Analog filters are an extremely important block in several electronic systems, such as RF transceivers, data acquisition channels, or sigma-delta modulators. They allow the suppression of unwanted frequencies bands in a signal, improving the system’s performance. These blocks are typically implemented using active RC filters, gm-C filters, or switched-capacitor (SC) filters.
In modern deep-submicron CMOS technologies, the transistors intrinsic gain is small and has a large variability, making the design of moderate and high-gain amplifiers, used in the implementation of filter blocks, extremely difficult. To avoid this difficulty, in the case of SC filters, the opamp can be replaced with a voltage buffer or a low-gain amplifier (< 2), simplifying the amplifier’s design and making it easier to achieve higher bandwidths, for the same power. However, due to the loss of the virtual ground node, the circuit becomes sensitive to the effects of parasitic capacitances, which effect needs to be compensated during the design process.
This thesis addresses the task of optimizing SC filters (mainly focused on implementations using low-gain amplifiers), helping designers with the complex task of designing high performance SC filters in advanced CMOS technologies. An efficient optimization methodology is introduced, based on hybrid cost functions (equation-based/simulation-based) and using genetic algorithms.
The optimization software starts by using equations in the cost function to estimate the filter’s frequency response reducing computation time, when compared with the electrical simulation of the circuit’s impulse response. Using equations, the frequency response can be quickly computed (< 1 s), allowing the use of larger populations in the genetic algorithm (GA) to cover the entire design space. Once the specifications are met, the population size is reduced and the equation-based design is fine-tuned using the more computationally intensive, but more accurate, simulation-based cost function, allowing to accurately compensate the parasitic capacitances, which are harder to estimate using equations. With this hybrid approach, it is possible to obtain the final optimized design within a reasonable amount of computation time.
Two methods are described for the estimation of the filter’s frequency response. The first method is hierarchical in nature where, in the first step, the frequency response is optimized using the circuit’s ideal transfer function. The following steps are used to optimize circuits, at transistor level, to replace the ideal blocks (amplifier and switches) used in the first step, while compensating the effects of the circuit’s parasitic capacitances in the ideal design. The second method uses a novel efficient numerical methodology to obtain the frequency response of SC filters, based on the circuit’s first-order differential equations. The methodology uses a non-hierarchical approach, where the non-ideal effects of the transistors (in the amplifier and in the switches) are taken into consideration, allowing the accurate computation of the frequency response, even in the case of incomplete settling in the SC branches.
Several design and optimization examples are given to demonstrate the performance of the proposed methods. The prototypes of a second order programmable bandpass SC filter and a 50 Hz notch SC filter have been designed in UMC 130 nm CMOS technology and optimized using the proposed optimization software with a supply voltage of 0.9 V. The bandpass SC filter has a total power consumption of 249 uW. The filter’s central frequency can be tuned between 3.9 kHz and 7.1 kHz, the gain between -6.4 dB and 12.6 dB, and the quality factor between 0.9 and 6.9. Depending on the bit configuration, the circuit’s THD is between -54.7 dB and -61.7 dB. The 50 Hz notch SC filter has a total power consumption of 273 uW. The transient simulation of the circuit’s extracted view (C+CC) shows an attenuation of 52.3 dB in the 50 Hz interference and that the desired 5 kHz signal has a THD of -92.3 dB
