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Analytical techniques are beyond the scope of this version of this version. However, some discussion is warranted as an introduction to the graphical techniques.
Modeling. The most common analytical approach to the problem of input filter interaction with switching-mode supplies is based on the state-space-averaged canonical model. From this analysis, the loop gain T(s), input-to-output transfer function F(s), and the output impedance Zo(s) can be calculated for the regulator without an input filter. By use of the extra-element theorem the effect of the input filter can then be determined in terms of the original analysis.
Stability. For duty-ratio (voltage) programmed control, which normally do not contain right-half-plane poles, adequate gain and phase margins in the open-loop voltage control loop Bode plots can be used to determine stability. Degradation of the closed loop output impedance also serves as an indicator of the onset of instability. For current-programmed converters, the onset of instability may not show in either the voltage-loop Bode plots or the output impedance. The best monitoring point for observing the onset of instability in current-mode converters is the regulator input voltage or current (the node/branch between the input filter and the regulator.) Since the cause of instability in current-mode converters is often the appearance of right-half-plane poles, the full Nyquist criteria is usually used to analyze stability. This criteria must be applied to the full loop, not just the voltage or current loops. A good description of the loops that have to be considered is in the Jang and Erickson paper.
Once Again. It is important to re-emphasize the fact that in current-programmed converters, the often measured external voltage-loop gain and closed loop output impedance used to indicate stability may show no indication of the onset of instability caused by adding input filters to these converters.
Do not use this information for design without independent verification of the information.
