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Showing papers on "Total harmonic distortion published in 1991"


Patent
16 Dec 1991
TL;DR: In this paper, a circuit is provided for generating a current that is a harmonic of the frequency of the utility system and which is of a selected amplitude and phase to reduce the total harmonic distortion of a system that converts alternating current to direct current, or vice versa.
Abstract: A circuit is provided for generating a current that is a harmonic of the frequency of the utility system and which is of a selected amplitude and phase to reduce the total harmonic distortion of a system that converts alternating current to direct current, or vice versa. The DC signal is sampled and by controlling switches, a sinusoidal current at the desired harmonic is generated, and is provided to impedance network that injects this current into the multiphase AC system used by the utility in a very low cost, easily controlled, and highly effective manner. The impedance network comprises a single inductor and capacitance connected in series through each of the phases of the utility, with the current signal having an amplitude that is selected to substantially eliminate harmonics which cause high distortion of the utility signal.

138 citations


Proceedings ArticleDOI
28 Apr 1991
TL;DR: In this paper, the authors introduced some common harmonic analysis techniques and applied them to voltage waveforms recorded on a typical REA transmission and distribution system, and the results showed that the voltage and current waveforms are becoming more distorted and the power quality is deteriorating.
Abstract: With the increase of nonlinear loads on utility distribution systems, the voltage and current waveforms are becoming more distorted and the power quality is deteriorating. Since this is becoming a wide spread problem today, and new, more strict, distortion guidelines are under development, utility engineers are having to deal with analyzing and planning for the control of the distortion. This paper introduces some common harmonic analysis techniques and applies them to voltage waveforms recorded on a typical REA transmission and distribution system. >

116 citations


Journal ArticleDOI
TL;DR: In this article, the Fourier series of the optimum APLC injection current waveform was determined using nonlinear optimization theory and applied to a single-phase APLC in a balanced three-phase network.
Abstract: Active power line conditioner (APLC) is a type of active filter that compensates for power system waveform distortion The objective is to develop and illustrate a procedure for calculating the APLC injection current needed to minimize voltage harmonic distortion throughout a power network The procedure is intended for use with APLC frequency domain correction in networks that are experiencing periodic harmonic distortion The injection currents are determined using nonlinear optimization theory The chief contribution lies in developing a simple procedure for finding the Fourier series of the optimum APLC injection current waveform The procedure is intended to apply in any of the following situations: (1) one single-phase APLC in a single-phase network; (2) one single-phase APLC in a three-phase network; or (3) one three-phase APLC in a balanced three-phase network >

113 citations


Journal ArticleDOI
TL;DR: In this article, a highly linear electrooptic modulator has been designed, fabricated, and evaluated, which consists of only a simple modification to the directional coupler, and two-tone testing has demonstrated that, for an optical modulation depth of 30% per channel, the third-order intermodulation distortion is more than 30 dB lower than that of the conventional directional coupling or Mach-Zehnder modulators.
Abstract: A highly linear electrooptic modulator has been designed, fabricated, and evaluated. The design of this modulator consists of only a simple modification to the directional coupler. Two-tone testing has demonstrated that, for an optical modulation depth of 30% per channel, the third-order intermodulation distortion is more than 30 dB lower than that of the conventional directional coupler or Mach-Zehnder modulators. This improvement was not observed to be accompanied by any increase in second harmonic distortion. Also included are results of two-tone computer simulations which predict the improvement in linearity of this device for a range of modulation depths. >

113 citations


Journal ArticleDOI
28 Sep 1991
TL;DR: In this article, the measured performance of compact fluorescent lamps (CFLs) and some rectified incandescent lamps, which can cause considerable harmonic distortion of the input power, is discussed.
Abstract: The measured performance of compact fluorescent lamps (CFLs) and some rectified incandescent lamps, which can cause considerable harmonic distortion of the input power, is discussed. These include both the electronically and magnetically ballasted CFLs with poor power factors and/or high harmonics. Using the model of a building's electrical load, it is shown that there is little cause for concern for power supply quality problems when the CFLs are less than 25% of the building's total load. Several reasonable low-cost passive circuits that can improve the power factor as well as suppress the harmonic distortion are described. The use of active circuits will be more effective but more costly and are best considered for CFLs above 30 W and for special applications where minimum harmonics are required. >

