a Hopf-link (dark cyan) and the drumhead region (orange) of elevated impedance it encloses, computed in the “clean” limit absent of parasitic resistances and component uncertainty. Simulation was performed with N = 30 unit cells at resonant frequency 795.7 kHz for the circuit Laplacian in Eqs. (15) to (18) (in “Methods”), truncated from that of Fig. 4a to facilitate experimental construction. b Impedance map of the same circuit, but simulated for our N = 9 experimental setup with empirically determined parasitic inductor and capacitor resistances RpL = 0.11 Ω and RpC = 0.03 Ω, and capacitor/inductor tolerances of 1%. c Corresponding experimentally measured impedance (crosses) with distinct elevated region, which agree well with simulation (lighter background contours from (b)). Frequency used is 740 kHz, offset from the predicted 795.7 kHz to account for uncertainties in the tuning circuitry (see “Methods” and Supplementary Table 3).