The Buck Converter has the following parameters ip Vin DA C= R Switching frequency: f, =...

  

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The Buck Converter has the following parameters ip Vin DA C= R Switching frequency: f, = 50 kHz; Carrie peak voltage: V 5V %3D Input Voltage: V = 20 V in Output Voltage: V = 10 V Output Current: I =5 A Inductor Parameters: L = 100 µH, R, = 0.52 (they are serial connected) Capacitor Parameters: C=10 mF; R = 0.022 (they are serial connected) 1. Derive the value of R. 2. Derive the state space model for the switching circuit. You need to derive the model for "on" and the model for "off" first, then combine them into a nonlinear model. 3. Solve for the steady-state values of the state variables. 4. Linearize the system around the operating point. 5. Derive the transfer functions (a) from the duty cycle d(t) to v, and (b) from Vin to va 6. Simulate the circuit system in Simulink. Run the step responses (a) from the duty cycle d(t) to v, and (b) from v, to v. The Buck Converter has the following parameters ip Vin DA C= R Switching frequency: f, = 50 kHz; Carrie peak voltage: V 5V %3D Input Voltage: V = 20 V in Output Voltage: V = 10 V Output Current: I =5 A Inductor Parameters: L = 100 µH, R, = 0.52 (they are serial connected) Capacitor Parameters: C=10 mF; R = 0.022 (they are serial connected) 1. Derive the value of R. 2. Derive the state space model for the switching circuit. You need to derive the model for "on" and the model for "off" first, then combine them into a nonlinear model. 3. Solve for the steady-state values of the state variables. 4. Linearize the system around the operating point. 5. Derive the transfer functions (a) from the duty cycle d(t) to v, and (b) from Vin to va 6. Simulate the circuit system in Simulink. Run the step responses (a) from the duty cycle d(t) to v, and (b) from v, to v.