How Does a Zurich Instruments Lock-In Amplifier Work?

February 7, 2022 by Heidi Potts

Have you ever wondered what is going on inside your Zurich Instruments lock-in amplifier? Lock-in amplifiers enable precise measurements of small signals buried in noise. While analog instruments have been used for decades, the development of analog-to-digital converters with high speed, resolution, and linearity has more recently enabled the realization of digital instruments where all signal processing is carried out numerically. This development helped to push the frequency range, input noise, and dynamic reserve to new limits. In addition, digital signal processing is much less prone to errors introduced by a mismatch of signal pathways, to cross-talk, and to drifts caused by temperature changes, for instance. The availability of field-programmable gate arrays (FPGA) with high computing power, abundant memory, and high speed has enabled to build instruments that contain several lock-in amplifier units, PID controllers, boxcar averagers, and arbitrary waveform generators - all in one box. In this blog post, we provide an overview of how this is done in a Zurich Instruments lock-in amplifier and illustrate how this implementation enables to perform many measurements in parallel.

Instrument Architecture

The heart of a Zurich Instruments lock-in amplifier is the FPGA where the entire signal processing is implemented. The FPGA is connected to an analog and digital interface as shown in Figure 1. This interface include the signal inputs, signal outputs, auxiliary and trigger channels and a digital DIO port. At the input, the signal is digitized using an analog-to-digital-converter (ADC) and then routed to the FPGA where it can be split into several paths. In the digital domain, a duplication of the signal is possible without any signal loss, which constitutes a great advantage over analog instruments where the analog signal has to be divided. Duplication of the digital signal in combination with the high processing power of the FPGA enables the operation of many signal-analysis tools in parallel.

Zurich Instruments' lock-in amplifiers are entirely computer-controlled through the LabOne® software. In addition to providing a variety of possibilities to display and analyze the results, this functionality is also useful when working remotely or discussing measurements with colleagues. The instrument is connected to a host computer where the dedicated LabOne Data Server is in charge of all communication to and from the instrument. Data from the FPGA is continuously streamed via USB or Ethernet to the LabOne Data Server, which distributes it to all the clients that subscribe to it. A client can be the web browser-based LabOne user interface or the application programming interfaces (APIs). It is important to note that the data server runs locally on the host computer, so no internet access is needed to operate the instrument and the data never goes out of the user's control. The LabOne software contains a set of versatile time- and frequency-domain analysis tools such as an oscilloscope, data plotter, parametric sweeper, and FFT spectrum analyzer. Additional functionality can be obtained on the instrument with upgrade options that increase the number of demodulators or add PID/PLL controllers, boxcar averagers or an arbitrary waveform generator. The measurement results from different analysis tools can be saved as numerical files; they can also be provided as analog signals on one of the Auxiliary Output channels and can be routed to another signal processing unit on the FPGA.

General architecture of a Zurich Instruments lock-in amplifier.

Figure 1: General architecture of a Zurich Instruments lock-in amplifier, which is controlled by the LabOne software through a user interface or APIs.

Analog and Digital Interfaces

While the analog path in a Zurich Instruments lock-in amplifier is very short, it is carefully optimized to reach an excellent performance in terms of signal distortion and noise. Figure 2 shows a schematic of one of the signal inputs at the front panel of the UHFLI. The analog input signal is amplified by a variable gain input range amplifier, it passes through a low-pass filter, and then gets digitized with an ADC. The variable gain of the input range amplifier in the analog domain allows to adjust the input range to the signal, and thus maximize the resolution by using the full bit depth of the ADC which operates with a fixed voltage range (e.g., 1 V). The low-pass filter removes frequencies above the Nyquist frequency to avoid aliasing effects due to the finite sampling rate of the ADC. In the case of the UHFLI, the bandwidth of the two signal input channels is 600 MHz, and the sampling frequency is 1.8 GSa/s. The analog output signal is generated using a digital-to-analog converter (DAC) followed by a variable output range amplifier. By choosing the same bandwidth for signal input and signal output, we make sure that the instrument can be used efficiently across the whole frequency range, from DC to 600 MHz in the case of the UHFLI.

Schematic representation of the analog part of a voltage input of the UHFLI.

Figure 2: Schematic representation of the analog part of a voltage input of the UHFLI. The signal is amplified and low-pass filtered before it is digitized using an ADC.

To realize complex measurement setups, every Zurich Instruments lock-in amplifier has several auxiliary channels and trigger channels. These channels can be used to provide the measurement results as analog signals, and for synchronization with other instruments. The auxiliary output channels have no variable gain amplifiers and ADCs with lower sampling rates compared to the signal channels since they are designed to provide the filtered measurement results or other slowly varying voltage signals. For example, the auxiliary channels can be used to control electrostatic gates, and to create feedback loops where an external parameter, such as the height of a measurement stage, is controlled based on a measurement result. The trigger channels can be used to acquire external reference signals and for synchronization with other instruments, such as an external scan engine. They are based on comparators with a variable threshold voltage, which enables to read and create TTL signals. 

