1. “ State space averaging approximates the switching converter as a continuous linear system “

2. It requires that the effective output filter corner frequency to be much smaller than the switching frequency

3. Procedures for state-space averaging

   a) Step 1: Identify switched models over a switching cycle. Draw the linear switched circuit model for each state of the switching converter (e.g., currents through inductors and voltages across capacitors).

   b) Step 2: Identify state variables of the switching converter. Write state equations for each switched circuit model using Kirchoff's voltage and current laws.

   c) Step 3: Perform state-space averaging using the duty cycle as a weighting factor and combine state equations into a single averaged state equation. The state-space averaged equation is

$$\dot{x}=[\bar{A_1d}+\bar{A_2}(1-d)]\bar{x}+[\bar{B_1}d+\bar{B_2}(1-d)]\bar{u}$$

d) Step 4: Perturb the averaged state equation to yield steady-state (DC) and dynamic (AC) terms and eliminate the product of any AC terms.

e) Step 5: Draw the linearized equivalent circuit model.

f) Step 6: Perform hybrid modeling using a DC transformer, if desired.