Basic Power-Converter Configurations

The inductive switch cell used in switching power converters is the basis for three converter types. These types are configurations of the basic inductive switch cell, just as transistors have three configurations, with one terminal in common with input and output circuits. This article presents the three basic converter configurations.

A two-port network, such as an amplifier or power converter, has an input and an output port. Each port has a pair of terminals, as shown below.

The relationship between output and input ports is usually expressed as a transfer function or transmittance. A device with three terminals, such as a transistor, has one input, one output, and one common terminal. The common terminal is shared by input and output ports, usually as the common ground terminal. This results in three configurations where each terminal assumes the common position.

The inductive switch is a simple circuit network that can be regarded as a circuit element or cell. The switch cell is shown below:

The inductor is in series with the single-pole, double-throw current switch. It is in the active position (connected to the A terminal) for D× T_s of the time, where T_s is the switching period and D is the duty ratio. The switch is in the passive position for D'× T_s = (1 – D)× T_s.

This switch cell can be regarded as a three-terminal active device, like the transistor. Consequently, it too has three configurations: They are, by name:

common passive (CP) or buck

common active (CA) or boost

common inductor (CI) or buck-boost

Variations of these configurations are flyback (common-inductor-coupled CI) and forward (transformer-coupled CP) converters.

The common-passive (CP) or buck configuration is shown below:

The diode is the passive switch, which connects to both output and input circuit loops, and is the common connection. During D× T_s (the on-time), the MOSFET is on, reverse-biasing the diode and applying V_g to the input side of the inductor. For V_g > V_o, V_g  – V_o is applied across the inductor, L, and its current ramps up. When the MOSFET turns off, the diode conducts this current, clamping the input side of L to 0 V. then L has –V_o across it, and its current ramps down. Under stable operation, the change in current during the off-time is the same in magnitude as during the on-time. Then the net inductor current over T_s is zero, and the inductor current is the same at beginning and end of the switching cycle. During the on-time, current flows from input to output. During the off-time, current flows only in the output circuit.

The static transfer function (with D constant) can be derived as follows. The change in flux linkage, l , of the inductor must be zero over the switching period, T_s. Otherwise, current would increase without bound, for l  = v× t = L× i. Consequently, the change in flux during the on-time must equal that during the off-time, or:

(V_g – V_o)× t_on = V_o× t_off

Then substituting for t_on and t_off,

(V_g – V_o)× D× T_s = V_o× (1 – D)× T_s

or

This equation assumes that V_g and V_o also remain constant with D, as is typical of a dc-dc power supply. For the ideal, lossless converter, the output power, V_o× I_o equals input power, V_g× I_g. Substituting the above voltage transfer function,

The common-active (CA) or boost configuration is shown below:

In this configuration, the active switch - the MOSFET - is the common element. During the on-time, inductor current only flows in the input circuit, through the MOSFET. During off-time, current flows from input to output.

Again applying the flux-balance condition over a switching cycle, and assuming V_g < V_o,

V_g× D× T_s = (V_g – V_o)× (1 – D)× T_s

or

which also equals, due to conservation of power, I_g/I_o.

The third and final two-port configuration of the inductive switch is the common-inductor (CI) or buck-boost configuration, shown below.

During on-time, only the input circuit conducts current; during off-time, only the output circuit conducts inductor current. In this configuration, the output voltage is inverted. The flux-balance equation is:

V_g× D× T_s = V_o× (1 – D)× T_s

and

Again, power conservation requires that this transfer function also equal I_g/I_o.

The three configurations share some common characteristics. First, note that the transfer function for the three has the general form of a rational function, as shown in the table below, where D' = 1 – D.

During the on-time, inductor current always flows from the input, and during the off-time, flows to the output. But when off-time inductor current flows only in the output circuit, D appears in the numerator. When on-time current flows only in the input, D' appears in the denominator. A converter for which inductor current would flow in both input and output for both on and off times has a transfer function of 1/1, or unity.

Second, keep in mind that the transfer functions are derived from inductor flux balance. In this case, voltages and currents are constant, and they apply only under steady-state operation. During power-on or power-off and for power-factor controllers with sine-magnitude inputs, currents are typically changing, and flux is not balanced, though for each cycle, the change in current may be small. But to the extent that the converter is operating in a transient mode, the steady-state equations are not exact. For large di/dt, they may not even be approximately correct.

Finally, these transfer functions also assume constant D, which is only true under steady-state operation. In actual converters, D is varied to keep the controlled quantity (usually V_o) constant. When D changes, the transfer function changes. Regard D as a parameter of the inductive switch cell just as a is a parameter of a bipolar junction transistor.

Ó Dennis L. Feucht, 2001