Figure 7

Proposed equivalent circuit of the Peano reconfigurable inductors and VO₂ switches in the off and on state for the 4 GHz-10 GHz frequency range. (a) Off state modelling of the VO₂ switch: R_{VO2_off} is modelling the undesired losses in between the adjacent turns where the VO₂ switches are present. Ideally R_{VO2_off} = ∞, however the non-zero conductivity of VO₂ (whose measurement in DC is present in Fig. 9-Methods) will generate undesired conductive losses between turns. Similarly, the frequency dependent dielectric constant of the VO₂ can in theory generate undesired couplings between the adjacent turns where the VO₂ is present: C_{VO2_off}. C_{VO2_ground1} and C_{VO2_ground2} are modelling the coupling losses between the VO₂ switches and coplanar waveguide ground planes. (b) Extracted equivalent circuit of the inductor: L_s stands for the series inductance, C_s stands for the inter-turns capacitance, C_ox1, C_ox2, C_sub1, C_sub2, R_sub1, R_sub2 describe the RF losses within the various substrates layers. R_p is modelling the undesired conductive losses between the adjacent turns due to the VO₂ conductivity. In the off state we would like R_p to be ∞, however the conductive losses in the VO₂ switches will make this term being un-unneglectable. R_S is modelling the series resistance-dependent on the Al deposition and trace width, (counting the on/off resistances corresponding to the current paths through the turns R_{turns_on}/R_{turns_off}), but including too the VO₂ resistive losses R_{VO2_on} in the on state of the switches. (c) On state modelling of the VO₂ switch: R_{VO2_on} is modelling the undesired resistive losses due to the limited conductivity of the VO₂ in the on state. This resistance will contribute to a higher value of the R_s in the on state since the current will pass through the switches.