Design of lock-in amplifier based on switched capacitor technology

With the development of electronics, information theory, physics, and computer technology, weak signal processing methods have been continuously developed to meet the needs of modern scientific research and technological development. Weak signal detection technology can be divided into two categories: 1) Using hardware circuits to realize the conditioning and acquisition of weak signals, the main methods are: filtering technology, correlation detection technology, synchronous accumulation method, switch capacitor network and photon counting method, etc.; 2) Using computer technology and information processing technology to extract weak signals from noise. Here, a new weak signal detection circuit design scheme is proposed mainly from the hardware aspect, which uses a combination of switch capacitor network and integrator to realize detection, while reducing noise, amplifying weak signals.

1 Lock-in amplifier working principle

The lock-in amplifier is a synchronous coherent detector designed based on the principle of cross-correlation, which can perform correlation operations on the detection signal and the reference signal. According to the mathematical expression of cross-correlation, the correlator includes two parts: a multiplier and an integrator. Considering the linear range and dynamic range, the correlator usually does not use an analog multiplier, but a switch-type multiplier with good linearity, large dynamic range and simple circuit. The reference signal of the lock-in amplifier is not an arbitrary function, but a square wave synchronized with the signal to be measured. The working principle of the lock-in amplifier is shown in Figure 1. In the figure, the multiplier and integrator realize the cross-correlation operation. The integrator forms a square wave signal by charging and discharging under the control of the synchronous square wave for subsequent circuit processing; the function of the bandpass filter (BPF) is frequency selection and amplification. According to the need of the amplification factor, a BPF of appropriate order is used; the phase-sensitive detector (PSD) multiplies the amplified modulated signal with the carrier signal, and uses the low-pass filter (LPF) to filter out the high-frequency component. The output DC level is proportional to the measured micro-current.

Figure 2 shows the relevant principles used by the lock-in amplifier.

It can be seen that the correlator output is a DC voltage whose value is proportional to the fundamental amplitude of the input signal and proportional to the cosine of the phase difference between the reference signal and the reference signal.

The switched capacitor is a circuit that uses switches to control the charging and discharging of capacitors. It consists of analog switches and capacitors. The basic circuit is shown in Figure 3. The two switches are controlled by square wave signals, and the equivalent resistance Req between U1 and U2 is:

In the formula, T represents the period of the square wave signal, and Ieq represents the charging current. The switched capacitor circuit is equivalent to the resistance of T/C, which can not only achieve high input impedance, but also form a filter with high accuracy and stability, and is also easy to integrate.

2 Design Methodology

As shown in Figure 4, replacing the resistor R1 in Figure 2 with the switch capacitor in Figure 3 can not only realize the function of the multiplier in the correlation detection, but also the circuit itself has a certain filtering performance. If the period of the control signal and the size of the integral capacitor are changed, the amplitude of the signal output can be changed, and it is easy to integrate. Due to the use of the integral link, the influence of noise on weak signals is reduced. At this time, equation (4) becomes

As can be seen from formula (6), the output voltage is a DC signal. In order to measure accurately, the same square wave signal is used to control the charging and discharging of the switch capacitor and the integral capacitor, that is, when C1 is charged, C2 is discharged; conversely, when C2 is charged, C1 is discharged. In this way, the circuit outputs a periodic square wave signal, which is a fixed-frequency sine signal after passing through the BPF. By changing the BPF level and the amplification factor, the multiple of the overall circuit can be changed to measure smaller weak signals. Finally, the signal outputs a stable DC signal after passing through the PSD, which is convenient for subsequent circuit collection. R0 can be regarded as the switch on-resistance, and a feedback resistor can be added. As can be seen from formula (6), by changing the size of C1 and the square wave frequency, the amplification factor of the circuit can be changed, but the adjustable frequency will increase the difficulty of BPF design. In order to improve the performance of the lock-in amplifier, the capacitance or frequency can be adjusted within the passband of the BPF.

The circuit for implementing the related algorithm using switched capacitors is shown in Figure 5. The switch control signal is provided by the square wave signal output by the signal source, and two analog switches CD4052 are used to control the charging and discharging of the switched capacitor and the integral capacitor. A2 is the first-level BPF circuit, and U0 is connected to the subsequent circuit.

3 Data Analysis

The weak signal used for measurement is obtained by resistor voltage division. In the circuit debugging, the values ​​of capacitors C1 and C2 are both 0.1 μF, the frequency of the switch control signal is 1 kHz, the input current is in the microampere level, and the input-output relationship of the circuit is shown in Figure 6. Figure 6 (a) shows the DC measurement data, and Figure 6 (b) shows the AC measurement data (the capacitor is 0.1 μF, the frequencies of the control signal and the input signal are both 1 kHz, the control signal is a square wave signal, and the input signal is a sine signal).

As shown in Figure 6, the linearity of the circuit is good, indicating that this method is feasible. Changing the size of the switch capacitor and the integral capacitor will change the size of the circuit sensitivity, but will not change the linearity and stability. The circuit has a simple structure. While reducing noise, it can amplify weak signals many times and convert them into corresponding DC signals, which is convenient for collection and display. The output voltage of the integrator cannot be too large, otherwise the waveform is easily distorted, which will cause measurement errors. In order to facilitate subsequent processing, the amplification factor of the overall circuit is increased by changing the number of stages and amplification factors of the BPF, so that smaller weak signals can be measured.

4 Conclusion

This paper uses a combination of switched capacitors and integrators to realize the function of a lock-in amplifier. The circuit has a simple structure and good linearity and stability. It can not only reduce noise, but also amplify weak signals many times and convert them into corresponding DC signals for collection and display. For picoampere current, the output voltage can reach the microvolt level by using this correlator, and can reach the volt level after passing through the BPF.