This paper follows on from the first paper, Part I, where a general formulation of a describing function approach to frequency response determination of switched linear networks, such as PWM converters, was simplified...This paper follows on from the first paper, Part I, where a general formulation of a describing function approach to frequency response determination of switched linear networks, such as PWM converters, was simplified and updated. The models assume a piecewise linear state space equation description of the system and results in a closed form solution for the sought after frequency response. In Part I, model derivation was demonstrated for the case of PWM converters operating in the continuous conduction mode (CCM). This operating mode does not feature any state dependent switching times. In this paper, Part II, frequency response models for any transfer function for PWM converters operating in discontinuous conduction mode (DCM) are derived based on the theory presented in Part I. This operating model features state dependent switching times. The describing function models developed are exact and therefore, in terms of accuracy, are to be preferred over averaged models which are widely used. The example of a boost dc-to-dc converter operating in DCM is simulated to obtain the control to output and input to output frequency responses and are compared with the models derived here. Excellent agreement between the simulated and model responses was found. Matlab code implementing the analytical models is also presented which the user can adapt for any other PWM converter topology. The models derived here may be used as a basis from which simplified models may be derived while still preserving required accuracy.展开更多
A general approach is presented by which the exact frequency response of any transfer function of switched linear networks can be determined. This is achieved with a describing function approach using a state space eq...A general approach is presented by which the exact frequency response of any transfer function of switched linear networks can be determined. This is achieved with a describing function approach using a state space equation formulation. This work presents a somewhat simplified set of equations to <span style="font-family:Verdana;">one previously given by one of the authors. To demonstrate application of the general formulation, the frequency responses of switched networks used as</span><span style="font-family:Verdana;"> PWM DC-to-DC converters operating in continuous conduction mode (CCM) under voltage mode control are derived. (The accompanying paper, Part II, will present results for converters operating in discontinuous conduction mode (DCM)). From the general sets of equations developed here, both the control to output and input source variation to output frequency responses are derived. The describing function approach enables exact frequency response determination, even at high frequencies where the accuracy using average models may be compromised. Confirmation of the accuracy of the derived models is provided by comparing the responses with those obtained using the commercial simulator PSIM on a PWM boost converter. The magnitude and phase responses are shown to match perfectly over the full range of frequencies up to close to half the switching frequency. Matlab code that implements the models is given such that the user can easily adapt for use with other PWM converter topologies.</span>展开更多
<span style="font-family:Verdana;">The second order dc-to-dc buck converter with input LC filter is widely used in industry. An alternative 4th order converter which has advantages in terms of control ...<span style="font-family:Verdana;">The second order dc-to-dc buck converter with input LC filter is widely used in industry. An alternative 4th order converter which has advantages in terms of control design leading to better transient performance is presented. A complete DC (steady state average and ripple quantities) and AC small-signal analyses of this converter for both uncoupled and coupled inductor cases is provided. Conditions for achieving, in a lossless manner, a minimum phase control-to-output transfer function are found, which ameliorates regulator design while maximizing loop bandwidth. A closed loop regulator design procedure is presented and the performance of a design example is examined with a prototype. It is believed that this converter is a good alternative in applications where the second order buck converter augmented with an input filter has been traditionally utilized.</span>展开更多
文摘This paper follows on from the first paper, Part I, where a general formulation of a describing function approach to frequency response determination of switched linear networks, such as PWM converters, was simplified and updated. The models assume a piecewise linear state space equation description of the system and results in a closed form solution for the sought after frequency response. In Part I, model derivation was demonstrated for the case of PWM converters operating in the continuous conduction mode (CCM). This operating mode does not feature any state dependent switching times. In this paper, Part II, frequency response models for any transfer function for PWM converters operating in discontinuous conduction mode (DCM) are derived based on the theory presented in Part I. This operating model features state dependent switching times. The describing function models developed are exact and therefore, in terms of accuracy, are to be preferred over averaged models which are widely used. The example of a boost dc-to-dc converter operating in DCM is simulated to obtain the control to output and input to output frequency responses and are compared with the models derived here. Excellent agreement between the simulated and model responses was found. Matlab code implementing the analytical models is also presented which the user can adapt for any other PWM converter topology. The models derived here may be used as a basis from which simplified models may be derived while still preserving required accuracy.
文摘A general approach is presented by which the exact frequency response of any transfer function of switched linear networks can be determined. This is achieved with a describing function approach using a state space equation formulation. This work presents a somewhat simplified set of equations to <span style="font-family:Verdana;">one previously given by one of the authors. To demonstrate application of the general formulation, the frequency responses of switched networks used as</span><span style="font-family:Verdana;"> PWM DC-to-DC converters operating in continuous conduction mode (CCM) under voltage mode control are derived. (The accompanying paper, Part II, will present results for converters operating in discontinuous conduction mode (DCM)). From the general sets of equations developed here, both the control to output and input source variation to output frequency responses are derived. The describing function approach enables exact frequency response determination, even at high frequencies where the accuracy using average models may be compromised. Confirmation of the accuracy of the derived models is provided by comparing the responses with those obtained using the commercial simulator PSIM on a PWM boost converter. The magnitude and phase responses are shown to match perfectly over the full range of frequencies up to close to half the switching frequency. Matlab code that implements the models is given such that the user can easily adapt for use with other PWM converter topologies.</span>
文摘<span style="font-family:Verdana;">The second order dc-to-dc buck converter with input LC filter is widely used in industry. An alternative 4th order converter which has advantages in terms of control design leading to better transient performance is presented. A complete DC (steady state average and ripple quantities) and AC small-signal analyses of this converter for both uncoupled and coupled inductor cases is provided. Conditions for achieving, in a lossless manner, a minimum phase control-to-output transfer function are found, which ameliorates regulator design while maximizing loop bandwidth. A closed loop regulator design procedure is presented and the performance of a design example is examined with a prototype. It is believed that this converter is a good alternative in applications where the second order buck converter augmented with an input filter has been traditionally utilized.</span>
