Low-Distortion Continuous-Time Integrated Filters for Low Frequency Applications

A technique for designing high-linearity continuoustime integrated filters for low frequency applications using transconductance network is presented. With this technique, an area-efficient transconductance network is used to replace the large resistors in low-frequency integrator-based continuous-time filters. The key challenge with this technique is in determining and realizing the appropriate relationship between the transconductance circuit and the nonideal frequency-dependent properties of the opamp. Simulation results for a third-order Bessel low-pass filter designed in a 0.5u CMOS process with a cutoff frequency of 5 KHz provide a THD in excess of 70 dB for a 2V p-p output with the 5 V power supply. I Background As the media between the “digital world” and the “analog world”, continuous-time filters are required in many mixed signal systems. Of particular interest are integrated continuous-time filters that can be used for antialiasing and reconstruction. Gm-C filter is the most popular technology to realize these continuoustime filters. However, there are several limitations along with Gm-C filters and some of them are very hard to be overcome. The first limitation is the process and temperature dependency. It is important to precisely control the Gm value when implement Gm-C continuous-time filters and that Gm values are strongly depend on the process and temperature. Although there are some techniques to compensate this dependency, the compensating circuit will increase the complicity of the overall design and thus increase the expense. Another limitation is its poor linearity. Because Gm-C filters use nonlinear elements, this limitation is inherent in this structure and no known solutions for high linear applications. Compared with the Gm-C approach, the RC filter has much higher linearity. However, when RC filter requirements specify low-frequency poles, the area for integrating the correspondingly large RC time constants will be unacceptably large. That is the why there it is seldom used in audio frequencies. The magnitude of the problem can be appreciated by considering, as an example, a lossy first-order integrator as depicted in Fig. 1. Figure 1 First Order Integrator If zero DC-loss and a low cutoff frequency are required, the large RC time product necessitates either a large resistor or a large capacitor. As we know RC f π π ω 2 1 2 0 0 = = , If choose 0 f =1 KHz, , 10 59 . 1 2 1 4 0 − × = = f RC π Assume that the capacitance density and resistance density are / 30 , / 9 . 0 2 Ω m fF μ □, respectively. If we set , c R A A = and choose the minimum resistor sheet squire as 1.2μm×1.2μm, (for AMI05 process), then we can approximate the total area needed to realize this RC product as 18.42× 2 4 10 m μ . When considering the design of a third order filter, the area for RC product will be approximately 1.5 2 mm . That is too large to be integrated on chip. However, on the other hand, if this area can be managed, RC filter can be viable for low frequency applications. Observation We observed that in figure 1, R1 and R2 act as transconductors because the input signal is voltage and output signal is current. So the question is that if we can find some other transconductors with the same transconductance value, small area and high linearity. The following is several kinds of transconductance network: Figure 2 Three kinds of transconductance network If the proper values are chosen, these three transconductance network will have the same transconductance value, high linearity and progressively small area. II The design of A third-order Bessel Low-pass Filter This design is presented as an example to show how this new technique, transconductance network, is used to build integrated continuous-time filters. The analysis of the relationship between the transconductance network and a non-ideal opamp is the high light in this design. Because in Tow-Thomas biquad, each resistor has terminals connected to virtual ground, a first order filter and Tow-Thomas C R2 R1 In Out V I