108 citations


Journal ArticleDOI
TL;DR: In this article, a voltage-dependent current injection load model is presented to determine voltage waveform characteristics and additional losses at harmonic frequencies, and the optimal capacitor sizes and locations depend heavily on the load model used at fundamental frequency and on harmonic signals, especially when limits are imposed on voltage waveforms.
Abstract: The nonlinear portion of electrical loads has increased significantly in recent years. Harmonic currents injected by these loads into the distribution system should be considered when solving the capacitor placement problem in order to assure that the optimal solution does not result in excessive harmonic distortion. A voltage-dependent current injection load model is presented to determine voltage waveform characteristics and additional losses at harmonic frequencies. Computer simulations show that the optimal capacitor sizes and locations depend heavily on the load model used at fundamental frequency and on harmonic signals, especially when limits are imposed on voltage waveforms. >

99 citations


Journal ArticleDOI
TL;DR: In this paper, the AC supply system harmonic impedance measurements are discussed, on the basis of a given and known switchable shunt impedance and/or nonlinear load and site measurements, three methods are presented.
Abstract: AC supply system harmonic impedance measurements are discussed. On the basis of a given and known switchable shunt impedance and/or nonlinear load and site measurements, three methods are presented. The first approach assumes a no-load distorted busbar and uses basic circuit theory to calculate the required harmonic impedance. The second method disregards any previous busbar distortion and the harmonic injection but it takes into account any busbar distortion prior to the nonlinear load connection. Using a laboratory model and by comparing harmonic impedance results it is shown that both no-load busbar distortions and the correct measurement of harmonic phase angles may strongly affect the accuracy of calculation. >

96 citations


Patent
09 Dec 1991
TL;DR: In this paper, a predistortion circuit for an optical communications system includes a main path for an RF modulating signal and a pre-distortion path for a precomputed signal, which signals are combined to modulate a laser diode.
Abstract: A predistortion circuit for an optical communications system includes a main path for an RF modulating signal and a predistortion path for a predistortion signal, which signals are combined to modulate a laser diode. The distortion path includes a distortion generator which generates a distortion signal which is substantially the same as the distortion generated by the modulation of the transmission system with the RF modulating signals. In one implementation, the distortion generator comprises a square law device which preferably is a field effect type device. The square law device operational characteristic closely mimics the major component of distortion in optical communications systems, composite second order (CSO) distortion. In a second implementation, two square law devices are coupled in an anti-phase arrangement to substantially cancel odd order distortion components from the distortion signal and to enhance even order distortion components, particularly CSO. Another implementation illustrates a dual output distortion generator which allows for the selection of either an in phase or inverted phase distortion signal to be able to compensate for sublinear and superlinear laser diode curves without a separate phase inverter. Still another implementation of the predistortion circuit provides for the independent amplitude adjustment of different bands of the CATV spectrum to permit compensation for different channel loadings, channel spacings and channel amplitudes.

96 citations


Journal ArticleDOI
TL;DR: In this article, a high-frequency large-signal very low-distortion voltage-to-current transducer is presented, where the transconductor noise is integrated over a bandwidth of 1 MHz.
Abstract: A high-frequency large-signal very low-distortion voltage-to-current transducer is presented. The total harmonic distortion (THD), for supply voltages of only +or-2.5 V, is smaller than 0.1% for fully differential input signals up to 2.4 V peak to peak (V/sub pp/). The dynamic range is on the order of 89 dB with the transconductor noise integrated over a bandwidth of 1 MHz. Moreover, this structure presents low sensitivity to transistor mismatches. An operational transconductance amplifier (OTA), based on this transconductor, has been used in an adjustable quality factor 1.8-MHz biquadratic continuous-time filter. The quality factor Q is controlled, from 2 to 50, with a novel current-source configuration. Both the OTA and the filter have been fabricated in a CMOS 3- mu m n-well process. >

90 citations


Journal ArticleDOI
TL;DR: In this paper, a two-channel differential 18-b bit-stream digital-to-analog converter implemented in a 2.5- mu m BiCMOS process with 7.3mm/sup 2/ chip area is described.
Abstract: A two-channel differential 18-b bit-stream digital-to-analog converter implemented in a 2.5- mu m BiCMOS process with 7.3-mm/sup 2/ chip area is described. The circuit contains two identical 1-b D-to-A conversion channels on one single chip. Each channel consists of a digital input part, a switched-capacitor D-to-A network, and two high-performance operational amplifiers. Total harmonic distortion plus noise is better than -102 dB. The dynamic range is more than 108 dB, giving a true 18-b resolution. Output operational-amplifier distortion is below 120 dB at full-scale signal. System design considerations, implementation, and measured results of the IC are discussed. >

