ols for symbolic circuit analysis. 4.3.2 Symbolic LPTV system analysis: outlining the flow Fig. 4.20 outlines the top-level flow used for the symbolic characterization of LPTV system behavior. At the heart lies the symbolic analysis engine that computes symbolic expressions for the input-output HTM elements given a description of the system's topology and building blocks. In this work, the input is required to be in the form of a block diagram (or, equivalently, a signal flow graph). As shown in Fig. 4.20, this may require an extra preprocessing step to convert, for example, a circuit netlist into a block diagram description. Finally, when numerical values for the building block parameters are available, they can be used to try and simplify the resulting expressions by discarding terms that have negligible contribution. In what follows, we discuss each of the steps of the SymbolicHTM algorithm in greater detail. Section 4.3.3 briefly discusses constructing the input block diagram. Next, sec- tions 4.3.4 and 4.3.5 deal with the operations of the engine for generating the expres- sions. Finally, use of the algorithm is illustrated in sections 4.3.7 and 4.3.8 for two types of downconversion stages. 4.3.3 Input model construction SymbolicHTM takes a block diagram of the system to be analyzed as input. The com- posing blocks can be LTI systems, represented by a symbol H(s) for their transfer characteristic, multiplications with a periodic signal p(t), represented by the symbols Pk for its Fourier coefficients, or even other LPTV systems, represented by the sym- bols for the elements of the 0-th column of the corresponding HTM (see section 4.3.4). 4.3 AUTOMATED SYMBOLIC LPTV SYSTEM ANALYSIS Ygs(s) Yfb(s) Yo(s) Hosd(s) Hi(s) A2(s) Hn1(s) H (s) Symbol Value 0.1 mS 1.6 pF Symbolic Analysis 16 pF Engine 10 pF 55 dB 0.15 V BVoscGo(s) H0,1(s) = H0,2(s) = L(s)Yfb(s + jwo) BVoscGo(s+jwo)G_1(s+jwo) L(s)L(s+jwo)Yfb(s+jwo) VB2VoscVn1,-1Go(s)Hi(s jwo) Figure 4.20: Top-level flow for generating symbolic expressions for the HTM elem