es expansion R. Large values of N and R hence lead to complex expressions that are hard to interpret. Term explosion is a problem inherent to all algorithms for symbolic circuit analysis that are based on ana- lytical methods. Avoiding term explosion is accomplished by keeping the input model complexity as low as possible, for example, by the introduction of extra hierarchy. Fur- thermore, it is required that (4.82) converges sufficiently fast, i.e. R can be chosen sufficiently small in order to prevent term explosion. 4.3.7 Application 1: linear downconversion mixer By nature, mixers are intended to operate as LPTV systems: they are designed to transfer information from one frequency band (carrier) to another. However, in almost any mixer, both wanted and unwanted signal transfers occur. Proper characterization of the mixer's behavior requires quantifying all of these transfers. In a first application, we use the SymbolicHTM algorithm to characterize the behav- ior of the linear downconversion mixer shown in Fig. 4.24. This is accomplished by generating symbolic expressions for the HTM elements H0,1 (s), Ho,o(s) and H0,2(s). These expressions are verified by comparison with numerical simulations for typical 14 This, however, could be overcome by allowing SymbolicHTM to also use rank-reduced techniques to perform HTM inversions. In that case, however, we need a heuristic that decides on which method to use to invert a particular HTM. This again requires expertise of the field. 4.3.7 Application 1: linear downconversion mixer Figure 4.24: Linear downconversion mixer topology. The amplifier is real- ized as a two-stage Miller-OTA. IDS (Vosc, Vin, Vn1) gm2(Vn2) Coutl Cout2 Sout1 gout2 Figure 4.25: Single-sided equivalent circuit of the linear downconversion mixer. The transistors have been replaced by (nonlinear) voltage-controlled current sources. values of the design parameters. The mixer topology, introduced in [Crol95], was modeled using a two-stage Miller-OTA. In what follows, the mixer building block models ar