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Showing papers on "Total harmonic distortion published in 1988"


Journal ArticleDOI
02 Oct 1988
TL;DR: In this paper, a critical evaluation of the programmed PWM schemes on the basis of applications for single-phase and three-phase inverters is used to provide a framework and guidelines for the selection of the appropriate technique for each application area.
Abstract: Programmed pulsewidth modulators (PWMs) eliminating several lower-order harmonics generate high-quality output spectra, which in turn result in minimum current ripple and reduced torque pulsations, thereby satisfying several performance criteria and contributing to overall improved performance. Several programmed PWM switching patterns to eliminate harmonics in the output spectra of single-phase and three-phase inverters are possible. Each of these leads to a specific advantage in single- and three-phase inverters, depending on the application. First, the superiority of programmed PWM techniques over the conventional carrier-modulated PWMs is established. Next, a critical evaluation of the programmed PWM schemes on the basis of applications for single- and three-phase inverters is used to provide a framework and guidelines for the selection of the appropriate technique for each application area. Evaluation criteria include harmonic loss factor and total harmonic distortion factors defined at the input and output of the inverter terminals. Finally, a simple low-cost solution for obtaining the required PWM switching points is proposed. Selected results are verified experimentally. >

570 citations


Journal ArticleDOI
TL;DR: In this article, a technique based on deadbeat control theory is proposed to obtain a nearly sinusoidal PWM (pulsewidth-modulated) inverter output voltage using only a voltage sensor.
Abstract: A technique based on deadbeat control theory is proposed to obtain a nearly sinusoidal PWM (pulsewidth-modulated) inverter output voltage using only a voltage sensor. The closed loop sampled-data feedback scheme inherently results in very fast response to load disturbance and nonlinear load, producing low total harmonic distortion. Parameter estimation of the plant provides a type of self-tuning of the proposed controller. A theoretical analysis, simulation, and experimental results are presented for a single-phase PWM inverter controlled by an Intel 8086 microprocessor. >

287 citations


Journal ArticleDOI
TL;DR: A CMOS op amp (operational amplifier) is reported which has a rail-to-rail voltage range at its input as well as its output and can drive a 9-V/sub pp//1-kHz sine wave across a 300- Omega load with -64 dB of harmonic distortion.
Abstract: A CMOS op amp (operational amplifier) is reported which has a rail-to-rail voltage range at its input as well as its output. An area-efficient output stage has been used. While the entire op amp occupies only 600 mil/sup 2/, when used as a unity-gain buffer and with +or-5-V supplies, the op amp can drive a 9-V/sub pp//1-kHz sine wave across a 300- Omega load with -64 dB of harmonic distortion. >

93 citations


Journal ArticleDOI
TL;DR: In this article, a low-power 16-bit CMOS D/A (digital/analog) converter for portable digital audio is described, which is based on current division.
Abstract: A low-power 16-bit CMOS D/A (digital/analog) converter for portable digital audio is described. The converter is based on current division. To guarantee monotonicity and a good small-signal reproduction, a dynamic segmentation technique is used. A geometric averaging technique is used to minimize the harmonic distortion of the converter at high signal levels. The dynamic range is 95 dB. The circuit operates in a time-multiplex mode at a sample frequency of 44 kHz in a power supply range of 2.5-5 V and has a power consumption of 15 mW. A 2- mu m CMOS technology is used and the active chip area is 5 mm/sup 2/. >

78 citations


Proceedings ArticleDOI
16 May 1988
TL;DR: In this paper, a 16-bit oversampling D/A (digital-to-analog) converter was designed using a fourth-order all-digital noise-shaping loop followed by a 3-bit converter.
Abstract: A 16-bit oversampling D/A (digital-to-analog) converter has been designed using a fourth-order all-digital noise-shaping loop followed by a 3-bit D/A converter. The 3-bit D/A converter, which uses a novel form of dynamic element matching achieves high accuracy and long-term stability without requiring precision matching of components. The harmonic distortion of the untrimmed monolithic CMOS prototype D/A converter is less than -90 dB. This converter achieves performance comparable to that of a 1-bit noise-shaping D/A that operates at nearly four times its clock rate. >

