# Current-Feedback Instrumentation Amplifier Using Dual-Chopper Fill-In Technique
## 1 Introduction  
An instrumentation amplifier (IA) is among the most crucial components of high-precision analog front-end (AFE) circuits [1; 2]. Particularly for sensor applications, the primary requirements of IAs are low noise, low offset, low gain error, and high input impedance characteristics [3]. Current-feedback instrumentation amplifiers (CFIAs) with a chopper structure, as depicted in Figure 1[4], are among the IA structures of the sensor AFE that can satisfy these criteria. The input signal of the CFIA is converted to current via transconductance (\(G_{m1}\)), and the output feedback voltage forms negative feedback by supplying current to the output  
Figure 1: Conventional CFIA structure with a chopper. of (\(G_{m1}\)) via transconductance (\(G_{m2}\)). The gain (\(G_{m3}\)) eliminates the difference between the output power currents of the transconductances (\(G_{m1}\) and \(G_{m2}\)) and the output voltage (\(V_{out}\)) shown in Figure 1 and expressed in Equation (1). \[V_{out(CPIA)}=\bigg{(}\frac{G_{m1}}{G_{m2}}\bigg{)}\cdot\bigg{(}1+2\cdot\frac{R _{2}}{R_{1}}\bigg{)}\cdot V_{in} \tag{1}\]  
As shown in Equation (1), the closed-loop gain of the CFIA is determined by the degree of matching between the input transconductances (\(G_{m1}\) and \(G_{m2}\)) and resistors \(R_{1}\) and \(R_{2}\). The chopper CFIA has a higher common-mode rejection ratio (CMRR) because the input common-mode can be isolated by converting the input differential voltage signal into the input differential current. By averaging the input mismatch using the input chopper, a higher-input CMRR can be achieved. In addition, the power consumption can be reduced because the input signal path (from \(G_{m1}\) to \(G_{m3}\)) and feedback signal path (from \(G_{m2}\) to \(G_{m3}\)) share the output stage (\(G_{m3}\)). When the junction capacitances of the chopper switches are disregarded, it is possible to obtain a high-input impedance in the CFIA because the gates of the input MOSFET differential pair form the input nodes. The input impedance of the CFIA can be expressed as Equation (2). \[Z_{IN(CPIA)}=\bigg{|}\frac{2}{sC_{g}}\bigg{|}=\bigg{|}\frac{2}{2\pi f_{C}H_{C} \big{|}}, \tag{2}\]  
where \(C_{g}\) is the gate input capacitance of the input transconductance (\(G_{m1}\)), and \(f_{CH}\) is the chopper clock frequency. The CFIA, with such a simple structure, has numerous advantages. However, it can still degrade the performance, owing to DC offset caused by the mismatch of MOSFETs at the input stage or flicker noise caused by dangling bonds at the interface of the gate oxide and silicon substrates in MOSFETs [5]. Therefore, the CFIA requires a dynamic offset compensation (DOC) technique for high-precision sensors. Auto-zeroing (AZ) and chopping are prevalent DOC techniques used in amplifiers [6]. Figure 2 shows two popular DOC methods: AZ and chopping. AZ is a sampling-based method used to remove the input end offset of an op amp. As shown in Figure 2a, the AZ is controlled by clocks \(P_{1}\) and \(P_{2}\), which are the offset sampling and amplifying phases, respectively. By storing the offset in the offset sampling capacitor (\(C_{s}\)) during sampling phase \(P_{1}\) and subtracting the offset from \(C_{s}\) in amplifying phase \(P_{2}\), it is possible to reduce the effect of the offset on the output. However, there is a disadvantage in that the high-frequency thermal noise is folded into the low-frequency band and integrated due to aliasing due to the use of offset sampling in the capacitor. In the chopping technique, as shown in Figure 2b, the frequency bands of the signal and noise are separated using amplitude modulation to implement the low noise characteristics of the circuit. To prevent the amplification of low-frequency noise, signals are modulated at high frequencies using chopper frequencies and amplified. Subsequently, low-frequency noise is sent to high frequencies through demodulation, and signals are sent back to low-frequency bands to achieve low-noise characteristics.