Hello all, I am just a newbie in this forum.
I am trying to get a differential equation for a series RL circuit
includes a switch for my study.
Vi(t) ----- sw ----- R ----- L ----- Vo(t)
i(t) →
GND ------------------------------ GND
When the switch is on or off, it is so easy to get equations as follows;
OFF: di(t)/dt = -(R / L) i(t) (Eq. 1)
ON: di(t)/dt = -(R / L) i(t) + (1 / L) {Vi(t) - Vo(t)} (Eq. 2)
I just want to simulate a broken switch, which can not turn off perfectly.
At first, I tried to replace the switch with a variable resistor "Rsw",
which ranges from 0 to larger value (maybe giga ohm).
Vi(t) ---- Rsw ----- R ----- L ----- Vo(t)
i(t) →
GND ------------------------------ GND
Then, a differential equation is derived as
di(t)/dt = -((R + Rsw) / L) i(t) + (1 / L) {Vi(t) - Vo(t)} (Eq. 3)
Eq. 3 is equal to Eq. 2 (switch is closed) when Rsw = 0, it is OK.
I believe that the Eq. 3 shall be equivalent to Eq. 1 (switch is opened)
when Rsw is quite large since the opened switch is like a resistor of which value is so large.
But, setting Rsw = ∞ doesn't give Eq. 1.
Where is the point that I am missing?
I need a equation that simulates opened / closed / half opened switch by alter Rsw dynamically.
I am trying to get a differential equation for a series RL circuit
includes a switch for my study.
Vi(t) ----- sw ----- R ----- L ----- Vo(t)
i(t) →
GND ------------------------------ GND
When the switch is on or off, it is so easy to get equations as follows;
OFF: di(t)/dt = -(R / L) i(t) (Eq. 1)
ON: di(t)/dt = -(R / L) i(t) + (1 / L) {Vi(t) - Vo(t)} (Eq. 2)
I just want to simulate a broken switch, which can not turn off perfectly.
At first, I tried to replace the switch with a variable resistor "Rsw",
which ranges from 0 to larger value (maybe giga ohm).
Vi(t) ---- Rsw ----- R ----- L ----- Vo(t)
i(t) →
GND ------------------------------ GND
Then, a differential equation is derived as
di(t)/dt = -((R + Rsw) / L) i(t) + (1 / L) {Vi(t) - Vo(t)} (Eq. 3)
Eq. 3 is equal to Eq. 2 (switch is closed) when Rsw = 0, it is OK.
I believe that the Eq. 3 shall be equivalent to Eq. 1 (switch is opened)
when Rsw is quite large since the opened switch is like a resistor of which value is so large.
But, setting Rsw = ∞ doesn't give Eq. 1.
Where is the point that I am missing?
I need a equation that simulates opened / closed / half opened switch by alter Rsw dynamically.