76 citations


Proceedings ArticleDOI
11 Apr 1988
TL;DR: In this paper, an active AC harmonic filter, composed of high-frequency inverters and a series-resonant LC circuit turned to the fundamental frequency, is proposed to solve harmonic distortion problems on distribution systems at lower cost and with higher efficiency.
Abstract: An active AC harmonic filter, composed of high-frequency inverters and a series-resonant LC circuit turned to the fundamental frequency, is proposed to solve harmonic distortion problems on distribution systems at lower cost and with higher efficiency. The design includes a voltage-source inverter for further decrease of the loss, a static-induction thyristor for instantaneous current response, control logic that takes into account the coupling circuit characteristics, and high-speed harmonic voltage detection to suppress overloading of the customer's LC filter. Operational experience with a prototype filter on a 6.6 kV system is presented, verifying reduction of the operating and improvement of the transient response. In particular, there is a sharp reduction of inverter rating and operating loss about one-third to one-fourth, compared to results for an active filter without a coupling circuit. >

62 citations


Journal ArticleDOI
TL;DR: In this paper, a low-distortion class AB output stage with improved stability suitable for monolithic power amplifiers (P/sub 0/>or=40 W) is described.
Abstract: A low-distortion class AB output stage with improved stability suitable for monolithic power amplifiers (P/sub 0/>or=40 W) is described. The concept has been verified on a 12-W breadboard version as well as on a partly integrated prototype, and is supported by computer simulations for P/sub 0/>or=40 W A biasing control law which guarantees predictable conduction of both output transistors at all times is implemented. This reduces crossover distortion and allows the customary quasi-p-n-p compound transistor to be eliminated, thus also improving stability. Linearity is improved by use of local negative feedback. Phase margin is improved by application of high-frequency feedforward. Measured phase margin is around 60 degrees and total harmonic distortion for a load of 7 Omega is about -80 dB at 20 kHz. >

60 citations


Proceedings ArticleDOI
06 Nov 1988
TL;DR: In this article, a simplified 3- mu m emitter, self-aligned base metal HBT process is used to fabricate transistors with f/sub max/ approximately 30-50 GHz, high linearity, and low 1/f noise, yielding significantly improved third-order intermodulation product intercept point (IP3) and oscillator performance.
Abstract: GaAs-AlGaAs heterojunction bipolar transistors (HBTs) have been used to demonstrate the capability of low harmonic distortion with high efficiency and low-phase-noise performance in the 12-40-GHz frequency regime. A simplified 3- mu m emitter, self-aligned base metal HBT process is used to fabricate transistors with f/sub max/ approximately=30-50 GHz, high linearity, and low 1/f noise, yielding significantly improved third-order intermodulation product intercept point (IP3) and oscillator performance. The HBT IP3 ranges from 20-35 dBm for 12-20 GHz with a linearity figure-of-merit ratio, IP3(mW)/input DC power (mW), approximately=4 to 20 times higher than comparable HEMTs (high-electron-mobility transistors) and MESFETs at 12 to 37.7 GHz with -82 dBc/Hz phase noise at 100-kHz offset. It is concluded that these capabilities make HBTs attractive for high-IP3 amplifiers and mixers and low-phase-noise voltage-controlled oscillators in advanced receiver applications. >

51 citations


Journal ArticleDOI
01 Sep 1988
TL;DR: The microprocessor implementation of new optimal PWM switching strategies are presented, and the special features, characteristics and advantages of various microprocessor configurations are demonstrated.
Abstract: The microprocessor implementation of new optimal PWM switching strategies are presented, and the special features, characteristics and advantages of various microprocessor configurations are demonstrated. All the necessary microprocessor hardware/software techniques and algorithms required to implement and generate the new optimal PWM strategy on-line and in real time are developed in detail, and demonstrated using practical results from an experimental microprocessor-controlled PWM inverter induction motor drive system. The techniques developed and presented in the paper are readily applicable to other currently available microprocessors, with minor modifications to reflect the special features of the particular microprocessor used. The presentation is based on the design of a typical PWM operating strategy for a variable speed drive system, which covers the complete voltage/frequency operating range up to, and including, quasisquare wave operation, with minimised total harmonic current distortion (THD). In addition to drive applications, the optimal PWM techniques and microprocessor implementations can be used for uninterruptible power supplies and static frequency changer systems.

51 citations


Journal ArticleDOI
TL;DR: It is shown that stray capacitances in the input circuitry are the major problem although the use of a phase sensitive demodulator can minimise this problem.
Abstract: This paper takes the circuit for a general purpose impedance imaging data measurement system and analyses the importance of several components. For high accuracy it is shown that stray capacitances in the input circuitry are the major problem although the use of a phase sensitive demodulator can minimise this problem. It is shown that harmonic distortion in the constant current generator can cause errors which are, however, reduced if a linear multiplying demodulator is used rather than a switching demodulator.