70 citations


Journal ArticleDOI
G. Morthier1, F. Libbrecht1, Klaus David1, P. Vankwikelberge1, Roeland Baets1 
TL;DR: In this article, the second-order harmonic distortion in the amplitude modulation-response of Fabry-Perot and distributed feedback (DFB) lasers is analyzed for modulation frequencies ranging from a few megahertz to well beyond the resonance frequency of the relaxation oscillation.
Abstract: Numerical calculations of the second-order harmonic distortion in the amplitude modulation-response of Fabry-Perot, and distributed feedback (DFB) lasers are presented, and the influence of several nonlinearities, such as longitudinal spatial hole burning, gain suppression, and relaxation oscillations are considered. This analysis is valid for modulation frequencies ranging from a few megahertz to well beyond the resonance frequency of the relaxation oscillation. The distortion of Fabry-Perot lasers for which the effects of spontaneous emission and gain suppression can be clearly illustrated is investigated. The distortion of DFB lasers where the emphasis is on the influence of spatial hole burning and its combination with other nonlinearities is discussed. Various effects are discussed. >

Journal ArticleDOI
28 Sep 1991
TL;DR: In this paper, a power flow program is developed to analyze the harmonic distortion of a power system with various types of harmonic loads, and the proposed program can be applied to solve the harmonic current flow, voltage harmonic distortion factor, resonance frequency, and current amplification factor at every bus in the system.
Abstract: A power flow program is developed to analyze the harmonic distortion of a power system with various types of harmonic loads. The proposed program can be applied to solve the harmonic current flow, voltage harmonic distortion factor, resonance frequency, and current amplification factor at every bus in the system. In this study, a large metal factory is selected for the harmonic power flow analysis. The current waveforms at every bus are measured and analyzed to determine various orders of harmonic components. These harmonic currents are used in the computer simulation to determine the harmonic voltage distortion factor at the buses of the system, and the variations of resonance impedance and amplification factor with frequencies are investigated. Finally, the program is used to calculate the harmonic load flow when the metal factory is expanded by including a new plant in the power system, and proper filters are designed to alleviate the harmonic problems. >

Proceedings ArticleDOI
10 Mar 1991
TL;DR: In this paper, the authors present power factor improvement methods, for switched-mode power supplies, by using harmonics elimination, three methods were valuated: a series connected resonant filter, a parallel connected resonance filter, and an active boost converter.
Abstract: The authors present power factor improvement methods, for switched-mode power supplies, by using harmonics elimination. Three methods were valuated: a series connected resonant filter, a parallel connected resonant filter, and an active boost converter. The two passive filters are commercial products, and the boost converter is an in-house design using a power MOSFET as the switching device and a dedicated commercial IC for the control circuit. An off-the-shelf PC power supply along with the two passive filters and a boost converter were used as the test specimen. The experimental results show input power factor, distortion factor, crest factor, total harmonic distortion, and harmonic components. Also identified are the power system impacts of nonlinear current, the relative cost of harmonic elimination, and the motivation that may come from new power quality standards. >

Journal ArticleDOI
TL;DR: In this article, the second-order harmonic and third-order intermodulation distortions of laser diodes with optical feedback were derived, and it was shown theoretically and experimentally that optical feedback from the transmission fiber considerably enhances inter-modulation and harmonic distortions.
Abstract: Analytical expressions for the second-order harmonic and the third-order intermodulation distortions of laser diodes with optical feedback are derived It is shown theoretically and experimentally that optical feedback from the transmission fiber considerably enhances intermodulation and harmonic distortions of laser diodes Third-order intermodulation distortions up to -15 dBc must be expected for two-tone modulation and low-intensity modulation indexes m approximately=7% per carrier, which affects the performance of subcarrier multiplexed (SCM) communication systems To avoid additional distortions the external feedback level must be two orders of magnitudes lower than the critical external feedback level of the laser diode >

Journal ArticleDOI
TL;DR: In this article, the reduction of intensity noise and distortion in a semiconductor laser by feedforward compensation is reported, and the intensity noise has been reduced by more than 10dB over the frequency range 1.7-3.0 GHz.
Abstract: The reduction of intensity noise and distortion in a semiconductor laser by feedforward compensation is reported. The intensity noise has been reduced by more than 10dB over the frequency range 1.7–3.0 GHz. In addition, a simultaneous reduction in second harmonic distortion and third-order intermodulation distortion has been observed.

