 . . ) and C3 independent functions of the building block parameters. Likewise, it holds for H0,2(s) (4.104) (4.105) with, again, D1 (Vosc,Wo, . . ) and D2 (Vosc,Wo, . . . ) frequency-independent functions of the building block parameters. AUTOMATED SYMBOLIC LPTV SYSTEM ANALYSIS HTM element Relative error H0,1 (s) -81.0 dB H0,0 (s) -53.8 dB H0,2(s) -33.5 dB Table 4.2: Relative accuracy of the symbolically computed downconversion mixer characteristics as compared to direct numerical computation. The accuracy of these symbolic models -as compared to HTM elements numerically extracted by means of an algorithm similar to the one in [Royc99]- is listed in ta- ble 4.2. The results show that the expressions, generated up to first order in the dummy variable u, allow us to model H0,0(s) and H0,2(s) up to accuracies of respectively 0.2% and 2%, with the expression for H0,1 (s) being even more accurate. This is quite suffi- cient for most purposes. Fig. 4.27 plots Ho,o(s) and H0,2(s) and their components for the design parameters chosen as in table 4.1. The solid bold line represents the ex- act overall transfer characteristic, while the marked lines correspond to the individual, symbolically generated components (after grouping). Computing contributions up to higher order in rapidly leads to an explosion in the number of symbolic terms. Simplification techniques [Fern98, Gie91, Gie94, Wamb98b] become unavoidable to control this explosion. This, however, requires numerical data concerning the building block parameters. Often, such data is not available at the stage in the design process where symbolic system characterization is desirable. The results in table 4.2, however, indicate that the contribution of these higher-order terms to the overall characteristic is negligible, making it in most cases unnecessary to compute them. Up to first order, the number of terms is small enough for the symbolic models to be useful and interpretable. 4.3.8 Application 2: Receiver stage with feedback across the mix- ing element Fig. 4.28 