38 citations


Journal ArticleDOI
TL;DR: In this paper, the authors describe the introduction of power-system harmonics in the power engineering curriculum by investigating the variation of the transformer parameters and the mutual coupling between the windings as a function of frequency by a laboratory experiment.
Abstract: The authors describe the introduction of power-system harmonics in the power engineering curriculum by investigating the variation of the transformer parameters and the mutual coupling between the windings as a function of frequency by a laboratory experiment. This test is based on a hybrid set of measurements on a single-phase and a three-phase transformer. The test procedure and comparison of the results with the available studies are shown. It is concluded that studying actual recorded data, simulating the distorted waveform in a laboratory experiment, and obtaining the results represent a good experience for the students who choose the power area as their careers. This experiment gave the students a better understanding of the impact of harmonics and distortion in power system analysis and modeling. >

Journal ArticleDOI
02 Oct 1988
TL;DR: Investigation showed severe distortion of the plant feeder-voltage waveform due to harmonic currents, which was traced to the thyristor controllers which regulated power to melter electrodes.
Abstract: Operation of a new all-electric glass melting furnace in a manufacturing plant caused severe disturbances to other plant functions. The problem was traced to the thyristor controllers, which regulated power to melter electrodes. Investigation showed severe distortion of the plant feeder voltage waveform due to harmonic currents. Corrective measures consisted of installing a set of series resonant harmonic traps and a high-pass filter on the 4160 V feeder. Harmonic distortion of the supply voltage was reduced from 5% to less than 1%, and the power factor was improved. Normal plant operations were resumed. >

Proceedings ArticleDOI
02 Oct 1988
TL;DR: In this article, a digital control technique is proposed to obtain sinusoidal three-phase PWM (pulsewidth-modulated) inverter output, based on the predicted voltages by an observer at 18 kHz sampling frequency.
Abstract: A digital control technique is proposed to obtain sinusoidal three-phase PWM (pulsewidth-modulated) inverter output. Sensing two line-to-line voltages the required pulse patterns for deadbeat response are computed in real time, based on the predicted voltages by an observer at 18 kHz sampling frequency. This closed-loop voltage control inherently results in a very low total harmonic distortion and a very quick transient response with less filter capacity. The authors describe the modeling technique, theoretical analysis, simulations, and experimental results. >

Journal ArticleDOI
TL;DR: In this article, a variable-speed generation (VSG) system that uses a series-resonant converter to excite the rotor windings of a doubly-fed generator is presented.
Abstract: Results of study and measurements are presented for a variable-speed generation (VSG) system that uses a series-resonant converter to excite the rotor windings of a doubly-fed generator The capabilities of this system include maximum-efficiency operation and limited converter rating for a speed range from stand-still (zero RPM) to well beyond synchronous speed, as well as flexibility for line-voltage control, reactive power generation, and synchronization at zero RPM Measurements of the harmonic distortion are provided showing the superiority of this converter as compared with a VSG system using a conventional cycloconverter or a DC-link converter A convenient tool for analyzing the operating modes of the system is discussed that can be developed under varying resource conditions >

Journal ArticleDOI
M.J.M. Pelgrom1, M. Roorda1
TL;DR: A digital-to-analog converter (DAC) has been designed which uses an algorithm based on interpolation which ensures monotonicity and differential linearity despite offset voltages, and hence eliminates the need for trimming.
Abstract: A digital-to-analog converter (DAC) has been designed which uses an algorithm based on interpolation. The algorithm ensures monotonicity and differential linearity despite offset voltages, and hence eliminates the need for trimming. The technique has been used to design a 15-bit DAC in a 2.5- mu m CMOS technology. The converter features S/(N+THD) of 74 dB with a dynamic range of 87 dB and a power consumption of 22 mW at 44-kHz sample frequency. >

Patent
17 Mar 1988
TL;DR: A portable instrument for locating and measuring harmonic distortion in a conductor is described in this paper, which permits harmonics to be easily read while the load is changing and may provide a great deal of insight as to the source of problem causing harmonics.
Abstract: A portable instrument for locating and measuring harmonic distortion in a conductor. The instrument permits harmonics to be easily read while the load is changing. Thus, the instrument may provide a great deal of insight as to the source of problem causing harmonics.

