Final answer:
Without additional specific parameters, it is not possible to provide values for L and C using the provided equations. A typical approach would involve solving for the duty cycle first, followed by the switching times, and subsequently using these to find L and C.
Step-by-step explanation:
To find the values of L (inductor) and C (capacitor) for a given frequency, gain, and output voltage in a power electronics circuit, one generally uses a set of equations that describe the behavior of the circuit components during each phase of the switching cycle. These equations are typically derived from the fundamental principles of circuit analysis, including Ohm's law, Kirchhoff's voltage and current laws, and the relationships between voltage, current, and impedance in reactive components (inductors and capacitors).
The equations provided mix elements of power electronics, such as duty cycle (D), switching frequency (f), and inductor current ripple (ΔIL), with properties of the inductor (L) and capacitor (C). However, due to the insufficient data and the complex nature of the equations, it is not possible to provide values for L and C without additional information. Specific parameters such as the switch-on voltage (VSPF), bus voltage (Vbus), and the maximum change in inductor current (ΔIL) are required to apply these formulas to determine L and C accurately.
As a general approach, one would first solve for the duty cycle (D) using the gain and output voltage relationship, Equation 4. With D known, the switching times (ton and toff) can be found using Equation 3. Finally, with all these parameters established, one can solve for L and C using the remaining equations that relate the ripple of the inductor current (ΔIL) and the change in voltage across the capacitor (ΔVc) to the properties of L and C.