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Extra info for Analog Circuit Design: Structured Mixed-Mode Design, Multi-Bit Sigma-Delta Converters, Short Range RF Circuits
Hence, gm’s that have common output nodes have to be scaled together. We choose a solution that finds a good discrete solution starting from the optimal DR solution. 15 dB is obtained which is only 1 dB less than the optimal solution. 1 dB. This illustrates that the DR optimization is necessary and yields a good starting point for the discrete problem. But also that for optimal dynamic range solutions of low-Q biquads, for example power consumption is another factor that can be optimized. Formalizing this discrete optimization process is a subject for future work.
2V. After 10 iterations still the distortion-GBW combination is not satisfactory. The bounds are changed to allow for a larger biasing current and larger transistors. After another 40 iterations a good result is obtained. 5 hours of work (mainly computer simulation time) but this without requiring any explicit knowledge about the working of the circuit. 2750 (=110*25) circuit evaluations is a normal amount for optimizations problems like this. In Figure 12 the sized circuit with all device sizes is depicted and in Table 2 some key performance results are summarized.
4 Optimization step At this point, a solution exists that realizes the desired transfer function, but this is maybe not yet a solution with optimal dynamic range. Next the dynamic range (DR) optimization will be explained: the values of and obtained in the previous step are scaled to improve the DR. In Figure 6 a general overview of the dynamic-range optimization is depicted. Starting point are the state-space matrices of the total filter. Additional inputs are the noise figures of the transconductors (a noise figure of one means a noise-free integrator), a starting value for the total capacitance the wanted dynamic range or none if there is no real goal other than to maximize the DR and the input voltage swing Usually the are not known at this point because no transconductors have been designed yet or have not been selected from the OTA library.