Contributions to the design of multiplier and RF mixer circuits

This thesis discusses the systematic design of mixers with a focus on the characterization of nonlinearity. Since multiplication is considered here as the core operation for implementing a frequency conversion, the first part of this work handles the electronic realization of multiplication. Based on a simple mathematical model for multipliers the „Multiplication Purity Index (MPI)“ is proposed as a quality factor for the characterization of the undesired nonlinear behaviour of multipliers. In the second part of this thesis the MPI is adopted as a specification parameter for characterizing the nonlinearity of mixers. In contrary to the conventional nonlinearity specification parameters, where each spurious spectral component is separately considered, the MPI indicates the deviation of the behaviour of the real mixer from that of an ideal one. Through the use of the MPI instead of the conventional parameters the dimension of the specification parameter space of mixers is reduced. This reduction simplifies the mixer design problem. The MPI can be determined either using the input-output-characteristics of the mixer circuit or from its output spectrum. Moreover, a mapping from the conventional specification parameters into the MPI-space is possible. The analytic determination of the MPI of a mixer circuit can also be performed using a method based on the Volterra series and the method of nonlinearly controlled sources without the need for an input-output description. This method enables the calculation of the spectral components of the state variables at an arbitrary node of networks with nonlinear time-invariant elements with small-signal excitations. This method is extended in this thesis to networks with a large-signal excitation as to be appropriate for the analysis of mixer circuits with switching behaviour. The extended method is then applied for the nonlinearity analysis of a mixer circuit and the calculation of the MPI. The noise behaviour of the mixer is explained in this work by means of an example MOS mixer circuit. Here, the contribution of each circuit element to the output noise is determined and a closed-form expression of the noise figure in dependency on the design parameters is derived. In the last part of the thesis a systematic design flow for mixers based on the MPI is proposed. Based on given design specifications and candidate mixer architectures, the proposed design flow enables the designer through the comparison of different architecture/technology-combinations to design a mixer circuit, which mostly fulfills the design specifications for a certain application.