I'm trying to model the buck converter. So here is a model schematic
to simplify the model, i divided it into 'on' phase and 'off' phase as follows:
on phase
derived equation: Vin here is the VCC symbol, to denote the driving input. Vo the output voltage is the voltage across C and R (load)
\[ V_{in} = L C \frac{d^2 V_o}{dt^2} + \frac{L}{R} \frac{d V_o}{dt} + V_o \\ where V_o = V_r = V_c \]
"off" phase
\[ L C \frac{d^2 V_o}{dt^2} + \frac{L}{R} \frac{d V_o}{dt}  V_o = 0 \]
so I took the equations, write a little program and simulated it
erm ok, it doesn't seemed to be a buck converter at all. The expected output is a DC output across R.
How the simulation is done is by using numerical integration Runge–Kutta methods. Those equations above are 2nd order ODE, the 'tools' used are those of apache commons math
I've attached the derivations of the ODE in the post attachments here
The problem is, are the derivations or equations incorrect?
to simplify the model, i divided it into 'on' phase and 'off' phase as follows:
on phase
derived equation: Vin here is the VCC symbol, to denote the driving input. Vo the output voltage is the voltage across C and R (load)
\[ V_{in} = L C \frac{d^2 V_o}{dt^2} + \frac{L}{R} \frac{d V_o}{dt} + V_o \\ where V_o = V_r = V_c \]
"off" phase
\[ L C \frac{d^2 V_o}{dt^2} + \frac{L}{R} \frac{d V_o}{dt}  V_o = 0 \]
so I took the equations, write a little program and simulated it
erm ok, it doesn't seemed to be a buck converter at all. The expected output is a DC output across R.
How the simulation is done is by using numerical integration Runge–Kutta methods. Those equations above are 2nd order ODE, the 'tools' used are those of apache commons math
I've attached the derivations of the ODE in the post attachments here
The problem is, are the derivations or equations incorrect?
Attachments

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