4.6 Calculating Total Inductance Needed

The DAB topology naturally behaves like a gyrator.

One presumption is that the maximum power operating point is at a primary to secondary phase at 90° ( ControlPhase = 180°).

Another simplifying presumption is the lossless plant where P_{MAX IN} = P_{MAX OUT}.

The end result will be an input voltage controlled current source (I_OUT proportional to V_IN).

Equation 4-2 is achieved using geometric methods. It presumes the approximation of a lossless plant, P_IN = P_OUT (90° primary to secondary, maximum power). Voltage waveforms are rectangles and the trapezoidal current waveforms are decomposed into rectangles and triangles. V_IN/V_OUT follows the exact ratio of transformer turns (unity gain).

Maximum output current depends on input voltage at a given PWM frequency by the ratio given as gyrator resistance.

For a given PWM frequency, the maximum output current is inversely proportional to total inductance L (Transformer Leakage + Shim inductance).

Gyrator resistance is the V_IN/I_OUT ratio.

Gyrator resistance for a given frequency is proportional to total inductance L.

N is transformer ratio (for this application N = 1.4).

Based on a specification of maximum output current and nominal input voltage at which this must be delivered, it is possible to calculate gyrator resistance and round down to accommodate for real-world losses (3%).

Next, calculate inductance needed at a given PWM frequency. The lowest allowable frequency should be considered at maximum power to avoid saturation of the inductor core.