Magnetic Field Measurement Using a SAW Delay Line Sensor and a GHz Lock-in Amplifier

Introduction

In recent years, magnetic sensing has become a vital tool across a range of applications, from navigation and current measurement to bio-magnetic sensing. A crucial aspect of any sensing scheme is the limit of detection (LOD) [1], which is influenced by both the sensitivity of the sensing element to magnetic fields and the performance of the measuring electronics.

Surface Acoustic Wave (SAW) based sensors have shown significant promise in these measurements. Traditional SAW devices comprise interdigitated transducers (IDTs) that are spaced over a substrate material. The electrode spacing within the IDT structure determines the device's operational frequency range. By applying amorphous magnetic layers on top of the SAW substrate, these devices can be made sensitive to external magnetic fields, allowing them to detect small magnetic signals.

Recently, we had the opportunity to visit the CRC1261 (biomagnetic sensing) at the University of Kiel, where SAW sensors are being in a delay line configuration for biomedical sensing applications. For more details, please visit their website.

What is a SAW Delay Sensor?

A Surface Acoustic Wave (SAW) delay line operates by using piezoelectric materials to convert electrical signals into mechanical waves that travel across a surface, inducing a time delay before the signals are converted back into electrical form. This is typically comprising of two interdigitated transducer (IDT) electrodes positioned at a specific distance apart while the mechanical wave propagates perpendicularly to the IDTs. The delay time is directly proportional to this distance and inversely proportional to the velocity of the wave. These devices are commonly used in applications such as filters, resonators, and sensors.

In this blog, the SAW sensor employed utilizes an ST-cut quartz substrate. A 150 nm thick magnetostrictive (Fe80Co20)78Si12B10 thin film is applied to the surface of the delay line, serving as the sensitive element. The sensor operates at a frequency of approximately 146.3 MHz and possesses a magnetic sensitivity of 7442.1 rad/T. Measurements are carried out in a transmission configuration, connecting the output and input terminals to our GHFLI 1.8 GHz lock-in amplifier as shown below in Figure 1.

Open loop Measurements

An initial measurement is conducted to compare the transmission of the SAW delay line to a reference phase. This process involves driving the SAW with a phase-stable reference source, such as the GHFLI Lock-in amplifier, and connecting the transmission output to the instrument directly as already shown in Figure 1.

Figure 2 illustrates an open-loop characterization of the aforementioned SAW delay line using the GHFLI's Sweeper module. This characterization is accomplished by conducting a lock-in measurement at a fixed drive voltage (100 mV) while plotting the amplitude and phase response of the delay line as a function of frequency within the Sweeper tool. The delay line demonstrates the expected linear phase dependence over a broad frequency range (only a few MHz shown here). However due to the resonance gain it is only effective within a narrow frequency band (144-149 MHz). The signal to noise ratio deteriorate outside this frequency range.

Thanks to the phase unwrap option in the Sweeper tool, high phase deviation (few kilo-degrees) could be nicely showcased over a frequency range spanning a few MHz. The fitting is performed (not shown) directly within the Sweeper toolbox utilizing the Math functionality revealing the expected linear phase dependence with a slope of  \(\delta \phi / \delta f\)  = -500 µdeg/Hz. At a specific operating point i.e. frequency, the phase is determined by the substrate's material properties. As a result, the delay line can be now used as a sensor. Any external magnetic field will alter the velocity of the propagating wave on the surface, resulting in a change in delay that can be captured as a phase shift relative to the reference phase.

Closed loop controlled measurement

Operating the Sensor in a configuration where its excitation is in a closed loop control enables the use of phase locked loops (PLLs) to maintain the drive at a desired phase on the phase response plot shown in Figure 2. Any offset in phase due to sensing measurements can now be accurately tracked thanks to the PLL. Closed-loop control offers the advantage of measuring magnetic signals with high bandwidth and dynamics while operating the sensor under optimal electrical conditions i.e. where the amplitude response is significantly higher (Figure 2). For a more detailed discussion of the advantages of using a closed-loop system compared to open-loop operation, see Ref. [2].

