e time- varying gain block A2(s), which represents the series connection of a multiplication with gm2(t) and filtering by output impedance. The remaining blocks in Fig. 4.26 are time-invariant and are determined by Yfb(s) = Gfb+sCfb (4.89) Ygs(s) = sCgs (4.90) Yo(s) = gout2+s(Cout2+Cc)+Yfb(s) (4.91) Yn1 (s) : (4.92) gin = 3(Vin,DC-VT) (4.93) Yn2(s) Bout1+s(Cou1+Cc) (4.94) (4.95) Hc(s) (4.96) (4.97) Numerical values for the most important parameters occurring in these formulas were already listed in Table 4.1. 4.3 AUTOMATED SYMBOLIC LPTV SYSTEM ANALYSIS 4.3.7.2 Computing the HTM elements of the overall mixer In a first step of the symbolic HTM algorithm, the loop equations (4.80) are con- structed. During this process, two loop variables and one auxiliary HTM G(s) are introduced. This auxiliary HTM corresponds to the part encircled by the dashed line in Fig. 4.26, and is generated as the intersection of the graphs corresponding to the open-loop HTMs of the second loop equation. It represents a system with Hi(s)(A1(s)(sm2,0+sCc)+Yfb(s)) (4.98) Gk,o(s) Yo(s+jkwo) Next, symbolic expressions are generated for the mixer's input-output HTM elements Ho,o(s), H0,1 (s) and H0,2(s). These elements, respectively, capture the downconversion behavior of the signal contents around 0, fo and 2fo to baseband. Computations were done up to first order in the dummy variable (see equation (4.82)), while taking 7 tones into account. They took about 3 seconds of CPU time to complete on a Sun Ul- tra30. In the absence of prior numerical data, these values were selected manually. In what follows, the resulting symbolic expressions are verified numerically for a mixer design with a bandwidth of 1 MHz and a local oscillator frequency fo = 20MHz. Nu- merical extraction of the HTM elements was done in MatlabTM using an algorithm similar to the one in [Royc99]. Comparison of the symbolic expressions generated by SymbolicHTM with numerically extracted HTM elements is done by integrating the difference between both over the interval [0,fo], wit