lock in amplifiers principles and applications pdf

Lock in amplifiers principles and applications pdf

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Introduction

Lock-in Amplifier SU-1

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In this work, we report on the design of a wide-band digital lock-in amplifier DLIA of up to 65 MHz and its application for electrical impedance measurements in microfluidic devices. The DLIA is comprised of several dedicated technologies. First, it features a fully differential analog circuit, which includes a preamplifier with a low input noise of 4. Second, the DLIA has an all-digital phase lock loop, which features a phase deviation of less than 0.

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In this work, we report on the design of a wide-band digital lock-in amplifier DLIA of up to 65 MHz and its application for electrical impedance measurements in microfluidic devices. The DLIA is comprised of several dedicated technologies. First, it features a fully differential analog circuit, which includes a preamplifier with a low input noise of 4.

Second, the DLIA has an all-digital phase lock loop, which features a phase deviation of less than 0. The phase lock loop utilizes an equally accurate period-frequency measurement, with a sub-ppm precision of frequency detection.

Third, a modified clock link is implemented in the DLIA to improve the signal-to-noise ratio of the analog-to-digital converter affected by clock jitter of up to 20 dBc. A series of measurements were performed to characterize the DLIA, and the results showed an accurate performance. Additionally, impedance measurements of standard-size microparticles were performed by frequency sweep from kHz to 30 MHz, using the DLIA in a microfluidic device.

Different diameters of microparticle could be accurately distinguished according to the relative impedance at 2.

The results confirm the promising applications of the DLIA in microfluidic electrical impedance measurements. Digital lock-in amplifiers DLIAs have been widely used for measuring weak signals in numerous fields [ 1 ], such as Raman spectroscopy [ 2 ], atomic force microscopy [ 3 , 4 ], multifunctional scanning tunneling microscopy [ 5 ], and sensors and actuators [ 6 , 7 ].

The measurement principle of LIAs [ 8 ] carries out a correlative demodulation with the same reference frequency as the carrier signal to single out the component of the signal at a specific reference frequency and phase. Recently, a variety of works have been published on the implementation of high-frequency and high-precision DLIAs.

Cheng et al. It included a low-noise amplifier LNA and a high-speed data-acquisition—processing system-in-package SiP. Gervasoni et al. It adopted a switched ratiometric technique based on two analog-to-digital converters ADCs that acquired signals alternately.

Even though all the above researchers have contributed tremendously to the improvement of the operation range and measurement precision of DLIAs, a method by which to realize a wide-band DLIA is still lacking. Andrew et al. Pangiotis et al. The magnitude measurement accuracy of the chip was Morgan et al. Hence, a method by which to implement a wide-band DLIA is proposed herein. In this work, a wide-band DLIA was developed, and its key features are elaborated.

The analog circuit consists of a fully differential preamplifier, a programmable-gain amplifier PGA , and a fully differential low-pass filter LPF. Architecture of the digital lock-in amplifier DLIA with two major parts: one is the fully differential analog circuit and the other is the reconfigurable hardware. A differential circuit has several properties that a single-ended circuit does not include.

With all these properties, a fully differential analog circuit for the DLIA was implemented in the following three major stages. The first stage of the analog circuit implementation was the preamplifier, which determines the equivalent input noise EIN.

For an N-stage amplification circuit, the EIN can be calculated as [ 16 ]:. Equation 1 shows that the noise of the first stage is completely added to the EIN, whereas the noise of subsequent stages is decreased by the amplification gain of the former stages. Hence, the design of the preamplifier has to consider the above features. The measured EIN of the preamplifier was 4. The input impedance was The gain—frequency response of the preamplifier is shown in Supplementary Figure S1.

The increase of the 0 dB gain curve and the decrease of the Structure of the preamplifier. These two stages composed the amplification unit of the DLIA, with its amplification gain as large as 65 dB.

The third stage is the fully differential LPF, which is used to prevent input signals from violating the Nyquist criterion. For the high-frequency range, two cascading fifth-order elliptic type LC filters were preferred because of their simple implementation, small area consumption, and sharp cut-off characteristics.

Figure 3 shows the corresponding schematic. Schematic of the fully differential low-pass filter LPF. The simulated and tested frequency—amplitude response of the LPF is shown in Figure 4. This difference could be attributed to the discrepancies of the passive components. The reconfigurable hardware was comprised of a demodulator module and an ADPLL module, as schematically illustrated in Figure 5.

The demodulator received a digitalized analog input signal through the ADC and output its amplitude and phase. The ADPLL generated a highly synchronized sine wave with the reference signal and transmitted it to the demodulator. Structure of the reconfigurable hardware including a demodulator and an all-digital phase lock loop ADPLL.

The demodulator consisted of a number of modules to realize the basic algorithm of the lock-in amplifier LIA. After acquiring the input signal, the reference signals from the NCO were multiplied by the input signal in the mixers. The NCO can also generate a synchronized sine signal for driving a device during a test through a digital-to-analog converter DAC. Since the amplitude and the phase information of the input signal were focused, the modulated signals needed to be filtered to remove the AC signals and obtain DC signals.

In the root-mean-square RMS module, the RMS amplitude R of the input signal can be calculated by Equation 8 and then transferred to the advanced reduced instruction set computer machine ARM for further data processing, such as calibration by piecewise polynomial fitting Supplementary Note S1 and data processing [ 17 ].

Compared with an analog phase lock loop PLL , an ADPLL has the advantages of the absence of thermal drift, better suppression of harmonics and interference, and flexible options for data processing [ 18 , 19 ].

This feature ensured that signals generated by the NCO had the same frequency as the reference signal. Conventional period measurement counts the number of rising edges of the standard signal in numerous periods of the testing signal, and then calculates the period of the testing signal [ 20 ].