Zurich Instruments lock-in amplifiers can be synchronized with the 10 MHz clock of any other measurement instrument. The multi-device synchronization protocol makes it possible to run synchronized measurements with several lock-in amplifiers in parallel.

Resolution and Sensitivity

In a digital lock-in amplifier, it is important to understand the difference between input vertical resolution and sensitivity. The vertical resolution is given by the bit depth of the ADC and the input range of the variable gain input range amplifier. The sensitivity, i.e., the the smallest change in signal than can be detected by a measurement, can be much higher than the vertical resolution. This is achieved by oversampling and taking advantage of noise. Since noise can trigger the least significant bits, the quantization error can be reduced by condensing many measurement samples into one data point. In image processing, this effect is known as dithering and can for example be used to convert a grayscale image into black and white. In the case of digital signal processing, it allows to have a sensitivity which is much higher than the resolution based on the input range and the bit depth of the ADC. Let's consider the MFLI as an example. In the MFLI, the ADC operates with a 16-bit resolution and the minimum input range is 1 mV, resulting in a resolution of 2 mV / 216 = 30 nV. Nevertheless, it is possible to achieve a sensitivity as low as 1 nV.

Figure 3a shows an example of the measurement values in binary format if a signal is measured with 30 nV resolution without any noise. If the amplitude of the signal is 160 nV, the measurement gives 0101, but if the signal is 140 nV, the measurement also gives 0101. In reality, noise causes fluctuations in the signal, typically with a Gaussian distribution. Thus, a signal of 160 nV usually gives 0101, but it sometimes also gives 0110 or 0100 or even values further away. Figure 3b shows an illustration of counts per voltage interval if 350 measurements are performed of a 160 nV signal with a voltage resolution of 30 nV. Assuming a Gaussian distribution, the true value of 160 nV can be extracted from the peak of the fitted histogram. This example shows how it is possible to achieve a sensitivity that is much higher than the resolution. Of course, the resulting sensitivity depends on the properties of the noise and the amplitude of the fluctuations (i.e., the width of the Gaussian distribution) compared to the bit resolution. As a rule of thumb, the effective bit resolution can be increased by half a bit, when the number of samples per data point is doubled. For the MFLI with the MF-DIG Digitizer option, reducing the sampling frequency from 60 MSa/s to 1.83 kSa/s, for example, results in an effective vertical resolution of 23.5 bits, corresponding to 0.2 nV.

Illustration of resolution and sensitivity.

Figure 3: Illustration of resolution and sensitivity. a) Measurement values in binary format for an ADC with 30 nV resolution. b) Counts per voltage interval if 350 measurements are performed on a signal of 160 nV. Gaussian noise leads to a randomization of the measurement, which enables recovery of the signal amplitude with higher precision compared to the voltage resolution.

LabOne User Interface and APIs

Configuration of the instrument and readout of the measurement results is done using the LabOne user interface or APIs. All LabOne time- and frequency analysis tools can be used in parallel to realize complex measurement schemes and visualize the results in real-time during the measurement. Setting files can easily be saved and shared with collaborators.

Figure 4 shows a recording from the LabOne user interface where an amplitude-modulated (AM) signal is created using two of the internal oscillators. The input signal is visualized using the Scope tool (bottom panel), and three demodulators are used simultaneously to measure the amplitude of the carrier signal and recover the envelope signal. The result of the first demodulator is recorded using the Data Acquisition tool as shown in the top panels of Figure 4. In this case, the first demodulator at the carrier frequency is operated with a high low-pass filter bandwidth, such that the modulation signal is not filtered out and leads to a sinusoidal modulation of the demodulator result. This can be observed using both in the time-domain (left top panel) as well as in the frequency domain where the two sidebands at are visible (right top panel).

Figure 4: Measurement recording from the LabOne user interface. An AM signal with a 100 kHz carrier frequency and a 2 kHz modulation frequency is generated using two internal oscillators. The signal is recorded using the Scope tool (bottom panel) and simultaneously demodulated at 100 kHz using the lock-in tool. The demodulated signal is captured using the Data Acquisition tool (top panels). The low-pass filter bandwidth was set to 4 kHz such that the 2 kHz modulation can be observed both in the time domain (left) and in the frequency domain (right).

While LabOne provides a convenient interface for configuration and readout, many applications require automation of the measurement. For this, we provide APIs in 5 different languages (Python, MATLAB®, LabVIEW™, C, and .NET). Integration into an existing measurement software is facilitated by the API Commands Log functionality in the LabOne user interface, which provides the full history of all commands that have been sent to the instrument. This makes it possible to first set up the measurement in the graphical LabOne user interface and then copy and paste commands directly from the API Commands Log into a custom measurement software. Drivers for common measurement environments such as QCoDeS, as well as a variety of practical examples, are found on GitHub.