Proceedings ArticleDOI
10 Mar 1991
TL;DR: In this article, current regulators are proposed and investigated for high-power three-phase power supplies with ultra-low total harmonic distortion (THD) (less than 0.5%).
Abstract: Current regulators are proposed and investigated for high-power three-phase power supplies with ultra-low total harmonic distortion (THD) (less than 0.5%). Two valid approaches to realize three-phase power supplies can be proposed. In the first approach, current regulated pulse-width-modulated (PWM) inverters along with high bandwidth voltage control loops are proposed. In the second approach, an internal voltage synthesizer under closed loop current control is used. Both approaches have mechanisms to decouple the LC filter interactions and to lower the THD. The tradeoffs of these two basic approaches are investigated. The influence of different current regulators in case of the current-regulated PWM (CRPWM) converter is investigated as well as different approaches to control the voltage synthesizer under current control. The study compares the effectiveness of these current regulator in soft-switching PWM inverters and describes a method to measure accurately ultra-low THDs. >

Journal ArticleDOI
TL;DR: In this paper, the authors describe two low-voltage switched-capacitor (SC) filters: one can operate from a minimum supply of 1.5 V and the other from a 2 V (for typical parameter values).
Abstract: The authors describe two low-voltage switched-capacitor (SC) filters: one can operate from a minimum supply of 1.5 V and the other from a minimum supply of 2 V (for typical parameter values). Both filters use a fully differential architecture and are fabricated in a standard BiCMOS technology. The lowest supply filter, operated from a 2-V supply, has an SNR (signal-to-noise ratio) of 92 dB and a THD (total harmonic distortion) of -70 dB for a 2.4-V/sub pp/ differential signal. Power consumption and area per pole are 60 mu W and 0.18 mm/sup 2/, respectively, with a clock frequency of 447 kHz. The realized filters can be used as building blocks to implement more complex functions, like the active synthesis of a given impedance in line-fed telecom systems. >

Journal ArticleDOI
TL;DR: In this article, the validity of assuming that the fundamental frequency load flow conditions of an AC-DC conversion plant are unaffected by the presence of harmonics is questioned, and an algorithm is derived which is capable of determining the true load flow condition of a power converter with harmonics.
Abstract: The validity of assuming that the fundamental frequency load flow conditions of an AC-DC conversion plant are unaffected by the presence of harmonics is questioned, and an algorithm is derived which is capable of determining the true load flow conditions in the presence of harmonics. The algorithm is unique in its three phase approach to the problem, which is essential if normally unfiltered uncharacteristic harmonics are to be represented. Results of a realistic and relevant test system are used to demonstrate the interaction which exists between the fundamental and harmonic frequencies in the power converter. >

Patent
30 Apr 1991
TL;DR: In this article, a digital-to-analog converter utilizing a PWM system for converting input digital data to PWM signals and finally to an analog signal divides the sampling period of the input data into an even number of sampling periods and produces PWM signal with equal pulse widths corresponding to the input digital signals each divided sampling period.
Abstract: A digital-to-analog converter utilizing a PWM system for converting input digital data to PWM signals and finally to an analog signal divides the sampling period of the input digital data into an even number of sampling periods and produces PWM signals with equal pulse widths corresponding to the input digital data each divided sampling period, whereby a simple structure is provided to reduce harmonic distortion and obtain a high quality analog signal.

Patent
18 Sep 1991
TL;DR: In this article, higher harmonic power components and fundamental wave reactive power components are derived from a load voltage and current, using theory (instantaneous p-q theory) regarding instantaneous real power and instantaneous imaginary power.
Abstract: Higher harmonic power components and fundamental wave reactive power components are derived from a load voltage and current, using theory (instantaneous p-q theory) regarding instantaneous real power and instantaneous imaginary power. Gains are then obtained which make the higher harmonic power components and fundamental wave reactive power components not exceed predetermined limit values. The higher harmonic power components and fundamental wave reactive power components are respectively multiplied by the gains to obtain limited higher harmonic power components and fundamental wave reactive power components. An output current command is generated in accordance with the limited higher harmonic power components and fundamental wave reactive power components. The output current command is supplied to an inverter which in turn supplies a compensation current to the power system.

