation rate by virtue of its internal dynamics and outputs the angle information directly. When a rate gyroscope is used to track the orientation, its output signal is integrated over time together with the associated errors and noise, leading to fast buildup of the orientation angle drifts (for example, white noise in the angular rate signal results in 1/f2drift, or random walk, of the angle). Successful realization of standalone gyroscope-based inertial navigation requires either angle gyroscopes or rate gyroscopes with extremely stable output and very low noise.

What is currently limiting the resolution: measurement technique, micromachining or something else?

This is a very intriguing question, as the noise and long term drift performance limitations of inertial MEMS are in fact active research fields. On the one hand, fabrication imperfections are a serious source of noise and drift, motivating the investigation into new, more robust device architectures and alternative fabrication methods. On the other hand, due to the inherently small mass and capacitance of MEMS, the electrical signals we are dealing with are tiny and prone to various noise sources and interferences. This is why we chose to use the Zurich Instruments lock-in amplifier as one of the main device characterization tools. The lock-in demodulation helps in extracting the small useful signals out of the background noise. Currently, we already own 2 fully loaded units and are having great successes in applying them to our research and development.

What are applications and interesting markets for MEMS gyros?

I would say there are 3 major categories of inertial MEMS applications and markets. Consumer electronic devices have a huge volume of units sold, with the emphasis on ultra-low cost and power devices for motional user interfaces, camera stabilization, etc. MEMS devices for this market often cost less than \$1 per sensitive axis, with a trend toward single-chip multi-axis systems for less than \$1. On the opposite end of the spectrum are defense and space applications, where a relatively small number of devices is needed for weapon platform guidance and control, satellite stabilization, etc. In this domain, a single axis gyroscope can easily cost

\\$1,000 due to the need for high performance and reliability sensors combined with a relatively small volume of units. In between these two markets is the automotive safety and active steering domain. Here, the emphasis is not so much on low noise performance or power minimization, but on extreme long-term (~15 years) output stability in the harsh under-the-hood environment.

Do you employ other materials than silicon?

Today, silicon vibratory rate gyroscopes with capacitive transduction comprise the majority of MEMS gyroscopes in development and production, while some research groups and manufacturers are pursuing quartz devices with piezoelectric transduction or silicon devices with alternative transduction mechanisms such as inductive or electromagnetic. Our group at the UC Irvine MicroSystems Lab has a very strong presence in traditional silicon based microdevices, where the main focus of innovation is the design of the sensor element and its control architecture. At the same time, we are currently developing a potentially revolutionary approach to wafer level 3-D fabrication using a microscale glassblowing process, which takes advantage of pressure and surface tension driven shaping of materials above the softening temperature. This approach allows the creation of smooth spherical structures from such advantageous materials as fused silica, which are notoriously hard to micromachine using conventional methods.

What are your motivation factors to keep you focused on your research?

I think it is very rewarding to push the boundaries of the current engineering state of the art and explore many different ideas. MEMS research can be capital investment heavy, but we are lucky to have a very well equipped fabrication and experimental facility. This also allows us to engage and train graduate students and postdocs in cutting edge research using the best available tools.

When will your first gyro go to space?

Most of our inertial sensors development is geared toward high performance applications like satellite control and stabilization. We have recently been approached by space satellite building teams from two different universities, so I am definitely hopeful to see our gyro in space over the next 5 years.

## Reducing Lab Complexity

### About pentodes and lock-in amplifiers (a historical research)

The lock-in amplifier is a measurement instrument that has fascinated users, programmers, developers and scientists all over the world for decades. The instrument's remarkable performance lies in its ability to recover signals whose amplitude is so small that they can be buried deep in noise, and in its very wide range of applications. The widespread use of lock-in amplifiers in most physics laboratories around the world reflects its importance in applied physics. No oscilloscope, no matter how sophisticated, compares to the lock-in amplifier in terms of conceptual beauty.

The technique used by lock-in amplifiers is well proven, as demodulation has been used for over 100 years in communications and engineering. Although today most lock-in amplifiers are implemented digitally for better performance and stability, they used to be analog for most of the 20th century. The continual improvement of integrated circuits over the last 20 years has enabled the implementation of more powerful features and superior performance.

The invention of the lock-in amplifier is often attributed to a founding member of Princeton Applied Research (PAR), Dr. Robert H. Dicke (1916 - 1997). However, in a 1985 interview, Dr. Dicke himself refuted this attribution. Dr. Dicke was a Professor at Princeton University who made important contributions in astrophysics, and he used frequency mixing widely during World War II for radar applications. He was also involved in bringing the first commercial lock-in amplifier to the market in 1962, one year after having founded PAR.

In the 1985 interview, Dr. Dicke remembers having considered the lock-in technique as described in a paper from Walter C. Michels (1906 - 1975). Whereas the exact paper is not mentioned during the interview, the term lock-in amplifier is mentioned in a paper from Michels in 1941. This paper even refers to an earlier implementation published in 1934. In other words, there are published references to the lock-in amplifier about 30 years before the founding of PAR.

