There are countless books, references, papers and application notes which try to shed some light on the topics that are involved in design.
In teaching power supply design courses for the last 20 years, I constantly face challenges in presenting material that is up-to-date, accurate, interesting, and most importantly, of immediate practical use in the workplace. Engineers attending the courses are expected to immediately increase their productivity at work, and they do.
One of the ways that practicality is kept to the forefront of training is by not getting weighed down with excessive equations. When presenting courses and showing some of the waveforms or transfer functions of converters, I am constantly asked — do you have the equation for that? Some equations are in the notes I present, but most are in the design software that goes with the courses. Of course I have the design equations, but something has always prevented me from writing them all out.
First, they are in the form of software equations, and it is a lot of work to extract them from their native format. But, secondly, I do not believe it would do a service to the engineering community to just provide the equations. It is a strange fact that for the simple set of the three main converters, the buck, boost, and buck-boost or flyback there is no single publication that summarizes all of the design and analysis equations in a single place.
It has been on my list of things to do for some time now to generate a complete set of equations and publish them as a poster for the basic converters operating in CCM and DCM, and with voltage-mode and current-mode control. Texas Instruments once provided a wall chart which made some progress toward this, but it had omissions, out-of-date models, or did not cover all of the functions needed by a designer. Compared with the conventional current-mode buck converter without the secondary LC filter, the new current-loop gain has one more pair of complex conjugate poles and one more pair of complex conjugate zeros, which locate very close to each other.
Figure 3 shows a plot of the current-loop gain with different values of external ramp. With added external slope compensation, the shape of the gain and phase curves do not change, but the amplitude of the gain will decrease and phase margin will increase. A new control-to-output transfer function is created when the current loop is closed.
The domain pole is mainly determined by load resistor R L , C 1 , and C 2. The lower frequency pair of conjugate poles is determined by L 2 , C 1 , and C 2 , while the higher frequency pair of conjugate poles locate at half of the switching frequency. Figure 4 shows a plot of the control-to-output loop gain with different values of external ramp. The additional resonant poles will give up to o additional phase delay. Besides, Figure 4 clearly shows the transition from current-mode to voltage-mode control as the slope compensation is increased.
This article presents a new hybrid feedback structure, as Figure 5 a shows. The idea of hybrid feedback is to stabilize the control loop by using an additional capacitor feedback from the primary LC filter. The outer voltage feedback from the output through resistor divider is defined as the remote voltage feedback and the inner voltage feedback though capacitor C F will be referred to as the local voltage feedback hereafter. The remote feedback and local feedback carry different information on the frequency domain.
Specifically, the remote feedback senses the low frequency signal to provide good dc regulation of the output, while the local feedback senses the high frequency signal to provide good ac stability for the system. Figure 5 b shows the simplified small signal block diagram for Figure 5 a. The resulting equivalent transfer function see Equation 31 and Equation 32 in Appendix II of a hybrid feedback structure differs significantly from the transfer function of conventional resistor divider feedback.
The new hybrid feedback transfer function has more zeros than poles, and the additional zeros will lead to o phase ahead at the resonant frequency determined by L 2 and C 2.
Therefore, with the hybrid feedback method, the additional phase delay in control-to-output transfer function will be compensated for by the additional zeros in the feedback transfer function, which will facilitate the compensation design based on the complete control-to-feedback transfer function. Apart from those parameters in the power stage, there are two more parameters in the feedback transfer function.
The feedback transfer function has been simplified to a new form see Equation 33 in Appendix II. As long as the condition is satisfied, the control system will be easily stable. The control-to-feedback transfer function G P s can be derived by the product of the control-to-output transfer function G vc s and the feedback transfer function G FB s. The compensation transfer function G C s is designed to have one zero and one pole. The asymptotic Bode plots of the control-to-feedback and compensation transfer function, as well as closed-loop transfer function T V s , are shown in Figure 8.
The following procedures show how to design the compensation transfer function. Determine the cross frequency f c. Ridley presents a summary of the buck-boost converter with voltage-mode control. Free analysis software—the fifth in a series of six—is provided to readers of this column to aid with the analysis of their voltage-mode buck-boost converters. In the early days of power electronics, there were three basic topologies: the buck, the boost, and the buck-boost.
Variations of these three topologies solved most power conversion problems, and continue to do so today.
In the last 4 articles, the buck and boost converter control characteristics have been presented, using voltage-mode or current-mode control. The final two articles of this series present the buck-boost converter or, in its isolated version, the flyback converter. Like the boost converter, the buck-boost can be a challenging converter to stabilize.
0コメント