However, the conventional measurement generates a large error in the high-frequency range. Therefore, frequency division is required to improve the precision of frequency measurement. Compared with the conventional period measurement, the frequency detector used here was optimized by means of the equally accurate period-frequency measurement with hysteresis. First, a measurement was conducted to estimate the frequency for selecting the appropriate division factor.

Afterwards, the high frequency was divided into lower scopes in order to maintain the maximum counting error. To make the division more stable, a hysteresis operation was performed.

In order to characterize the frequency precision, a mVrms sine wave generated by a signal generator, Keysight A, was transmitted to the DLIA. A series of frequencies, i.

The ratio of measured frequency deviation to the standard frequency of the Keysight A was then calculated and expressed in ppm. The measured frequency precision of 10 MHz is exemplarily displayed in Figure 6. Concurrently, the digitalized reference signal from the ADC passed through a LPF, which extracted the fundamental sine wave from the rectangle input reference signal, and then the filtered signal was fed back to the mixers. After the LPF filtering behind the mixers, the phase difference can be calculated by the arc tangent function:.

After the phase difference was detected, the PID controller was used to adjust the output phase of the NCO to lock in the phase of the reference signal. In high-frequency applications, the clock jitter caused by the clock link usually downgrades the SNR of ADCs significantly.

Equation 13 assumes an infinite resolution for an ideal ADC, in which the clock jitter is the only factor determining the SNR. Moreover, its theoretical maximum value decreases if the ADC has a finite resolution or when other factors are considered.

Conventional clock link. This configuration theoretically limits the maximum clock jitter to less than 7 ps. However, practical tests yielded a value of 8. The measured SNR decreased from The result showed that the modified clock link with new oscillator could give a maximum improvement of 20 dBc of the SNR.

An Ethernet port 1 at the top edge of the board conveyed the differential output of the LPF and was connected to the analog input port 2 of the digital board. Two D-SUB connectors at the top left were the power and control input. The SMA at the top right was used as a monitor of the output of the analog board. The entire board was installed in a shielding box to prevent EMI from the external environment. The digital board used XC7Z to implement the digital algorithm.

Here, the reference input was connected through the lower right BNC. In order to avoid same-frequency interference, the analog input Ethernet port 2 was intentionally placed away from the reference input and the sine wave output [ 26 ]. Additionally, an Ethernet port on the top left was also integrated onto the board for data transformation.

A D-SUB connector was used to control the analog board. The dynamic reserve was the same as other LIAs. The sizes of the LIAs were similar. In order to verify the performance of the DLIA, a signal generator Keysight A and an attenuator Keysight A were used to generate the input signal, and the Sync signal of the Keysight A was used as the reference signal.

In order to measure the deviation and stability of the phase detection, a mVrms sine wave was fed into both the signal input and reference input of our DLIA. The frequency changed from 10 Hz to 65 MHz. The data were saved every 0. The phase deviation was calculated as:. Figure 11 shows that the phase deviation of the DLIA was less than 0. In addition, the standard deviation of the phase was 0. Test results of other frequencies also yielded good performance of the DLIA.

Deviation of the phase detection. In addition, the amplitude—frequency response of the DLIA was tested. A mVrms sine wave was used as the input, and the frequency was swept from 10 Hz to 65 MHz.

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The principle of operation of SU-1 is based on orthogonality of two sinusoidal functions. When a product of two sinusoidal functions with non-matching frequencies f 1 and f 2 is integrated over time well above their periods, the result is zero. SU-1 multiplies input signal to reference signal from built-in generator or external source and integrates the product over specified time usually from milliseconds to a few seconds. The result is a DC signal, and the effect of any other signal not matched by frequency to the reference is dampened to almost zero. Same-frequency component that is not in phase with the reference signal is attenuated too since same-frequency sinusoidal and cosinusoidal waves are orthogonal. SU-1 is to be used to amplify high-noise signal produced by the following means of detecting of THz radiation: electro-optical detection of pulsed THz radiation and of detection of THz radiation using the following detectors: Golay detectors, cooled bolometers, pyro-electric THz radiation detectors, semiconductor THz radiation detectors, novel THz radiation detectors. Signal level at various gain factor settings.


An e-edition of the classic textbook Lock-in Amplifiers: principles and applications​, originally published by the UK Institution of Electrical.


Introduction

This article extends the discussion by looking at some design considerations for sensor signal conditioning using synchronous demodulation in systems with strict power and cost constraints. When carefully designed, analog systems are hard to beat for simplicity, low cost, and low power consumption. This architecture performs most of the signal processing in the analog domain. Sensors, which are ubiquitous, are used to measure temperature, light, sound, and a variety of other environmental parameters. Some sensors act as parameter-dependent voltage or current sources.

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Gabal and N. Medrano and B.

A lock-in amplifier is a type of amplifier that can extract a signal with a known carrier wave from an extremely noisy environment. Depending on the dynamic reserve of the instrument, signals up to 1 million times smaller than noise components, potentially fairly close by in frequency, can still be reliably detected. It is essentially a homodyne detector followed by low-pass filter that is often adjustable in cut-off frequency and filter order.

Lock-in Amplifier SU-1

You've discovered a title that's missing from our library. Can you help donate a copy? When you buy books using these links the Internet Archive may earn a small commission. Open Library is a project of the Internet Archive , a c 3 non-profit. This book was written for all users of lock-in amplifier equipment and for those with an interest in the practical aspects of signal recovery and measurement using synchronous detection. Among the topics included are the principles of phase-sensitive detection, applications for two-phase lock-in amplifiers, the problems of phase-locking to very noisy signals, a review of system configurations for heterodyne and PWM lock-in amplifiers and the use of lock-in amplifiers in computer-controlled measurements.

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