In 1934, R. C. Cosens published a paper on a balanced detector for alternating current bridges. The author proposed a circuit with high frequency selectivity composed of several valves and transformers. He mentioned applications for radio frequencies and foresaw operation of the detector at a wide range of frequencies. The terminology used in the paper is interesting: unipivotal galvanometer, rheostat, electrodynamometer, etc. Cosens concluded his paper by indicating that a commercial, single-box implementation was available on the market by Cambridge Instruments Co. Ltd. What happened to this product we do not know, but today the descendants of this company manufacture products for the analytical market under the brand name Ellutia.

In 1941, W.C. Michels and N.L. Curtis published a paper in the Review of Scientific Instrumentation. A lock-in amplifier with 4 transformers and 2 pentode valves was proposed. They described a circuit with high frequency selectivity and sensitivity for a wide range of applications, in particular to eliminate noise and to balance the in- and out-of-phase components. The operating range of the circuit was 10 kHz. This is the oldest reference to the lock-in amplifier that we have found. Whereas Cosens did not mention the term lock-in amplifier, it seems to have been an accepted term in 1941; apparently the name was established during the years 1934 to 1941.

Between the 1960s and 1990s, the lock-in amplifier market flourished, and many companies produced commercial lock-in instrumentation. What happened during those years will be covered in a forthcoming Newsletter from Zurich Instruments.

### References

• R. C. Cosens, A Balance-detector for Alternating Current Bridges, 1934 Proc. Phys. Soc. 46 818, doi:10.1088/0959-5309/46/6/310
• W. C. Michels and N. L. Curtis, A Pentode Lock-In Amplifier of High Frequency Selectivity, 1941, Rev. Sc. Instr. Volume 12, 444-447, doi:10.1063/1.1769919
• Interview with Dr. Robert Dicke by Martin Harwit at Princeton University, June 18, 1985, http://www.aip.org/history/ohilist/4572.html

## Detailed Application Know-How

Interaction between the laser light field and a resonator, in this case a membrane placed into an optical cavity. The plot shows the light transmission through the optical cavity as a function of the cavity length change (y axis in nm) and membrane position inside the cavity (x axis in nm). The multiple wavy lines are the result of driving the resonator into non-linear response. (Courtesy of Dr. Nathan Flowers-Jacobs, Harris Lab, Yale University)

### Optomechanics - the coupling of light to macroscopic mechanical resonators

As predicted by Maxwell, the radiation pressure of light exerts a force on physical objects when light reflects off their surface. This small force is responsible for turning comets' tails away from the sun, and at microscopic scales, it is used as optical tweezers to trap tiny particles. Radiation pressure is predicted to become increasingly relevant in MEMS circuits, as their physical dimensions shrink. Optomechanics deals with understanding and controlling the interaction between light and macroscopic mechanical objects with applications ranging from more precise control and measurements of mechanical motion to the detection of individual phonons.

In practical applications, this dynamic interplay of light-matter can be used to remove energy from a mechanical system, thereby achieving cooling without cryogenics. Indeed in recent experiments, researchers from several groups have exploited lasers to cool down different kinds of resonators (membranes, vibrating toroids, cantilevers) from room temperature down to temperatures below 1 K.

Further cooling towards the mechanical ground state would permit to explore the fundamental properties of dissipation in macroscopic systems, or to place them in an entangled state with the light field. Conversely, by pumping energy coherently into a resonator, amplification of the mechanical motion can be realized, leading eventually to nonlinear dynamics and to instability. Light can also mediate the coupling of membranes to other quantum systems, such as a cold atomic cloud affecting directly the membrane dissipation rate.

Radiation pressure also imposes the fundamental limit to precise position measurements, for example in gravitational wave interferometers, in which the random arrival of the light quanta on the interferometer mirror will result in the reflected photons impressing random kicks to the mirror (shot noise). This quantum back-action differs from Brownian thermal motion and reflects the true quantum mechanical zero point motion.

### High Performance Lock-in Amplifier Required

To detect the resonator periodic vibrations, the lock-in amplifier is an instrument of choice and the Zurich Instruments HF2LI 50 MHz lock-in amplifier has several advantages. With typical resonator natural frequencies around 100 kHz - 1 MHz, researchers benefit from the HF2LI's wide frequency range, its ability to demodulate simultaneously up to 6 arbitrary frequencies (HF2LI-MF option), and they may also find it useful to mechanically drive the resonator at its resonance frequency by means of an integrated phase-locked loop (HF2LI-PLL option). Moreover, when trying to detect the smallest position displacement (which reflects the resonator temperature), it is of fundamental importance to differentiate the signal from the noise; so the HF2LI's 120 dB of dynamic reserve is particularly important when the researcher's measurements are in the shot-noise limited regime. Lastly, since the resonators must have high Q factors for an efficient coupling, an ultra high stability reference oscillator (HF2LI-UHS option) ensures a reference clock with a very low frequency drift.

