in this paper, newton harmonic balance method (nhbm) is applied to obtain the analytical solution for an electron beam injected into a plasma tube where the magnetic field is cylindrical and increases towards the axis in inverse proportion to the radius. periodic solution is analytically verified and consequently the relation between the natural frequency and the amplitude is obtained in an ana...

In this paper, Newton Harmonic Balance Method (NHBM) is applied to obtain the analytical solution for an electron beam injected into a plasma tube where the magnetic field is cylindrical and increases towards the axis in inverse proportion to the radius. Periodic solution is analytically verified and consequently the relation between the Natural Frequency and the amplitude is obtained in an ana...

We consider oscillators consisting of a reactance circuit and a negative resistor. They may happen to have multi-mode oscillations around the anti-resonant frequencies of the reactance circuit. This kind of oscillators can be easily synthesized by setting the resonant and antiresonant frequencies of the reactance circuits. However, it is not easy to analyze the oscillation phenomena, because th...

duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. this paper presents he´s energy balance method (ebm) for solving nonlinear differential equations. two strong nonlinear cases have been studied analytically. analytical results of the ebm are compared with the solutions obtained by using he´s frequency amplitude formulation (faf) and numerical solu...

| In this paper, we present a new implementation of the harmonic balance method which extends its applicability to circuits 2-3 orders of magnitude larger than was previously practical. The results reported here extend our previous work 1] which only considered large circuits operating in a mildly nonlinear regime. The new implementation is based on quadratically convergent Newton methods and i...

Nonlinear vibration behavior of beam is an important issue of structural engineering. In this study, a mathematical modeling of a forced nonlinear vibration of Euler-Bernoulli beam resting on nonlinear elastic foundation is presented. The nonlinear vibration behavior of the beam is investigated by using a modified multi-level residue harmonic balance method. The main advantage of the method is ...

An active antenna for transmitter application in S frequency band is designed and analyzed using harmonic balance technique which is based on the nonlinear model of active devices. In this active antenna, the amplifier is integrated with the radiator which is a rectangular patch antenna. This patch antenna is analyzed employing full-wave momentum method. By applying nonlinear model of transisto...

The harmonic balance method is used in most current commercial RF simulation tools. This is due to the fact that it has certain advantages over other common methods used in SPICE, namely (modified) nodal analysis (MNA), which make it better suited to simulate stiff problems and circuits containing transmission lines, nonlinearities and dispersive effects. In this project, the harmonic balance a...

Harmonic balance (HB) methods are frequency-domain algorithms used for high accuracy computation of the periodic steady-state of circuits. Matrix-implicit Krylov-subspace techniques have made it possible for these methods to simulate large circuits more efficiently. However, the harmonic balance methods are not so efficient in computing steady-state solutions of strongly nonlinear circuits with...