The harmonic balance method is a technique for the numerical solution of nonlinear analog circuits operating in a periodic, or quasi-periodic, steady-state regime. The method can be used to efficiently derive the continuous-wave response of numerous nonlinear microwave components including amplifiers, mixers, and oscillators. Its efficiency derives from imposing a predetermined steady-state form for the circuit response onto the nonlinear equations representing the network, and solving for the set of unknown coefficients in the response equation. Its attractiveness for nonlinear microwave applications results from its speed and ability to simply represent the dispersive, distributed elements that are common at high frequencies.

The last decade has seen the development and application of harmonic balance techniques to model analog circuits, particularly microwave circuits. The first part of this article reviewed the fundamental achievements made during this time. In this part, the extension of the method to quasi-periodic regimes, optimization analysis, oscillator analysis, studies of various convergence strategies, and practical applications are discussed. A critical assessment of the various types of harmonic balance techniques is given. Examples of designs which have been modeled using the harmonic balance technique and built both in hybrid and MMIC form are presented.

Nonlinear circuit analysis using the method of harmonic balance—a review of the art. II. Advanced concepts

InP TED (transferred electron device) oscillators have been experimentally investigated for frequencies between 170 and 279 GHz. It has been found that output powers of more than 7 and 0.2 mW are possible at 180 and 272 GHz using second- and third-harmonic mode operation, respectively. Conversion efficiencies of more than 13% and 0.3% between fundamental and second harmonic and fundamental and third harmonic, respectively, have been found. The conversion efficiencies are comparable to GaAs TEDs. The output powers, conversion efficiencies, and tuning ranges (more than 22%) are the biggest reported for InP TEDs at these frequencies. The output power at third harmonic was sufficient for supplying a superconducting mixer with local oscillator power. >

High efficiency and output power from second- and third-harmonic millimeter-wave InP-TED oscillators at frequencies above 170 GHz

The authors present a newly developed free-running steady-state oscillator analysis algorithm suited to large-signal oscillator analysis. Kurokawa's oscillation condition is coupled with the modified nodal admittance form of the circuit equations to avoid degenerate solutions. The algorithm was implemented by using both harmonic balance and frequency-domain spectral balance techniques. It was used in the simulation of monolithically integrated varactor-tuned MESFET oscillator. Good agreement between simulated power and oscillation frequency results was obtained. >

Computer-aided analysis of free-running microwave oscillators

Frequency-domain nonlinear analysis techniques for the simulation of active microwave circuits solve the linear and nonlinear network equations entirely in the frequency-domain. by so doing, they avoid the aliasing problems inherent in piecewise harmonic balance approaches. Consequently, frequency-domain techniques have extremely wide dynamic range and easily accommodate high order multitone excitation. However, this is at the expense of requiring more restrictive nonlinear device models. There are a large number of frequency-domain nonlinear analysis techniques but all are based on functional expansions which enable the frequency components of the output spectrum to be calculated directly from the input spectrum. These techniques have been used to analyze many nonlinear circuits and are the only candidates for the hierarchical simulation of nonlinear microwave circuits. This paper first uses frequency-domain concepts to discuss nonlinear distortion phenomena, then, a review of the frequency-domain nonlinear analysis literature is made with the aim of presenting the major advances in these techniques.

Computer-aided analysis of nonlinear microwave circuits using frequency-domain nonlinear analysis techniques: The state of the art

Second harmonic InP-TED oscillators are investigated for frequencies above 110 GHz using different mounts and TED's. It is found that state of the art output powers, comparable to Schottky-varactor multipliers, of more than 2 mW can be generated above 190 GHz by reducing the capsule parasitics. Output power up to 216 GHz are observed. The tuning range above 110 GHz is found to be more than 40%. Using theoretical waveguide models the tuning behaviour of the oscillators is also investigated.

A contribution to the design of wideband tunable second harmonic mode millimeter-wave InP-TED oscillators above 110 GHz

In this paper a feedback model of second harmonic oscillators is developed. By using describing functions of nonlinearity of active devices, the performances of second harmonic oscillators are studied. Frequency dependence of I–V characteristics of active element are taken into account. The ratio of maximum output power of second harmonic to fundamental is given. The maximum harmonic locking bandwidth of injected harmonic oscillator is derived. The theoretical prediction is compared with experimental results.

A feedback model of millimeter wave harmonic oscillators and its application

This paper presents a generalized field analysis method for calculating the external circuit impedances looking outside from the active devices of some millimeter wave oscillators. For a simple oscillator model with a radial disc and a diode existing in a rectangular waveguide, the numerical results are in agreement with the experimental data. Impedance characteristics for several different oscillator configurations are given, and some useful conclusions for oscillator design are derived.

Calculation of external circuit impedances of mm-wave oscillator cavities by a rigorous field analysis method

In this paper, the new technique of time-domain analysis of discontinuities in a planar transmission line is presented. In the process of time-domain analysis, the analysis model of system and the concept of transfer function are employed and the frequency-domain method of lines and the technique of the fast Fourier transform are used. The results of time-domain data and frequency-domain characteristics for the shielded microstrip with step discontinuity are given and compared with the published results of other authors.

The new method of time-domain analysis of a planar transmission line with discontinuity

This paper presents a generalized field analysis method for calculating the external circuit impedances looking outside from the active devices of some millimeter wave oscillators For a simple oscillator model with a radial disc and a diode existing in a rectangular waveguide, the numerical results are in agreement with the experimental data Impedance characteristics for several different oscillator configruations are given, and sane useful conclusions for oscillator design are derived

Sifan Li

Papers

A feedback model of millimeter wave harmonic oscillators and its application

Calculation of external circuit impedances of mm-wave oscillator cavities by a rigorous field analysis method

The new method of time-domain analysis of a planar transmission line with discontinuity

Rigorous Field Analysis Of Impedances Of Some Millimeter Wave Oscillator Cavities