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A Unified SPICE Compatible Model for Large and Small Signal Envelope Simulation of Linear Circuits Excited by Modulated Signals . Simon Lineykin and Sam Ben-Yaakov*

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## A Unified SPICE Compatible Model for Large and Small Signal Envelope Simulation of Linear Circuits Excited by Modula

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**A Unified SPICE Compatible Model for Large and Small Signal**Envelope Simulation of Linear Circuits Excited by Modulated Signals Simon Lineykin and Sam Ben-Yaakov* Power Electronics LaboratoryDepartment of Electrical and Computer EngineeringBen-Gurion University of the NegevP. O. Box 653, Beer-Sheva 84105, ISRAEL Phone: +972-8-646-1561, Fax: +972-8-647-2949Email: sby@ee.bgu.ac.il, Website: www.ee.bgu.ac.il/~pel**A Primer to Envelope Simulation**• Any analog modulated signal (AM, FM or PM) can be described by the following expression: • The Current in the network excited by u(t):**Phasor Analysis**• Inductance**Phasor Analysis**Capacitance Resistance**Splitting the Network into Two Cross-Coupled Components -**Imaginary and Real**Real Load Component**Imaginary Load Component Splitting the Network into Two Cross-Coupled Components - Imaginary and Real**Simulation Alternatives**• Cycle-by-cycle (full simulation) • High and low frequencies • Very long simulation • Only transient • AC transfer function -> point-by-point • Envelope simulation (Large Signal -Previous study) • Only low frequency • Only transient • AC transfer function -> point-by-point**Example: Piezoelectric Transformer Driven by FM Signal**(SPICE)**Example: Piezoelectric Transformer Driven by FM Signal**(SPICE)**Example: Piezoelectric Transformer Driven by FM Signal**(SPICE)**Example: Piezoelectric Transformer Driven by FM Signal**(SPICE) - Harmonic modulating signal**Example: Piezoelectric Transformer Driven by FM Signal**(SPICE)**OrCAD Schematics for Envelope Simulation**(Large Signal)**Results of Full and Envelope Transient Simulations**The modulating input signal Envelope The Frequency modulated signal Cycle-by-cycle Envelope Cycle-by-cycle Output signal**Objectives of this Study**• To extend the envelope simulation method to AC analysis • A method that would not need an analytical derivation • Same model compatible with DC, AC, and Transient analysis types**Proposed Method – Small Signal Analysis Using**AC–Simulation • Amplitude modulation phasor The source is linear and suitable for AC analysis – as is**=Ac**Small signal =Ac*kp*u(t) Small signal Linear source Linearization of Sources for Angle Modulation • Phase Modulation phasor PM – Nonlinear source**=Ac**Small signal =Ac*kp*u(t)dt Small signal Linear source Linearization of Sources for Angle Modulation • Frequency Modulation phasor FM – Nonlinear source**Results: Piezoelectric Transformer Driven by FM signal (AC**and Point-by-Point) for Different Carrier Frequencies**Results: Piezoelectric Transformer Driven by FM signal (AC**and Point-by-Point) for Different Carrier Frequencies**Frequency Response of the Network (unmodulated input signal)**using DC-sweep • DC-sweep in envelope simulation is equivalent to frequency sweep in full simulation • The parameter of DC sweep is a carrier frequency fc • The source for DC sweep:**Example: Frequency Response of Piezoelectric Transformer**with Different Resistive Loads**Conclusions**• Envelope simulation method was extended to cover all simulation types: Transient, AC, DC. • Method is suitable for any linear circuit. • Method is also suitable for nonlinear circuits that can be linearized for small signal.

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