ll small-signal input components are set to 0. Note that it varies pe- riodically with time. AI(t) is the small-signal current that comes on top of Iop(t). It is due to a non-zero small-signal input Au(t). This small-signal current is proportional to Au(t) with a proportionality constant that varies periodically with time. For this reason, (3.10) is said to model the LPTV system that describes the small-signal current flowing through the mixing transistor. As will be proven in section 3.4.1, the HTM that corresponds to the multiplication in (3.10) equals Amixer( = (3.11) 3/2 0 This (frequency-independent) HTM relates the small-signal transistor current variation Al to the small-signal gate voltage variation Au. The example above illustrates the procedure used to extract a HTM from a set of circuit equations. This procedure, also depicted in Fig. 3.5, consists of the following steps: 3.1.3 LPTV behavior and circuit small-signal analysis Extract MNA equations QQ(x(t), vosc(t), u(t)) + J (x(t), vosc(t), u(t)) = 0 Compute steady-state operating point set u(t)=u0 Linearize MNA equations around operating point H_1,-1(s) H_1,0(s) H_1,1(s) H(s) = H0,-1(s) H0,0(s) H0,1(s) H1,-1(s) H1,0(s) H1,1(s) Figure 3.5: HTMs are derived from circuit behavior by linearizing the circuit equations in the neighborhood of a periodically time-varying operating point. The operating point is obtained by neglecting the small-signal component of the input signal u(t). However, in computing the operating point, the large periodic oscillator signal that drives the mixer is not neglected. This results in periodic operating point waveforms with spectra that contain discrete tones at multiples of the oscillation frequency. PRIOR ART 1. Construct the circuit's MNA equations. This can, for example, be accomplished using the algorithm described in [Freu95]. 2. Compute the operating point voltages and currents. In doing so, input small- signal variations are to be neglected, i.e. they are set to 0. However, the periodic large-signal oscillations that d