Small-signal transmittances of DC-DC step-down PWM converter in various operation modes

Abstract

Small-signal transmittances: input-to-output and control-to-output of BUCK converter power stage working in CCM or DCM mode are discussed. Ideal converter case and converter with parasitic resistances are considered separately. Derivations of small-signal transmittances, based on different approaches to finding the converter averaged models, are presented and the results are compared. Apart from theoretical considerations, some results of numerical calculations are presented. θ -small-signal representation of duty ratio in s-domain, CCM -continuous conduction mode, DCM -discontinuous conduction mode.

Characteristic frequencies in averaged description of step-down (BUCK) DC-DC power converter

“…(5), without a term with zero pulsation. There is only one characteristic pulsation in the above transmittances of an ideal converter in DCM and, in accordance with [16] it is described by equation:…”

“…Equations describing the dependence of small-signal transmittances of a non-ideal BUCK converter on s-variable for a CCM mode corresponds to general formula (4) but parameters Q, ω 0 , ω Z are different than for an ideal converter. Using the expression for transmittance H d for the non-ideal converter given in [16] one obtains:…”

“…As a consequence, the denominator of converter small-signal transmittances is not practically influenced by parasitic resistances. Parasitic resistance of capacitor R C (known as equivalent series resistance) introduces additional zero to expressions for H d transmittance in DCM as well as in CCM [16], therefore this transmittance for a non-ideal converter in DCM may be approximated by expression:…”

“…In some sources discussing dynamic characteristics of switch-mode converters, the influence of parasitic effects is neglected [1], or considered only to a limited extent [11][12][13][14][15], for example -by including only parasitic resistances of capacitors and inductors. In papers [4,5] and [16], the parasitic effects are represented by resistances in series with an ideal transistor, diode, capacitor and inductor. The same description is accepted in the present paper with notation R T , R D , R C and R L respectively (see Fig.…”

“…Several transmittances may be used in the small-signal, s-domain description of the converter power stage including control-to-output and input-to-output transmittances, output impedance and input admittance [1][2][3][4][5]16]. Control-to-output and input-to-output transmittances H d and H g are defined as:…”