Nonlinear modeling and analysis of buck converter using volterra series
01 Dec 2017-pp 222-226
TL;DR: Harmonic distortion associated with a 12 V to 1.2 V open-loop buck converter (designed in the BCD 180 nm technology of STMicroelectronics) has been analyzed and the nonlinear behavior of a buck converter has been modeled using Volterra series for expected power supply ripples of 50 Hz.
Abstract: The presence of harmonic components in a power delivery network affects the performance of the high-speed systems. In this paper, harmonic distortion associated with a 12 V to 1.2 V open-loop buck converter (designed in the BCD 180 nm technology of STMicroelectronics) has been analyzed. The nonlinear behavior of a buck converter has been modeled using Volterra series for expected power supply ripples of 50 Hz. The analysis has been compared with simulation results and shows 5 %, 1 % and 7 % of mean relative error. The difference between the analytical and the simulation results for IP 2h and IP3 h are 2.7 dB and 3 dB, respectively.
Citations
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TL;DR: The primary focus of this paper is to discuss the modeling of jitter caused by power supply noise (PSN), named power supply induced jitter (PSIJ).
Abstract: The primary focus of this paper is to discuss the modeling of jitter caused by power supply noise (PSN), named power supply induced jitter (PSIJ). A holistic discussion is presented from the basics of power delivery networks to PSN and eventually to the modeling of PSIJ. The in-depth details and a review of several methodologies available in the literature for the estimation of PSIJ are presented.
45 citations
TL;DR: This work presents a robust hierarchical evolutionary technique which employs a heuristic initialization and provides robustness against noise in the Volterra series and improves on the computational complexity of existing methods without harming the identification accuracy.
17 citations
01 Dec 2018
TL;DR: A close matching is seen between the results obtained by proposed and conventional methods with a significant speedup reported.
Abstract: A nonlinear analysis of a DC-DC buck converter is presented in context of its harmonics in a power delivery network (PDN). The closed-form relationships of the harmonic distortions associated with the DC-DC buck converter are derived by Volterra series to estimate the effects in a practical environment using S-parameters. For the validation of the proposed method, the buck converter is designed in a 180 nm LDMOS technology and three test cases are considered by using three different practical PDNs. A close matching is seen between the results obtained by proposed and conventional methods with a significant speedup reported.
1 citations
Cites methods from "Nonlinear modeling and analysis of ..."
...Volterra series based methods are particularly very useful to define the input-output relationship for a weakly nonlinear system [8], [9]....
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...1 shows a commonly used PDN which consists of an open-loop DC-DC buck converter with a board and a package (modeled as S-parameters) [9]....
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...In [9], the closed-form expressions of harmonic distortion quantities for a DC-DC buck converter has been discussed using Volterra series....
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01 Dec 2018
TL;DR: Results show that, Volterra filter can be utilized as an efficient tool for appliance modelling in a supply voltage fluctuating environment and can be extended to achieve the non intrusive load monitoring task.
Abstract: Availability of large quantities of residential electrical consumption data is bringing considerable attention towards load monitoring, load forecasting, load disaggregation and demand response. Load modelling is the first and most essential step in achieving all the above said tasks. Even though many appliance modelling schemes are presented in the literature, no considerably influential work has been done on modelling appliances under voltage fluctuating environment. Motivated by this fact, we present the design and analysis of a Volterra based appliance modelling scheme which can be used in a voltage fluctuating environment. Principles of Volterra filter, least mean square algorithm for Volterra filter coefficient approximation and applicability of Volterra filter for appliance modelling are discussed. Further, a case study is presented to validate and identify the performance of the model using a data set obtained from a real household. Obtained results show that, Volterra filter can be utilized as an efficient tool for appliance modelling in a supply voltage fluctuating environment. Finally, how Volterra filter modelling can be extended to achieve the non intrusive load monitoring task is discussed.
1 citations
Cites background or methods from "Nonlinear modeling and analysis of ..."
...buck converters [10] and for for acoustic echo cancellation [11], [12]....
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...Performance of a system modelled using Volterra filter is quantified using statistical parameters such as root mean square error (RMSE) and the mean absolute percentage error (MAPE) [8], [10]....
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TL;DR: In this paper , a relationship between duty cycle and power supply noise (PSN) for a feedback control circuit of a dc-dc buck converter is presented, based on the derived relation, the closed-form expressions of the harmonics quantities for the DC buck converter and power delivery network (PDN) are developed.
Abstract: This article presents a novel relationship between the duty cycle and power supply noise (PSN) for a feedback control circuit of a dc–dc buck converter. The derived relation is equally valid for the other high-speed circuits. Based on the derived relation, the closed-form expressions of the harmonics quantities for the dc–dc buck converter (including feedback circuitry) and power delivery network (PDN) are developed. The derived expressions of the distortions include the effect of small variations at the power supply and input dc terminals. A combination of two techniques, the Volterra series and the estimation-by-inspection methods, are used to derive the nonlinear quantities. The estimation-by-inspection method is used to model the feedback circuit, including the effects of PSN. The Volterra series derive the nonlinear quantities of the converter. The analytical results are compared with the simulation results for both the examples (designed in 180-nm LDMOS technology) in terms of mean percentage error (MPE) and computational (CPU) time.
