System-Oriented Harmonic-Balance Algorithms for Circuit-Level Simulation

Smart Wireless Power Transfer Operated by Time-Modulated Arrays via a Two-Step Procedure

“…technique [17]. According to the Piecewise HB (PHB) formulation, the circuit is divided into a linear and a nonlinear subnetwork, described in the frequency and time domains, respectively.…”

“…The fast RF carrier (GHz) and the slow modulation frequency (up to a few MHz) may differ by several orders of magnitude. This circumstance allows the numerical analysis to be considerably simplified by resorting to the envelopeoriented PHB method [17]. According to this method the quasiperiodic two-tone regime is approximated by a sequence of fast periodic regimes (of period 0 = 2 / 0 ) slowly changing in time.…”

Nonlinear/electromagnetic approach for time-modulated array simulation

“…The piecewise HB principles [4] can be briefly recalled by referring to the schematic view of the system under test, reported in Fig. 1: it consists of an array of 16-planar monopoles aligned along the x-axis (element spacing = λ/2) with associated corporate feed network in microstrip technology, both on a 0.635 mm-thick Taconic RF60A (ε r = 6.15, tanδ=0.0028 @ 10GHz), 16 PIN diodes, and 8 bias ports (since symmetric switching modulation patterns are considered).…”

“…In the case of system operation under modulated RF drive (due to the time-modulated switching sequence of the PIN diodes) the standard HB method resorts to the MHB method [4]. According to this approach the constant complex k-th phasor I k of (1) is replaced by the timedependent complex k-th envelope (or modulation law) I k (t), whose period T B = 2π/ω B is much bigger than the carrier period T 0 = 2π/ω 0 (as in all TMA applications) (3) where N B is the number (typically high) of significant harmonics (sidebands) of the modulation law, and I kh are the corresponding current physical harmonics of the modulated regime.…”

“…This paper tries to increase the level of accuracy in the simulation/design of TMAs by exploiting well-established design techniques [3] based on the electromagnetic (EM) description of the array, on the accurate description of the nonlinear switches, and of their combination by means of the modulation-oriented piecewise harmonic-balance (MHB) method [4].…”