Figure 8
Fabricated VO2 reconfigurable Peano inductor equivalent circuit modelling within 4 GHz-10 GHz for the inductor with 2 switches, in on state and off state compared to measured ones. (a) The resulted fitting of the equivalent circuit extracted Lseries_circuit and Lseries from the measured S parameters. The values are extracted optimizing simultaneously the Lseries_circuit, Q_circuit, module and phase of the Sij_circuit(jω) (2 scalar parameters and 3 complex values due to reciprocity). Off state values: LS = 1.48 nH RS = 2.79 Ohms, Rp = 1341Ohms, Cs = 0.17fF, Cox1 = Cox2 = 721 fF, Csub1 = Csub2 = 201 fF, Rsub1 = Rsub2 > 108 Ohm. On state values: LS = 0.90 nH, RS = 4.01 Ohms, Rp = 107 Ohm, Cs = 0.15fF, Cox1 = Cox2 = 724 fF, Csub1 = Csub2 = 201 fF, Rsub1 = Rsub2 > 108 Ohm. (b) Scalar Q and extracted Q_circuit resulted fitting (c), Simultaneous 3D Smith chart representation for Lseries_circuit, Q_circuit, Sij_circuit(jω), and Lseries, Q, S parameters of the measured inductors. The fitting of the S21 parameters is almost perfect, the fitting of the S11 parameters (whose values are extremely small in magnitude) is not perfect-but it overlaps on a specific frequency range too. S11 is more sensitive to the frequency dependency of the elements neglected in the simplified equivalent circuit in Fig. 7b. (d) Simultaneous 3D Smith chart representation for all the S11 (Sij_circuit(jω) and measured S11(jω)) parameters and their frequency dependency. It is interesting to notice their change of hemisphere just below 10 GHz for the off state modeled and measured inductors (this happening before their Q becomes 0-the radius of the cylinders in c is not yet zero, or in b one may see still the positive values of Q). This means that the imaginary part of S11 becomes “capacitive” before its Y11 imaginary part becomes 0-which determines the sign changes in Q. Referring to56,57 the classical quality factor34,35,36,37,38,39 analysed and implemented here too is a measure of the inductor performances while short-cutting the second port. If the inductor is connected in shunt in the final circuit the change of hemisphere of S11 below 10 GHz can be neglected, else depending on the configuration in which this is finally used- the change of hemisphere warns that under 50 Ohm load the inductor starts behaving capacitive before 10 GHz.
