Design of a Wireless Passive Mixer Circuit Under Low-Power RF Excitation Based on the Mathieu–Duffing Nonlinear Dynamics Model

Some passive wireless frequency-conversion approaches require an additional local oscillator or dual-frequency excitation, increasing circuit complexity. This paper proposes a single-frequency-excited wireless passive sensing mixer that exploits the nonlinear parasitic junction capacitance of a field-effect transistor (FET) coupled to a sensing resonator. By utilizing the voltage-dependent parasitic capacitance normally suppressed in conventional RF design, the circuit couples device nonlinearity with the characteristic response of the sensing resonant network to generate frequency-converted components separated from the incident carrier without an additional external local oscillator. First, the resonant response formed by the voltage-dependent FET gate–source (GS) capacitance and the front-end equivalent inductance is analyzed in terms of its operating-point-dependent natural frequency and nonlinear forced response. Under the modeling assumption that the internal sensing mode approximately modulates the front-end equivalent parameters periodically, a generalized forced Mathieu–Duffing model is used to describe the coupling among nonlinear restoring behavior, parametric modulation, and frequency conversion. A complete circuit is then simulated in ADS at 433 MHz. The input impedance and single-frequency spectrum are first characterized with the normal gate–drain parasitic capacitance Cdg. The Cdg branch is then set to zero while all surrounding circuit parameters and RF excitation conditions are kept unchanged; the normal Cdg model is subsequently restored for a separate optimization of the matching network. With only a 433 MHz RF excitation, the complete circuit produces non-harmonic frequency-conversion components near 420 and 446 MHz. These components remain observable when Cdg is set to zero, whereas the carrier response and input-impedance characteristics change. Matching optimization changes the input impedance at 433 MHz from 24.511 + j85.561 Ω to 49.529 + j2.150 Ω and increases the spectral response at the designated 420 and 446 MHz frequencies. Repeated measurements on fixed-parameter printed circuit board (PCB) configurations demonstrate repeatable converted-frequency output, and a separate wireless loading experiment shows a load-dependent received-frequency response. Over the 0–200 g loading range, the mean return-frequency shift reaches approximately 70.76 kHz. The simulations and measurements jointly support the feasibility of single-frequency-excited frequency conversion and wireless sensing readout, providing an approach to simplified, low-power wireless sensing systems.