Journal ArticleDOI
TL;DR: A survey of current and voltage distortion levels measured at 76 different sites is presented in this paper, where the authors use data at a particular nonlinear load site to show how US utilities may be failing to collect the correct revenues from power factor penalty clauses.
Abstract: A survey of current and voltage distortion levels measured at 76 different sites is presented. Over 5000 pairs of current and voltage waveforms were recorded and analyzed for this study. In addition to summarizing the harmonic levels at the various industrial, commercial, and substation sites, the authors use data at a particular nonlinear load site to show how US utilities may be failing to collect the correct revenues from power factor penalty clauses. The instrumentation used to collect the field data is briefly described. The results of the field measurements are discussed, with particular emphasis on the problem sites identified during the project. >

Journal ArticleDOI
TL;DR: A method for real-time implementation of any two-level three-phase pulse-width-modulator (PWM) invertor waveform is discussed, and the suggested scheme realizes the PWM waveforms without harmonic distortion.
Abstract: A method for real-time implementation of any two-level three-phase pulse-width-modulator (PWM) invertor waveform is discussed. The hardware and software of the scheme are built around the 16 b 8086 microprocessor and its peripherals, with a few additional digital ICs. The suggested scheme realizes the PWM waveforms without harmonic distortion. The implementation procedure is a universal one and it generates in real time any two-level three-phase PWM waveform with the chosen hardware structure. There is no need for hardware alteration for realization of different types of PWM waveforms. >

Journal ArticleDOI
TL;DR: In this paper, an optical feed-forward compensation circuit for linearisation of analogue modulated semiconductor lasers is described, and a reduction in the second harmonic distortion of greater than 14dB and the third-order intermodulation distortion over the frequency range 100 MHz-1.5 GHz is reported.
Abstract: An optical feedforward compensation circuit for linearisation of analogue modulated semiconductor lasers is described. A reduction in the second harmonic distortion of greater than 14dB and the third-order intermodulation distortion of greater than 10dB over the frequency range 100 MHz- 1.5 GHz is reported.

Journal ArticleDOI
TL;DR: In this paper, a CMOS differential line-driver amplifier that uses positive feedback in the input stage to give transconductance multiplication and pole-zero doublet insertion is reported, which operates from a single 5V power supply and can achieve a total harmonic distortion (THD) of -78 dB for a 6-V/sub pp/ differential output signal at 40 kHz and for a load of 100 Omega and/or 150 pF.
Abstract: A CMOS differential line-driver amplifier that uses positive feedback in the input stage to give transconductance multiplication and pole-zero doublet insertion is reported. The gain-bandwidth product at 60 kHz is 30 MHz and the unity-gain frequency is 2.7 MHz. The circuit operates from a single 5-V power supply and can achieve a total harmonic distortion (THD) of -78 dB for a 6-V/sub pp/ differential output signal at 40 kHz and for a load of 100 Omega and/or 150 pF. For the same measuring condition but with a load of 50 Omega and/or 150 pF, the THD is -73 dB. A power supply rejection of more than 76 dB up to 150 kHz was obtained. The chip occupies an area of 1200 mil/sup 2/ in a 1.5- mu m CMOS technology and dissipates 20 mW. >

Journal ArticleDOI
TL;DR: In this article, a preliminary analysis of the effect of randomly varying harmonic voltages on the temperature rise of squirrel-cage motors is presented, based on a first-order approximation of the motor losses and on the Monte Carlo method.
Abstract: A preliminary analysis of the effect of randomly varying harmonic voltages on the temperature rise of squirrel-cage motors is presented. The stochastic process of random variations of harmonic voltages is defined by means of simple statistics (mean, standard deviation, type of distribution). Computational models based on a first-order approximation of the motor losses and on the Monte Carlo method yield results which prove that equipment with large thermal time-constant is capable of withstanding, for a short period of time, total harmonic distortions larger than 5%. >