 

Data Routing and Data Acquisition

Simultaneous operation of many tools requires sophisticated data routing pathways. Figure 5 shows a block diagram of the main functional blocks and associated signal pathways of the UHFLI. The input signal can be processed by different signal processing units simultaneously and the measurement results can be routed internally to other modules on the FPGA. Let's look at the orange arrow from the Signal Output of the Demodulator as an example. We can see that the result can be sent to the PID unit, to the Arithmetic Unit (AU), to the Scope tool, to the Trigger Engine, the Auxiliary Output channels, or it can be routed to the input of another demodulator.

Main functional blocks and signal pathways of the UHFLI lock-in amplifier.

Figure 5: Main functional blocks and signal pathways of the UHFLI Lock-in Amplifier.

For any measurement device, a big question is how to acquire the results and save them in a useful format for post-processing. In a Zurich Instruments lock-in amplifier, the server-based implementation facilitates data acquisition. The measurement data is continuously streamed to the data server on the host computer using a USB or Ethernet connection and can be acquired using different LabOne tools, such as the Plotter tool for time traces and the Data Acquisition tool for triggered measurement results. A detailed explanation of different data acquisition tools can be found in this blog post.

How fast can the data be acquired? Applications such as video-rate microscopy, require ultra-fast measurements and data acquisition. With a minimum timeconstant of 30 ns, the UHFLI is an ideal instrument to perform these measurements, and the data transfer using the Ethernet connection in combination with the internal data buffer of the instrument enable to acquire the results fast and efficiently. The maximum data transfer rate depends on several factors, including the number of data transfer channels running simultaneously, and the performance of the host computer. For the UHFLI, up to 1.6 MSa/s of one active demodulator can be sent continuously to the host computer. An even higher data acquisition speed is possible by using the data buffer of the instrument: based on a trigger condition, the data is acquired during a short time interval at a very high rate, saved in the internal memory of the instrument, and then transferred to the host computer at a slower rate (see also this blog post). The data transfer rate can be chosen for each channel individually which allows to efficiently use the bandwidth when several data transfer channels (e.g., several demodulators) are used in parallel. If data is lost between the instrument and the host computer, sample loss is indicated in the LabOne user interface to avoid measurement artifacts. When setting up the experiment it is advisable to adjust the data transfer rate to the speed of the measurement, i.e., to the low-pass filter bandwidth of the demodulators. A transfer rate which is much higher than the low-pass filter bandwidth results in a large amount of data but no additional information is gained because many data points correspond to the same measurement value.

Upgrade Options

A choice of upgrade options enables to adapt the instrument to changing experimental requirements. The upgrade options can be installed at the time of purchase or at any later point in time, without returning the instrument to us. While some upgrade options are available on all our lock-in amplifiers, others are specific to a particular instrument platform. A full list of all available upgrade options can be found on the MFLI, HF2LI, and UHFLI product pages. Let's look at a few examples in more detail.

  • Instead of buying several separate instruments, all our lock-in amplifiers offer an upgrade option for increasing the number of numerically controlled oscillators and demodulators. This enables to capture information from several frequencies or from several harmonics of the fundamental frequency simultaneously (see also this blog post). Frequency multiplexing is possible by assigning several oscillators to a single output channel. The maximum number of demodulators depends on the instrument: four demodulators are provided on the MFLI with the MF-MD option, six on the HF2LI with the HF2LI-MF option, and eight on the UHFLI with the UHF-MF option. 
  • A PID/PLL upgrade option is available on all our lock-in amplifiers to create feedback loops. The PID/PLL controllers are implemented directly on the FPGA of the instrument, and the input parameter can be a measurement result (X, Y, R, Theta) or an external signal. The feedback can be applied to a variety of parameters, such as oscillator frequency, output amplitude, or an offset voltage. Feedback loops are commonly used for scanning probe applications, such as atomic force microscopy. In combination with the multi-frequency and amplitude/frequency modulation options, the PID/PLL option enables complex measurement techniques such as dual-frequency resonance tracking.

Additionally, each lock-in amplifier comes with a choice of upgrade options that are specific to the instrument. Here are two examples:

  • The MFLI supports the MF-IA Impedance Analyzer option, which takes advantage of the separate current and voltage inputs of the instrument. By measuring current and voltage simultaneously, this upgrade allows users to accurately measure the impedance of a device over a wide range of impedance values and frequencies (see also this webinar).
  • With the UHF-BOX Boxcar Averager option, the UHFLI is equipped with two boxcar units. Boxcar averaging is an ideal technique to measure pulsed signals fast and with a high signal-to-noise ratio (more information can be found on this page).

Thanks to the high processing power of the FPGA, all upgrade options can be used in parallel with the standard LabOne time- and frequency-domain analysis tools. Great care is taken to ensure accurate timing and phase-synchronous signal processing when using several modules in parallel.

Conclusion

In this blog post, we have discussed the main architecture of a Zurich Instruments lock-in amplifier and illustrated how the signal is processed from the analog input stage to the final measurement results. In all Zurich Instruments lock-in amplifiers, the entire signal processing is implemented on FPGAs with high processing power. This architecture gives access to a large set of time- and frequency-domain analysis tools in addition to a choice of upgrade options such that the instrument can grow with the experimental needs. All tools and options can be used simultaneously to realize complex measurements while keeping the setup simple.