The many applications of the MF-MD Multi-Demodulator option

During my research days, lock-in amplifiers were a standard fixture in a transport measurement setup, and there were many of them. Each lock-in measured one signal in the experiment. Adding more lock-in amplifiers in the setup was the only way to learn more about the device transport properties, but this made setups complicated and measurements less reliable. Today I see many of our customers work with lock-ins such as the MFLI and adopt a modern measurement approach that enables multi-point simultaneous data acquisition in the time and frequency domain without compromising the quality of the measurements. To simplify the setup and study more device properties at once, it is indeed sufficient to add the MF-MD Multi-Demodulator option to a basic MFLI unit. This blog post is about how the MFLI lock-in amplifier becomes a powerful measurement and signal generation instrument capable of doing so much more than what I used to be able to achieve in my laboratory days.

Almost every lock-in amplifier on the market has a voltage and a current  input where signal is amplified, with phase sensitive detection through demodulation, as a main working principle behind one or the other input. Let’s first see what a demodulator is and what to expect from a basic lock-in amplifier.

The demodulator measures the amplitude and the phase of a periodic signal at a reference frequency and further increases the signal-to-noise ratio using a low pass filter. This is done by mixing (or multiplying) the input signal with a reference signal. The multiplication is split in two orthogonal paths, depicted in Figure 1a, one in phase with the reference, and the other out of phase (90 deg) with the reference. This way the signal is captured around the reference frequency, after which adjustable low pass filtering is applied to reduce the surrounding noise. The schematic of the so-called dual-phase demodulator is shown in Figure 1a, where its output consists of the in-phase and out-of-phase component, x and y, or R and θ. Adjusting the parameters in the Zurich Instruments lock-ins is done via LabOne user interface, graphically represented in the Figure 1b so you can better understand how the signal is progressed through the device from inputs to outputs.

Figure 1. a) Demodulator schematics and b) LabOne user interface demodualtor graphical representation.

Another way to represent the signal flow from input to the output via demodulator is shown in Figure 2. This in-line representation gives us a good overview of all the available measurement possibilities. In the case of a basic unit, the two available inputs Voltage and Current can use 1 oscillator and 1 demodulator for measurement (data transfer enabled) and an external reference demodulator (no data transfer available) that is also connected with the output. The two demodulators have a different role, the top servers as a measurement unit of the amplitude and phase and the bottom to define the reference signal which is directly connected to the output and defines its Frequency,  Amplitude and Phase. 

 

Figure 2. LabOne user interface with in-line representation of the basic MFLI Lock-in Amplifier unit with one demodulator.

Together with the included LabOne toolset this is a powerful combination, but it becomes insufficient when we want to measure current and voltage at the same time – which is a must for transport and impedance measurements; having AC and DC signals . In SPM, having the ability to form feedback loops for both amplitude and phase requires closing them with separate demodulators that have different filter settings (different loop bandwidths). Furthermore, in thermal-transport studies, 3-omega measurements require extracting higher harmonics, for spin Hall effect 2nd harmonic is measured in addition, etc. Having the ability to test your system at several arbitrary frequencies at the same time is invaluable for semiconductor component performance testing. Typical pump-and-probe measurements require two modulation frequencies who’s mixing again requires at least two demodulators, similarly the 2D time-domain spectroscopy requires multi-modulation approach.  Let’s see how this is done.

Adding the MF-MD option to the basic MFLI unit

First, you get 4 demodulators instead of 1, a total of 4 oscillators and 4 separate output amplitudes, 1 for each demodulator. With this you have the freedom to mix and assign the 4 oscillators to any available demodulator with which each output can be adjusted for frequency, phase, and amplitude.

 

Figure 3 MF-MD option installed for MFLI Lock-in Amplifier. Highlighted are 4 oscillators, demodulators and corresponding output paths.

What does this mean in terms of measurement possibilities? The additional demodulators unlock and enable several measurement capabilities that involve measurement parallelism with additional oscillators and demodulators. It enables signal output configuration with flexible amplitude and phase assignment for each signal.

Measuring signals at 4 frequencies simultaneously

As we mentioned already, with the MF-MD option, the 4 demodulators are equipped with 1 independent oscillator each. This means that you can output and measure at maximum 4 arbitrary frequencies at the same time. The oscillator assignment is not fixed to a demodulator and you can easily change it depending on your need. The 4 outputs are outputting sine wave signals with  frequency equal to the Demod Frequency and with phase assigned to that demodulator with respect to a reference. Changing the phase and outputting the signal at the same demodulator line will not produce any measurable phase shift as we have in that case rotated the whole frame of reference.

The output frequency is determined by the demodulator frequency as:

Demod Freq (Hz)= Osc Frequency (Hz) x Harm                                   (1).

A simple example of measurement of 4 signals at the same time is shown in Figure 4. A single BNC cable connects signal output with the voltage input with 4 signals at 10, 20, 30 and 40 kHz and variable amplitudes.

 

Figure 4 Measurement configuration and MFLI instrument setting for outputing and measuring signals at 4 different frequencies and amplitudes.

We can observe the raw signal using the built in Scope and follow the demodulator amplitude and phase in real time using the built in Plotter tool. A simple application is to probe your experiment at different frequencies at the same time. This is needed in a device and component testing, microfluidics applications for impedance spectroscopy With the outputs and demodulators enabled and individual output amplitudes set, you can create a signal observed in the FFT of the Scope tool as shown in Figure 5. In linear systems, the signals do not mix so we don’t have additional peaks in the spectrum.

 

Figure 5 The simultaneous measurement of 4 signals at frequences 10 20, 30 and 40 kHz and amplitudes of 100, 110, 120, 130 mV, using the Scope and Plotter tools.