Proceedings ArticleDOI
16 Jun 1991
TL;DR: In this paper, the authors developed three schemes for cancelling the signal-dependent clock-feedthrough in switched-current circuits based on replicating the current track-and-hold to produce an output current with less than 0.03% THD.
Abstract: The authors have developed three schemes for cancelling the signal-dependent clock-feedthrough in switched-current circuits. Two of the schemes are based on replicating the current track-and-hold to produce an output current with less than 0.03% THD for a signal to bias current ratio of 0.5 and current mirror sizes of W/L=20 mu m1/2 mu m. In the third scheme, by adapting the clock signal to the signal level, a constant clock-feedthrough is produced. All of the cancellation schemes presented have been integrated in a 2 mu m CMOS process. >

Journal ArticleDOI
TL;DR: In this article, a carrier-based three phase pulsewidth-modulated (PWM) technique for invertor drives using a stepped reference waveform is presented, where each waveform was divided into 30 degrees intervals, with each interval being controlled individually to control the magnitude of the fundamental harmonic.
Abstract: The theoretical derivation of a carrier-based three phase pulse-width-modulated (PWM) technique for invertor drives using a stepped reference waveform is presented. The reference waveform is divided into 30 degrees intervals, with each interval being controlled individually to control the magnitude of the fundamental harmonic. This process contrasts with the commonly used approach of amplitude modulating the entire reference waveform to control the fundamental harmonic. The resultant PWM technique is shown to be similar to a square-wave strategy but with a lower current distortion being obtained at high fundamental magnitudes and high carrier frequencies. The practical realization of the PWM technique is described using performance criteria such as minimum pulse widths, peak carrier frequencies, and the current distortion. >

Proceedings ArticleDOI
11 Jun 1991
TL;DR: Extensive computer simulations have confirmed that a third-order Sigma - Delta A/D converter using a 3-bit quantizer and the new dynamic element matching internal DAC can achieve 104 dB (17+bit) dynamic range and a harmonic distortion below 100 dB with an oversampling ratio of only 64.
Abstract: A novel class of dynamic element matching techniques is applied to multibit Sigma - Delta A/D (analog-to-digital) converters. The approach translates the harmonic distortion components of a non-ideal DAC (digital-to-analog converter) in the feedback loop of the Sigma - Delta A/D converter to high-frequency components, which can then be filtered out by the decimation filter. Extensive computer simulations have confirmed that a third-order Sigma - Delta A/D converter using a 3-bit quantizer and the new dynamic element matching internal DAC can achieve 104 dB (17+bit) dynamic range and a harmonic distortion below 100 dB with an oversampling ratio of only 64. A chip has been designed in 1.2 mu m CMOS technology. >

Journal ArticleDOI
TL;DR: In this paper, a stand alone, three-phase, delta-modulated, current-source PWM rectifier has been built and has been shown to be capable of operating with near sinusoidal current waveforms, unity power factor and good DC current regulation.
Abstract: A stand alone, three-phase, delta-modulated, current-source PWM rectifier has been built and has been shown to be capable of operating with near sinusoidal current waveforms, unity power factor. and good DC current regulation. A mathematical model that has been justified against experimental measurements and results from digital simulations is presented. The current waveform distortion limit and the asymptotic stability limit are established. It is shown that the rectifier can operate safely within these limits in the entire range of its power ratings. >

Journal ArticleDOI
TL;DR: In this article, the basic design of the quasi-optical Josephson oscillator (QJO) is presented, and a series of measurements were made with a network analyzer to find properties of the structure when all elements in it are operating in phase.
Abstract: Work with large two-dimensional arrays of Josephson junctions for submillimeter power generation is discussed. The basic design of the quasioptical Josephson oscillator (QJO) is presented. The reasons for each design decision are discussed. Superconducting devices have not yet been fabricated, but scale models and computer simulations have been done. A novel method for characterizing array RF coupling structures is described, and initial results with this model are presented. Microwave scale models of the radiation structure were built, and a series of measurements was made with a network analyzer. These measurements were summed in a computer to find properties of the structure when all elements in it are operating in phase. The goal of these measurements was to develop structures for oscillators which are tunable over a very broad band. Computer programs simulating a Josephson junction in any frequency-dependent coupling structure have been developed. An iterative harmonic balance technique finds the time-domain current and voltage waveforms across the junction for an arbitrary frequency-dependent RF load impedance. DC bias, and therefore oscillator frequency, can be held fixed in this technique, in contrast to time-domain techniques where the oscillation frequency is found after the waveform is found. With these programs design goals for maximum oscillator power and design limits to achieve tolerable harmonic distortion were found.