References
More filters
TL;DR: Based on the derived expressions, the effects of important parameters on the THD, PSRR, and PS-IMD of the bang-bang control class D amplifier are investigated, providing good insight to the design of thebang-bang amp to meet given design specifications.
Abstract: The total harmonic distortion (THD) and the power supply noise, qualified by the power supply rejection ratio (PSRR) and by the power supply induced intermodulation distortion (PS-IMD), are recognized to be potential drawbacks of class D amplifiers. In this paper, analytical expressions for the THD, PSRR, and PS-IMD of the bang-bang control class D amplifier (bang-bang amp) are derived; the bang-bang amp is arguably the most power-efficient class D amp for low-voltage power-critical applications including hearing aids. Based on the derived expressions, the effects of important parameters on the THD, PSRR, and PS-IMD are investigated, providing good insight to the design of the bang-bang amp to meet given design specifications. The analytical analyses are verified by comparing them against HSPICE simulations and hardware measurements. The bang-bang amp is also compared against the prevalent pulsewidth modulation class D amp, and in most cases, the former is shown to possess superior parameters, including lower power dissipation and hardware advantages for low-voltage power-critical applications.
46 citations
"Nonlinear modeling and analysis of ..." refers background in this paper
...These entities can be determined from harmonic analysis [7]–[9]....
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Dissertation•
01 Jan 2008
37 citations
"Nonlinear modeling and analysis of ..." refers background in this paper
...The entities such as power supply rejection ratio (PSRR), ground supply rejection ratio (GSRR), total harmonic distortion (THD) and signal-to-noise ratio (SNR) decide the figure of merit (FOM) of a PDN....
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...I. INTRODUCTION In high-speed systems of sub-micron technologies, the analysis of power delivery network (PDN) is indispensable to ensure the quality of power supply within the system [1]....
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...1 shows a simplified equivalent model of a typical PDN [2]....
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...A typical PDN consists of a power supply (AC-DC rectification stage output), the DC-DC buck converter (also called as voltage regulator modules or VRMs), decoupling capacitors and wire interconnects [2]....
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TL;DR: In this paper, the results of a harmonic distortion analysis for a differential pair are presented, including the effects of mismatches and of the finite nonlinear common-mode rejection ratio (CMRR) or power-supply rejection ratio(PSRR).
Abstract: The results of a harmonic distortion analysis for a differential pair are presented, including the effects of mismatches and of the finite nonlinear common-mode rejection ratio (CMRR) or power-supply rejection ratio (PSRR). Due to mismatches, a differential pair produces second-harmonic distortion. The presence of a finite common-mode gain limits the amount of feedback which can be usefully applied to suppress the harmonic distortion. When the common-mode gain is nonlinear, additional distortion is generated which is not suppressed by the feedback. When the amplifier has to drive a large load and when the supply line impedance is large, the finite PSRR causes similar effects. >
28 citations
TL;DR: A new modeling approach for the spectral analysis of pulsewidth modulated (PWM) converters with independent inputs is developed, to extend the Volterra functional series to nonlinear systems with multiple independent inputs.
Abstract: A new modeling approach for the spectral analysis of pulsewidth modulated (PWM) converters with independent inputs is developed. The key of this approach is to extend the Volterra functional series to nonlinear systems with multiple independent inputs. After formulating the state-space equations describing the dynamical behavior of PWM converters, the Volterra transfer function characterizing the output frequency response can be obtained, which is then symmetrised to form the spectral model. Since the model is developed in a closed form, it is suitable for computer analysis. The modeling approach has been applied to various PWM converters, and the results are verified. The spectral models of different power converters can readily be obtained by using this general approach. >
25 citations
"Nonlinear modeling and analysis of ..." refers methods in this paper
...[15], [16] are based on spectral method and need state-space function to model the buck converter....
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TL;DR: In this paper, the effect of source voltage fluctuations on the harmonics and the power factor of a six-pulse line-commutated converter is analyzed for a wide class of switching networks.
Abstract: The effect of source voltage fluctuations on the harmonics and the power factor is analyzed for a six-pulse line-commutated converter. Exact expressions are derived for currents in the filter network and the ac supply lines as a function of the size of a series inductor in the LC type low-pass filter connected to a resistive load. The harmonics are calculated according to a method which is unorthodox in power engineering and which is based on the convolution theorem. Switching functions required for the discontinuous conduction mode are derived from time-domain analysis. The method is applicable to a wide class of switching networks.
22 citations