Proceedings ArticleDOI
11 Apr 1988
TL;DR: In this article, a closed-loop voltage control is proposed to obtain a sinusoidal three-phase PWM output with a very rapid transient response with less filter capacity, which results in a very low total harmonic distortion.
Abstract: A digital control technique is proposed to obtain a sinusoidal three-phase pulsewidth-modulated (PWM) inverter output. By sensing two line-to-line voltages, the required pulse patterns for deadbeat response can be computed in real time using the predicted voltages at 9 kHz sampling frequency. This closed-loop voltage control inherently results in a very low total harmonic distortion and a very rapid transient response with less filter capacity. The modeling technique, theoretical analysis, simulations, and experimental results are described. >

Journal ArticleDOI
TL;DR: In this article, a line-current-modulated high-frequency (HF) link DC to utility interface power conditioning system using a square-wave output resonant inverter is proposed.
Abstract: A line-current-modulated high-frequency (HF) link DC to utility interface power conditioning system using a square-wave output resonant inverter is proposed. The proposed system consists of a square-wave output HF resonant inverter, a rectifier, and a line-connected inverter (LCI). The system is modeled using the constant current model for the HF inverter and the step model for the DC link current. The operating modes, analysis, design, and experiment results are presented. It has been shown that systems operating with less than 5% line current harmonic distortion are realizable when the type II commutation scheme is used for the LCI. A typical application of the system presented is in interfacing photovoltaic arrays to utility lines. >

Proceedings ArticleDOI
07 Jun 1988
TL;DR: A circuit design technique for continuous-time all-MOS integrated filters makes use of novel MOSFET-C building blocks which use MOS transistors as voltage-controlled resistors and achieve complete cancellation of MOS nonlinearities without requiring fully balanced signals.
Abstract: A circuit design technique for continuous-time all-MOS integrated filters makes use of novel MOSFET-C building blocks which use MOS transistors as voltage-controlled resistors and achieve complete cancellation of MOS nonlinearities without requiring fully balanced signals. The resulting filter structures possess low sensitivity to MOSFET mismatches and hence low total harmonic distortion. The technique demonstrates the possibility of developing MOSFET-C integrated filters exclusively in the 'MOS-domain' without having to obtain topologically the MOS filter structure from a known active-RC prototype circuit. >

Journal ArticleDOI
TL;DR: In this paper, the harmonic voltage distortion caused by static convertors can be greatly affected by the presence of local salient-pole synchronous generators or compensators, and an accurate equivalent circuit for the synchronous machine in the multiharmonic space is provided.
Abstract: The harmonic voltage distortion caused by static convertors can be greatly affected by the presence of local salient-pole synchronous generators or compensators. Such machines act as harmonic converters and are sensitive to the sequence of the fundamental and harmonic frequencies. An accurate equivalent circuit for the synchronous machine in the multiharmonic space is provided. The model used is integrated with other AC system components, and an iterative sequential algorithm is presented for deriving harmonic interaction between the synchronous machine and static convertor. >

Journal ArticleDOI
TL;DR: In this paper, it was shown that the simple three-phase wave generator presented by V.P. Ramamurthi and R.B. Ramaswami is able to exhibit a higher performance when more stringent design considerations are adopted.
Abstract: It is shown that the simple three-phase wave generator presented by V.P. Ramamurthi and R.B. Ramaswami (see ibid., vol.IE-29, no.3, p.235-40 (1982)) is able to exhibit a higher performance when more stringent design considerations are adopted. The results show improvements in linearity and distortion as well as an extension in the frequency range with only small changes in circuit implementation. >

Proceedings ArticleDOI
02 Oct 1988
TL;DR: A 3 phi PWM (three-phase pulsewidth-modulation) modulator, producing a reliable inverter bridge switching pattern, is described, and theoretical predictions of the PWM waveform harmonic content are verified with experimental results.
Abstract: A 3 phi PWM (three-phase pulsewidth-modulation) modulator, producing a reliable inverter bridge switching pattern, is described. The digital architecture for the modulator was developed using an EPLD CAD (erasable programmable logic device computer-aided design) system. A low-frequency ratio, synchronous-PWM switching pattern was adopted with fundamental frequency ranges varying from 0.60 Hz up to as high as 1 kHz. A square-wave reference waveform is used whereby the switching of each phase is limited to defined periods of the fundamental cycle. A linear relationship exists between the fundamental voltage and the modulation depth up to square-wave operation. These features allow the inverter bridge to be operated reliably with minimal electrical stresses being exerted on the inverter bridge power devices. The total harmonic distortion and fundamental percentage error are used to assess the modulator performance. The effects of minimum pulse widths on these performance factors are also demonstrated. Theoretical predictions of the PWM waveform harmonic content are verified with experimental results. >

