The above picture is the first order circuit model of battery. I'm trying to calculate the value of R1 and C1 with specified time varied input and output. In order to calculate that, I have to know the value of time constant first but I have no idea how to calculate that without knowing the value of C1.
Is this an assignment or homework?
Vem is the O/C voltage.
R1 + R0 govern the voltage droop under load.
Vo = Vem - Iload.(R1 + R0).
The Vo/c sags after a load is removed and then restores with time to Vem.
In fact, the action is more complex than this as Vem will drop over time as the battery is depleted - but this model does not show that.
- Vem drops to say Vl under load of Iload,
- recovers instantly to Vr1 when load is removed
- then recovers to Vem after time Tr
Vload = Vem - (R0+R1) x Iload - rearrange to get R0 + R1.
Vc = Vem-- Vr1. -> Calculate ratio of R0 to R1.
Recovery time t = time constant or R0 and C. As T=RC.
Tr = R0.C -> calculate C