Buck Power Stage Steady-State Analysis
3
Understanding Buck Power Stages in Switchmode Power Supplies
2 Buck Power Stage Steady-State Analysis
A power stage can operate in continuous or discontinuous inductor current mode.
Continuous inductor current mode is characterized by current flowing
continuously in the inductor during the entire switching cycle in steady state
operation. Discontinuous inductor current mode is characterized by the inductor
current being zero for a portion of the switching cycle. It starts at zero, reaches
a peak value, and returns to zero during each switching cycle. The two different
modes are discussed in greater detail later and design guidelines for the inductor
value to maintain a chosen mode of operation as a function of rated load is given.
It is very desirable for a power stage to stay in only one mode over its expected
operating conditions, because the power stage frequency response changes
significantly between the two modes of operation.
For this analysis, an n-channel power MOSFET is used and a positive voltage,
V
GS(ON)
, is applied from the Gate to the Source terminals of Q1 by the drive circuit
to turn ON the FET. The advantage of using an n-channel FET is its lower
R
DS(on)
but the drive circuit is more complicated because a floating drive is required. For
the same die size, a p-channel FET has a higher
R
DS(on)
but usually does not
require a floating drive circuit.
The transistor Q1 and diode CR1 are drawn inside a dashed-line box with
terminals labeled a, p, and c. The inductor current I
L
is also labeled i
C
and refers
to current flowing out of terminal c. These items are explained fully in the Buck
Power Stage Modeling section.
2.1 Buck Steady-State Continuous Conduction Mode Analysis
The following is a description of steady-state operation in continuous conduction
mode. The main result of this section is a derivation of the voltage conversion
relationship for the continuous conduction mode buck power stage. This result
is important because it shows how the output voltage depends on duty cycle and
input voltage or, conversely, how the duty cycle can be calculated based on input
voltage and output voltage. Steady-state implies that the input voltage, output
voltage, output load current, and duty-cycle are fixed and not varying. Capital
letters are generally given to variable names to indicate a steady-state quantity.
In continuous conduction mode, the Buck power stage assumes two states per
switching cycle. The ON state is when Q1 is ON and CR1 is OFF. The OFF state
is when Q1 is OFF and CR1 is ON. A simple linear circuit can represent each of
the two states where the switches in the circuit are replaced by their equivalent
circuits during each state. The circuit diagram for each of the two states is shown
in Figure 2.