Proceedings ArticleDOI
M.G. Egan1, J.M. Murphy1, E.J. Heffernan1, S.U. Lidholm1, M.L. McGrath1 
07 Jun 1988
TL;DR: In this paper, an application-specific integrated circuit (ASIC) is presented which acts in conjunction with a standard microcontroller (the 8051 family) to produce a compact and effective AC motor control system.
Abstract: An application-specific integrated circuit (ASIC) is presented which acts in conjunction with a standard microcontroller (the 8051 family) to produce a compact and effective AC motor control system. The system is based on synchronous pulsewidth modulation (PWM) and is capable of implementing both natural and regular sampling PWM as well as the optimum harmonic elimination and distortion minimization techniques. Lookup table size is minimized using information stored over one 30 degrees segment of the three-phase switching patterns. Disturbance-free carrier ratio changes are implemented under microprocessor control giving a wide speed range and a smooth efficient transition to six-step operation. The necessary dead-time circuitry to ensure that a delay exists between commutation of the devices in the power converter is also implemented on the ASIC, as well as an output inhibit control for power converter protection. >

Proceedings ArticleDOI
02 Oct 1988
TL;DR: In this paper, a gate-array-based, dedicated, three-phase PWM (pulsewidth-modulated) modulator for electric drive control is presented. But the performance of the modulator is limited.
Abstract: The task of designing a gate-array-based, dedicated, three-phase PWM (pulsewidth-modulated) modulator for electric drive control is addressed. A novel slope-modulated PWM strategy is presented. Sine-wave and square-wave signal references, under several operating modes, are used to demonstrate the modulation properties. Performance parameters, such as reliable inverter switching, minimum on/off times, peak inverter switching frequency, total harmonic distortion, and pulse dropping are described. The modulator is shown to generate high-resolution PWM waveforms, with excellent performance when a variable-frequency ratio strategy is used with a sine-wave reference signal. The square-wave reference signal uses less complex digital circuitry, with a reliable operation of the inverter bridge. >

Proceedings ArticleDOI
Schouwenaars1, Groeneveld, Termeer
01 Jan 1988
TL;DR: Careful system analysis of the distortion produced by this D/A converter has resulted in a geometric averaging technique to improve coarse current accuracy, as is shown in Figure 2.
Abstract: I N PORTABLE DIGITAL AUDIO APPLICATIONS low-power consumption of the D/A converter is of great importance. Moreover, external components and trimming techniques have t o be avoided. The 16b dynamic range and the monotonicity of the D/A converter remain the important spccitications and they should not be affected by the desired low-power solution. One of the basic techniques which is capable of fitting these demands is the segmented D/h converter which divides the digital input word into a coarse part and a fine part’. Figure 1 shows the output current of a converter as a function of input code. A digital input word is assumed which corresponds with an analog value A . The dots indicate the different output current levels of the coarse converter. The unit coarse currents 1 to m-1 of ttre N available currents are switched directly to the output line while unit coarse current m is used as the segment current. This current is then divided into binary weighted currents which are switched to the output line, controlled by the least significant data bits, t o obtain the required output value A. To realize a binary-weightcd current divider, an Rj2R ladder network is often used. An other method, recently reported in a bipolar technology, is wholly based upon transistor matching2. Measurements on test circuits on different wafers and batches have shown that it is possible to construct a 0.5 LSB 1 Ob CMOS binary weighted current divider. This divider forms the basic design consideration o f the partitioning of coarse and fine currents. A 6b coarse current generation network is added t o the 10b fine divider to obtain a 16b dynamic range. This coarse network consists of only individual transistors. The absolute linearity of the converter, which determines the total harmonic distrotion, is determined principally by the accuracy of thc individual unit coarse currents. Careful system analysis of the distortion produced by this converter has resulted in a geometric averaging technique to improve coarse current accuracy. To explain the operation of the geometric averaging technique, an assumption of a linear-graded distribution of the unit coarse currents i s mdde, as is shown in Figure 2. The valur of an unit coarse current 1, can be expressed,

