Research On Symbolic Analysis Methods For Mixed-Signal Integrated Circuit Design Automation

The shrinking size of semiconductor processes makes it possible to integrate circuit of different functions on one single chip.A mixed-signal integrated circuit is a circuit that integrates analog circuit parts and digital circuit parts on the same chip.Due to insufficient advances in the automation technology for analog integrated circuit design,the level of automation of mixed-signal integrated circuit design remains at a primitive state,requiring a lot of manual intervention.The urgent need for methods and tools for mixed-signal circuit design automation is to improve circuit design efficiency,reduce design errors,and shorten verification cycles.In mixed-signal chip design,the degree of automation of analog circuit design and the ability to quickly respond to design specifications can often greatly improve the design efficiency and the yield of the entire mixed-signal chip.Considering the wide variety of mixed-signal circuits,the dissertation takes the design of Sigma-Delta Modulator(SDM)circuits as the representative research subject,because SDM circuits are a kind of mixed-signal circuits that are difficult to design.SDM circuits are a kind of error correction circuits with feedback,including analog amplifiers,integrators,comparators,switched-capacitors and other analog circuits.They also contain digital circuits related to analog-to-digital and digital-to-analog conversion.Hence,they are typical mixed-signal circuits.Although the SDM circuits can self-correct many non-ideal circuit characteristics,it is still necessary to carefully analyze how the non-ideal characteristics of the analog circuit part affect the overall performance of the SDM circuits,so that the lowest cost circuit modules can be adopted to meet the design specifications of the system-level SDM circuits.Good design automation methods can provide design assistance to the system-level design work and improve the efficiency of circuit design.This dissertation proposes and solves several key problems outlined below.Firstly,we have studied a method for the fast calculation of the Signal-to-Noise Ratio(SNR)and Signal-to-Noise and Distortion Ratio(SNDR)characteristics of SDM circuits.The computational problem of SNR or SNDR in SDM circuits design is a critical problem for the automatic synthesis of SDM circuits.A fast and accurate SNR/SNDR calculation method can speed up the optimization iteration speed of SDM circuits,so that it can find the optimal solution in a much wider design space.On the other hand,since SDM circuits contain continuous-time elements and discrete-time elements,and run under the control of a periodic clock signal,the traditional SNR/SNDR evaluation methods use transistor-level circuit simulation,which are prohibitively time consuming.In the literature some designers use behavioral simulation to obtain the estimation of SNR/SNDR,but the accuracy depends on the accuracy of the behavioral circuit models,and most of the time modeling has to be performed manually.We developed a symbolic circuit analysis method for the estimation of SNR/SNDR.The analytical formulas of SNR/SNDR for system-level synthesis are obtained by symbolic Taylor series analysis.The symbolic SNR/SNDR computation method can circumvent repeated simulation work when circuit parameters change frequently.Meanwhile it ensures high computation accuracy.The proposed SNR calculation method eliminates a calculation obstacle to automating the synthesis of SDM circuits.In particular,we have developed a symbolic SNR computation method for switched-capacitor SDM circuits.We also developed a special program to automate the analysis procedure.In order to help the circuit designer to easily apply this method,we have further redeveloped the SNR calculation module in the industry-standard Verilog-A language to enable its practical application.We have tested this Verilog-A model for a variety of SNR calculations including fast statistical SNR analysis,analysis of the non-ideal circuit effects on the SNR/SNDR performance.Comparing to the traditional circuit simulation methods,we have demonstrated significant speed up by using the proposed simulation with a minimal precision loss.Furthermore,we have studied the time-domain response model of the switched capacitor integrator by a symbolic analysis method.The constructed time response model is parameterized by the circuit small-signal parameters while considering the current saturation effect.By this symbolic model,the non-ideal behavior caused by the high-order effects of the switched capacitor integrators can be predicted quickly and accurately.This model is an important part of the behavioral models for the system-level simulation of SDM circuits.We have further studied the analysis method of Opamp nonlinearity which can affect the performance of SDM circuits.We developed a simplified stage-based circuit model and a nonlinear parameter extraction method.And we proposed a symbolic method for nonlinear analysis of integrators and generated the symbolic equations for the harmonic distortion.A nonlinear parameter extraction method based on an application of the gm/ID method is proposed.Combining analytical formulas with data fitting methods,the formulas of parameters of the simplified stage-based circuit model can be obtained,which can mitigate the non-reusability problem of the data fitting methods in circuit synthesis.The nonlinear representation method based on analytical formulas can be used to the optimization of harmonic distortion reduction in Opamp and integrator design.Based on the above work,we have further studied the symbolic modeling methods for the harmonic distortion analysis of continuous-time SDM circuit.The closed-form equations for the harmonic distortion of continuous-time SDM can be generated directly by the symbolic modeling method.The symbolic method can reduce the work load of the traditional harmonic distortion analysis method based on transistor-level circuit simulation while improving the behavioral simulation efficiency with reliable accuracy.The symbolic methods proposed in this dissertation are neutral methods.The ideas and methods can be extended to the other mixed-signal circuit design problems after appropriate modification.