Fig. 2

Schematic diagrams of the impedance (a) and phase (b) profiles (impedance and phase as a function of the input frequency f). a1 Band-pass filter (resonance). a2 Low-pass filter (no resonance). b1 Zero-frequency phase crossing (phase-resonance). b2 Monotonically increasing and positive phase (no phase-resonance). a The resonant frequency $f_{\mathrm{res}}$ is the input frequency f at which the impedance $Z(f)$ reaches its maximum $Z_{\max }$. The resonance amplitude $Q_Z=Z_{\max }-Z(0)$ measures the resonance power. The half-width frequency band ${\Lambda }_{1/2}$ is the length of the frequency interval in between $f_{\mathrm{res}}$ and the input frequency value at which $Z(f)=Z_{\max }/2$, and measures the system’s selectivity to incoming frequencies close to $f_{\mathrm{res}}$. b The phase-resonant frequency $f_{\mathrm{phas}}$ is the zero-crossing phase frequency. The minimum phase ${\varphi }_{\min }$ measures the magnitude of the negative phase