Design of Switched-Capacitor Filter Circuits using Low Gain Amplifiers

This chapter gives a brief description of SC circuits and the motivation behind the work. The book organization per chapter is also described.

This chapter introduces SC circuits. A brief description is given for the main building blocks of a SC filter (operational amplifiers, switches, capacitors, and non-overlapping clock phases). A few examples of SC resistor emulation circuits are presented along with their equivalent resistance. Two examples of SC integrators are also shown, one with the resistors implemented with a T branch (parasitic-sensitive integrator) and another with a branch in π (parasitic-insensitive integrator). A signal flow graph is presented which allows large circuits to be analyzed graphically. The chapter ends with the two Sallen-Key topologies designed in this book, in their continuous time version.

Low-pass filters are systems that allow the passing without attenuation of signals with frequency below the cutoff frequency, while attenuating those with frequency above it. The amount of attenuation the signals with higher frequency suffer is dependent on their frequency and the order of the filter. In this chapter low-pass SC filters based on the continuous-time version of the Sallen-Key low-pass filter [8] will be presented and discussed when using ideal components. Higher order low-pass SC filters using cascaded sections will also be discussed in this chapter.

Band-pass filters are systems that allow the passing of signals within a band of frequencies, while attenuating the frequencies outside the defined ranged. The amount of attenuation the signals suffers outside the frequency range is dependent on the signals frequency and the order of the filter. In this chapter band-pass SC filters based on the continuous-time version of the Sallen-Key band-pass filter, implemented with a VCVS, will be presented and discussed when using ideal components. Higher order band-pass SC filters using cascaded sections will also be discussed in this chapter.

In the third and fourth chapters, the topologies of a low-pass and a band-pass filter have been presented using ideal components. In this chapter the non-ideal effects from using real components will be presented and discussed. Initially, the non-ideal effects due to the switches are described. The distortion of a first-order low-pass SC filter is simulated using different switch configurations, including with the use of clock boost circuits, in order to determine which configuration is better from a distortion point of view. Two clock boost circuits, one of them capable of operating at lower voltages, are presented. A voltage buffer, and a low gain amplifier are described in several configurations; the low and medium frequency small signal models are presented and the respective transfer functions derived; the thermal noise referred to the input is also derived. The chapter ends with some simulation results, showing power dissipation, gain, gain-bandwidth product, THD, and thermal noise for each version of the circuits.

In this chapter the filter circuits will be simulated taking into account the non-ideal effects described in fifth chapter. Due to these effects the band-pass filter will be altered, adding a new capacitor to the circuit. This is done in order to take into account the input capacitance of the low gain amplifier and facilitate the compensation of this capacitance. The simulated circuits include second-order low-pass filters, two operating at 1.2 V using the buffers presented in the fifth chapter, one operating at 0.9 V, and a sixth-order filter obtained from cascading three biquadratic sections operating at 1.2 V. The band-pass filter circuit was also simulated for a second-order filter, and a fourth-order filter obtained from cascading two biquadratic sections, all operating at 1.2 V.

This chapter summarizes the work performed to design low-pass and band-pass Sallen-Key SC filters, using low gain amplifiers, in modern nm CMOS technologies.