Proceedings ArticleDOI
07 Jun 1988
TL;DR: In this paper, the authors proposed a synthesis of fully integrated canonical continuous-time filters with a high degree of linearity, based on a differential current-integrator with a simple capacitor.
Abstract: The authors propose a synthesis of fully integrated canonical continuous-time filters with a high degree of linearity. The synthesis method is based on a differential current-integrator with a simple capacitor. A method to reduce the number of MOS transistors has also been presented. A third-order leapfrog filter is realized by the proposed method as an example. A total harmonic distortion less than 0.03% is obtained by SPICE analysis. The proposed method is advantageous, especially in the realization of higher-order filters, because of the reduction of higher-order filters, because of the reduction in chip area and manufacturing cost. >

Proceedings ArticleDOI
02 Oct 1988
TL;DR: Well-designed filters and protection reactances, suitably inserted in the plant, can satisfactorily compensate both reactive and distortion power and lead to compliance with standard limits on harmonic distortion even for electrical plants with a low short-circuit ratio.
Abstract: Low-voltage electrical plants supplying static power converters are often affected by current and voltage harmonic distortion. The effectiveness of harmonic filters and protection reactance in compensating the distortion factor and, in general, nonactive power, is shown by theoretical and experimental results. Good agreement of voltage notch and distortion factor estimates, after filter and protection reaction insertion, with experimental data measured on a model of an electrical plant has been found. The strong contribution to voltage notch and distortion factor reduction of filters connected at the converter-side of protection reactance is pointed out. The final result is that well-designed filters and protection reactances, suitably inserted in the plant, can satisfactorily compensate both reactive and distortion power and lead to compliance with standard limits on harmonic distortion even for electrical plants with a low short-circuit ratio. >

01 Feb 1988
TL;DR: In this paper, the authors investigated the electrical properties of a variable-speed, constant-frequency system with wound-rotor induction generator and a cycloconverter and found that the voltage distortion was low and the total harmonic distortion in the utility voltage was less than 3 percent/ (within the 5/percent/ limit required by most utilities).
Abstract: Variable speed electric generating technology can enhance the general use of wind energy in electric utility applications. This enhancement results from two characteristic properties of variable speed wind turbine generators: an improvement in drive train damping characteristics, which results in reduced structural loading on the entire wind turbine system, and an improvement in the overall efficiency by using a more sophisticated electrical generator. Electronic converter systems are the focus of this investigation /emdash/ particularly the properties of a Westinghouse variable-speed, constant-frequency system with wound-rotor induction generator and a cycloconverter. Experience with solid-state converter systems in large wind turbines is extremely limited. This report presents measurements of electrical performances of the Westinghouse system and is limited to the terminal characteristics of the system. Variable speed generating systems working effectively in utility applications will require a satisfactory interface between the turbine/generator pair and the utility network. The electrical testing described herein focuses largely on the interface characteristics of the generating system. A MOD-0 wind turbine was connected to a very strong system; thus, the voltage distortion was low and the total harmonic distortion in the utility voltage was less than 3/percent/ (within the 5/percent/ limit required by most utilities). The largest voltagemore » component of a frequency below 60 Hz was 40 dB down from the 60-Hz component. 7 refs., 30 figs., 14 tabs.« less

Journal ArticleDOI
TL;DR: In this paper, the amplitude transients in the twin-T bridge RC-oscillator with an amplitude control system employing multipliers were considered and a closed form solution was obtained without recurring to the linearization of the transfer function relating the oscillator output to the displacement of the above-mentioned poles on jω axis poles.
Abstract: This paper considers the amplitude transients in the twin-T bridge RC-oscillator with an amplitude control system employing multipliers. The application of such a control system is feasible because this oscillator has two nodes where the sinusoidal steady-state voltages are shifted by 90°. The voltages at these nodes are squared and summed and the resulting DC voltage is compared with the reference voltage. The difference is amplified and is applied to the voltage control resistor ( VCR) which is able to control the displacement of the poles on jω axis. Restricting ourselves to the case of step modulation of the reference voltage we obtain the solution for the amplitude transients in a closed form. This result is obtained without recurring to the linearization of the transfer function relating the oscillator output to the displacement of the above-mentioned jω axis poles. The effect of a loop filter for further reducing total harmonic distortions ( THD) in a practical oscillator is also analyzed....

Journal ArticleDOI
TL;DR: In this article, a novel analytical expression for approximating the error function erf(x) is presented, and analytical closed-form expressions are obtained for the overall record and playback nonlinear distortion resulting from large recording-signal levels.
Abstract: A novel analytical expression for approximating the error function erf(x) is presented. Using this expression, analytical closed-form expressions are obtained for the overall record and playback nonlinear distortion resulting from large recording-signal levels. The results are shown to agree qualitatively with previously published results. >