Now, these 4 signals can be simultaneously measured at a single or other available inputs: voltage, current, or split between them. This way you can replace 4 lock-in amplifiers and use only one MFLI with the MF-MD option. More options are available on the detection side as the Input can be chosen between Aux Ins, Aux Outs, Voltage, Current inputs, and even Aux Outs.

 

Figure 6 The MF-MD option allows the selection of several available inputs including the AuxIn and AuxOut.

 

Measuring voltage and current at the same time

Lock-ins by default come with both current and voltage inputs, but we are always faced with a choice: current or voltage? Typical experiments in transport require performing 4-terminal measurements where we want to measure the current and differential voltage at the same time. This is where a second lock-in usually comes in, but with the MF-MD option on the MFLI you can measure both at the same time as shown in Figure 7.

 

Figure 7. Measuring current and voltage at the same time is enabled using the MF-MD option. The measurement frequency and demodulator assignment is freely adjustable.

 

Simultaneous DC and AC current and voltage measurements

Another consequence of arbitrary frequency choice is that it allows us to pick zero frequency, i.e., you can perform DC measurements without the need to add a DC meter in the setup as shown in Figure 8 LabOne setting. This is important because you can use this possibility for I-V characteristics measurements, leakage current detection. For this measurement we have split the voltage signal in two and fed one signal to Voltage and second to Current Input. Note that you cannot output a DC signal off the demodulator but you can do it digitally from the main output. This is what we have done here by applying an 87 Hz signal together with the 100 mV peak DC bias from the output. The raw signal can be seen on the scope.

 

Figure 8 Measurement setting for DC and AC signal shown in the LabOne user interface with digital DC signal of 100 mV peak applied together with AC signal at frequency of 87 Hz and amplitude 100 mV peak. The raw signal in the time domain at the voltage input is shown with the DC red dashed DC line.

 

The rms amplitues for DC signals (V demod 1, I demod 3) are highlighted in red. Note that the signal is in demod Y only as the phase is always set to 90 deg. The AC voltage and current are not highlighted, they are measured by demod 2 and demod 4.

 

Figure 9 Enabled demodulators measure DC and AC voltage and current signals. The DC demodulators are highlighted.

 

Measuring up to 4 higher harmonics

The MF-MD option will allow you to measure several higher harmonics at the same time. This is practical when we deal with the non-linearity of the signal. Below we see a situation where we set up to work with only one oscillator and we capture higher harmonics at the same time. Depending on the experiment and the excitation, we could be measuring only odd harmonics in the case of a square wave we want to capture. Similarly, for pulsed measurements, we could pick the most important harmonics in the spectrum and reconstruct the measured pulse. For more accurate measurements you can use the Boxcar averager available with UHFLI Lock-in Amplifier.

 

Figure 10 Higher harmonics  demodulator frequency is calculated according to the equation 1.

Typical examples are found in magnetism where the hysteretic behavior can be captured and reconstructed using the lock-in amplifier. In thermal transport, the signal of interest is proportional to the power and happens will be represented by the second harmonic. Similarly, the spin Hall effect requires the second harmonic to capture the spin-related signal.

2 external references

In addition to all of this you can have up to two external references that you can use for your measurements. Note that ExtRef signals are assigned to oscillators 1 and 2 only and that they are reserved for the demodulators 1 and 3 only. The reference signals are provided to Aux In 1 and Aux In 2, where a sine wave signals and not necessarily TTL ones needed for the Trigger Inputs 1 and 2 in the back can be provided.

 

Figure 11 2 external measurement frequencies setup where AuxIn 1 and 2 are used to detect external references.

A number of applications require this capability, such as the pump-probe experiments, and any setup with double modulation.

Changing the output phase with respect to a reference

Changing the output phase with respect to a reference is essential for many applications where a bridge-type of circuit needs to be setup or in the parametric feedback cooling application where a trapped particle needs to be brought to a standstill by three laser beams that act in each direction of particle motion.

Let’s look at the example of a single external reference provided to the lock-in where we we will show how adding the phase to the reference, output and side demodulator affects the output by looking at the scope (on a reference device) and how this has an effect on the output and demodulators measuring the signal. The setup is the following: MFLI receives a reference signal of 100 kHz on a voltage input and maps it onto oscillator 1. The output of MFLI is set on the second demodulator that uses oscillator 1. An external (reference) Zurich Instrument device measures the reference signal (blue on the scope) and the output signal from the MFLI is shown in the scope as red trace (see scope traces in Figures 12 a, b, c, d)

  • All phases are set to zero and the Scope shows the blue trace from the reference and red that of output of demodulator 2. We see that both the reference and output demodulators are in phase.

 

 

  • When we set the phase of the reference demodulator to 90 degrees, we see that the lock-ins reference is lagging by 90 degrees and the demodulators 2 and 3 now measure +90 degrees phase shift. We see that the output 2 lags the external reference by 90 degrees.

 

 

  • In this example the phase of the output demodulator is shifted by 90 degrees and we see that the output signal is shifted by 90 degrees as well with respect to a reference signal. The demodulators will change there phase as seen in the measurement below.

 

 

  •  Changing the phase of the demodulator 3 will neither produce phase shift on the output neither on the demodulator 1 and 2. Only the demodulator 3 phase will show -90 degrees due to the initiated shift for demodulator 3.

 

 

Conclusion

The MF-MD option gives you the opportunity to perform measurements you may have thought to be impossible. Let us know what your measurement challenge is, and we’ll be able to discuss if the MF-MD option can help you tackle it with the MFLI Lock-in Amplifier.