CataM
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Hello everybody,
In DC-DC converters (SMPS) for example, in order to focus on the steady state, we assume the inductor for example has an initial current through it if the converter is working in CCM. In order to find equations and that initial value, we then say that as it is in steady state, current(t=0) = current (t=Period) i.e. Δcurrent in a period = 0 .
Another example is a 1st order low pass filter.
Let us consider a simple 1st order RC low pass filter with the input a square wave and the output across the capacitor with NO load.
Focusing on the steady state, we would say Vcapacitor(0)=Vinitial and solve its differential equations for each period of time.
When Vin is positive:
-its differential equation
-Vcapacitor(0)=Vinitial
When Vin is negative:
-its differential equation
-Vcapacitor(t=T)=Vinitial
By making Vcapacitor(t=T)=Vinitial=Vcapacitor(0) we are able to find Vinitial which is the voltage in the steady state.
The steady state is the following one:
My question is: For more complex circuits which make the differential equations more difficult to solve, what would be the approach ?
Example is this circuit: The Switches changes position as the voltage of the capacitor "C" crosses 0.
Any hint or comment is welcomed !
In DC-DC converters (SMPS) for example, in order to focus on the steady state, we assume the inductor for example has an initial current through it if the converter is working in CCM. In order to find equations and that initial value, we then say that as it is in steady state, current(t=0) = current (t=Period) i.e. Δcurrent in a period = 0 .
Another example is a 1st order low pass filter.
Let us consider a simple 1st order RC low pass filter with the input a square wave and the output across the capacitor with NO load.
Focusing on the steady state, we would say Vcapacitor(0)=Vinitial and solve its differential equations for each period of time.
When Vin is positive:
-its differential equation
-Vcapacitor(0)=Vinitial
When Vin is negative:
-its differential equation
-Vcapacitor(t=T)=Vinitial
By making Vcapacitor(t=T)=Vinitial=Vcapacitor(0) we are able to find Vinitial which is the voltage in the steady state.
The steady state is the following one:
My question is: For more complex circuits which make the differential equations more difficult to solve, what would be the approach ?
Example is this circuit: The Switches changes position as the voltage of the capacitor "C" crosses 0.
Any hint or comment is welcomed !