We choose to implement the PLL around the peak amplitude (~146.27 MHz) mainly due to its higher signal-to-noise ratio (SNR) as discussed before. The PLL is set with a target phase of 93.7 degrees and a bandwidth of 1 kHz, as depicted in Figure 3(a). To determine the proportional (P), integral (I), and derivative (D) parameters of the PLL, we utilize the advisor tool, leveraging the gain \(\delta \phi / \delta f\) calculated in the previous section.

How does the sensor work?

In the open loop configuration, a drive is injected in the SAW delay line sensor at a carrier frequency \(f_{c}\) and measured in a transmission configuration directly at the input of the GHFLI. Any time varying external magnetic field \(B(t)\) will induce additional phase modulation on this signal. This transmitted signal, \(s(t)\) can be written as [3, 4]:

Where, \(G\) is the so-called sensitivity, \(\phi_{Noise}(t)\) is the combined zero mean phase noise contribution that comes from various electronic sources and \(\phi_{SAW}\) is the constant phase shift coming from the SAW sensor itself.

The demodulated phase of the transmitted signal can be written as:

When there is no magnetic field applied i.e. \(B(t) = 0\), \(\phi_{demod}\) is constant and one can implement a PLL directly at this detected phase. The locked phase will then have a Gaussian profile with a mean of \(\phi_{SAW}\) and a standard deviation related to \(\phi_{Noise}\). This data as a function of time was already displayed in Figure 3(b).

In order to showcase the sensor, an external sinusoidal magnetic field is applied with a frequency of \(f_m = 100\) Hz as the sensing field. This magnetic field periodically alters the group velocity of the surface waves, which in turn modulates \(\phi_{demod}\) at the same rate of \(f_m\). When the resonator is phase locked at \(\phi_{SAW}\), the PID shift directly reflects the modulation \(f_m\)while the bandwidth of the PLL, \(f_{BW}\) satisfies the following criteria, \(f_{BW}>f_m\). In this particular example we choose \(f_{BW} = 1\) kHz.

The Lab One software facilitates not only the direct streaming of this PID shift but also allow examination of the signal's representative spectrum. Figure 4 illustrates how the modulated magnetic field appears in the PID shift by the blue shaded region. The limit of detection (LOD) for this measurement is determined by the ratio of the modulation peak to the background noise, which in this instance is significant, with the modulation peak being approximately two orders of magnitude larger.

Conclusion

In this blog post, we explore the measurement of a Surface Acoustic Wave (SAW) delay line sensor using the GHz frequency lock-in amplifier, GHFLI. The GHFLI, with its integrated Sweeper tool and PID feedback schemes, enables both open-loop and closed-loop measurements without the need of any additional electronics.

Moreover, the LabOne software's in-built spectrum analyzer allows for direct streaming of the PID error in the frequency domain. This capability facilitates the immediate identification of sensing fields within a single software framework, streamlining the sensing process and enhancing measurement efficiency.

Acknowledgements

We thank Henrik Wolframm from the group of Michael Höft at CAU Kiel for the possibility of performing these measurements, sharing the data with us and his valuable feedbacks regarding the blog post. I would also like to thank my colleague Heidi Potts for her valuable suggestions and feedbacks.

References

[1] Durdaut et al. “Noise Analysis and Comparison of Phase- and Frequency-Detecting Readout Systems: Application to SAW Delay Line Magnetic Field Sensor”. IEEE Sensors Journal, Vol.. 19, 18 September 15, 2019.

[2] Durdaut et al. ”Equivalence of open loop and closed-loop operation of SAW resonators and delay lines,” Sensors (Switzerland), vol. 19, pp. 1-16, 2019, doi: 10.3390/s19010185.

[3] Kittmann et al. “Wide Band Low Noise Love Wave Magnetic Field Sensor System”. Scientific Reports, 8:278 (2018).

[4] Elzenheimer et al. "Key Metrics and Experimental Test Bench for Assessing Highly Sensitive Magnetometers in Research". IEEE Sensors Journal, 25(2), 2432–2455.