Relations of Time-Varying Circuit Parameters and Idlerless Parametric Harmonic Generation for Reconfigurable Frequency Multipliers

The idlerless relations between parametric harmonic generation and time-varying circuit parameters, such as elastance (
${S}$
), capacitance (
${C}$
), conductance (
${G}$
), and resistance (
${R}$
), are described in this work. It is shown that the time-varying response of the
${S}$
,
${C}$
,
${G}$
, or
${R}$
parameter is periodic with
${N}-1$
periods over one sinusoidal pumping cycle for
N-
times multiplication in idlerless reactive and resistive parametric multipliers. Under sinusoidal pumping and with the
${N}-1$
periods of the time-varying response described by Chebyshev polynomials of the first kind, the generation of odd- and even-order harmonics is realized. An approach of representing a transient train of impulses under sinusoidal pumping is also described to model the resistive multipliers. The minimum conversion loss (CL) and the maximum conversion efficiency of parametric multipliers are derived. It is shown that, at high relative frequencies, the proposed time-varying response is theoretically capable of achieving higher maximum efficiency than what is calculated with conventional idler-based multipliers. A millimeter-wave (mm-wave) switched-capacitor varactor (SCV) with tunable capacitance–voltage curves is utilized to build third-, fourth-, and fifth-order
${D}$
-band reconfigurable frequency multipliers (RFMs). The simulations and measurements demonstrate the validity of the proposed theory of the tunable parametric harmonic generation. The relative bandwidths of the
${D}$
-band RFM are 38.8%, 35.4%, and 25.5% with the output power at −26.6, −37.2, and −40.5 dBm for three-, four-, and five-times multiplications, respectively. An example of a
${D}$
-band resistive multiplier with a tunable nonlinearity is also given.