### Zurich Instruments Blogs

Earlier this year, we introduced a customer-oriented blog on our website. In this Newsletter, we would like to bring the blog closer to our user community and ask for your feedback. In the blog, advanced users and software developers exchange their experiences using our instruments, and also share their findings and suggestions with other users around the world.

Are you an HF2 user and do you like to post on lock-in amplification & relevant applications? Please let us know if you have any remarks that you would like to publish on our blog by contacting us at support@zhinst.com.

For example:

• In his blog, Zurich Instruments' Jürg Schwizer explains how to control an HF2LI lock-in amplifier with MATLAB for powerful, repetitive measurements and scripting. Do not miss this contribution if you prefer MATLAB as a programming environment. You are also encouraged to rate your appreciation with a Facebook Like.
• In her posts, Zurich Instruments' Lara Juricic demonstrates how to communicate with the HF2LI lock-in amplifier using the Python programming language. This is achieved with an interface library that transforms the ziAPI into a native Python interface.
• If you need guidance to program with LabVIEW, then the blog of Zurich Instruments' Andrin Doll will be of interest to you. Andrin provides an overview of the Zurich Instruments LabVIEW library categories. In a detailed example, the programming concept, blocks, settings and a typical programming task are explained. Andrin also provides hints on how to simplify the programming and improve the settings.

### Scientists for world-wide customer support

As of the 15th of September 2011, two Application Scientists have joined the Zurich Instruments Customer Support Team.
Dr. Jan Benhelm ( ) obtained his PhD degree in experimental quantum optics from the University of Innsbruck, Austria, and brings in-depth knowledge in laser spectroscopy and radio-frequency techniques to Zurich Instruments. During his PhD, Jan worked extensively with lock-in amplifiers and PLLs. Jan also has 3 years work experience in the product management of technical products and in consulting to a wide range of customers in Europe. Zurich Instruments' customers will benefit from Jan's wide application knowledge and world-class technical customer support.
Dr. James Wei (james.wei@zhinst.com) obtained his PhD degree in RF electronics design from l'Institut National des Sciences Appliquées de Lyon, France. James has in-depth knowledge of analog and digital signal processing with 11 years of experience in integrated circuits design, including the design of complex ICs that have been mass-produced in the millions of units. James is familiar with both Asian and Western cultures, he speaks several languages fluently, and he focuses on Zurich Instruments' customers in Asia. James will travel frequently to Singapore, Hong Kong, Shanghai, Beijing and Taipei.

## Tips & Tricks

### How does one set the sampling rate in a lock-in amplifier?

The demodulated signal sampled by the HF2 is sent to the host PC through the USB cable. For single shot measurements, the sampling rate is not relevant, but if one is interested in the signal dynamics, selecting the wrong sampling rate may result in artificial distortions of the detected signal. In particular, a too low sampling rate (undersampling) leads to aliasing, which cannot be corrected in post-processing. The good news is that oversampling does not cause any problems except for wasted USB bandwidth. (The demodulated signal is also available on the auxiliary outputs of the HF2, for which the sampling rate is always fixed to 960 kS/s and aliasing does not occur.)

To fulfill the Nyquist-Shannon Criterion, the minimum readout sampling rate needs to be twice the maximum frequency present in the signal. One has to make sure that the spectral content of the signal above the Nyquist frequency (half of the sampling rate) is negligible: in other words, that the signal is sufficiently attenuated by the filters.

The amount of aliasing depends on the filter bandwidth and order. So, for instance, if a 90% aliasing suppression is sufficient, the readout sampling rate should be 20 times the f-3dB filter bandwidth for a 6 dB/octave filter, and 7 times for 24 dB/octave. If instead 99% aliasing suppression is desired, the sampling rate should be 200 times for a 6 dB/octave filter and 12 times for a 24 dB/octave filter.

### Example

In Atomic Force Microscopy (AFM), one would like to achieve a scan rate of 1,000 pixels per second (1 ms per pixel). The filter should allow the signal to settle to 99% of its final value within 1 ms. A fourth order filter settles to 99% within 10 time constants. Therefore, the time constant needs to be 100 µs (1 ms / 10), or f-3dB = 690 Hz. So, the sampling rate should be set to at least (690 Hz ⋅ 7 =) 5 kS/s.

## Company Agenda

• uTAS 2011 (Miniaturized Systems for Chemistry and Life Science),Seattle, Washington USA, October 2 - 7, 2011
• MESURExpoVISION and International Metrology Congress,Paris, France, October 4 - 6, 2011
• AVS 58th International Symposium & Exhibition,Nashville, Tennessee USA, November 1 - 3, 2011
• Annual Meeting of the Physical Society of the Republic of China 2012,Chiayi, Taiwan, January 17 - 19, 2012
• SPIE Photonics West 2012,San Francisco, California USA, January 24 - 26, 2012

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