For an RC circuit, I wanted a simple formula to calculate how many seconds it will take to charge a capacitor starting from an initial Low Voltage mark (L) to a target High Voltage mark (H); and then to do the reverse by discharging from H to L.
I was not able to find something that laid this out easily and so I came up with this:
**Note: "LN" in the formula represents the Excel Function "LN", which returns the Natural Logarithm of a number; it's the inverse of the EXP function that is used for calculating e raised to an exponent--which is used in the Universal Time Constant Formula that we often see
V=Source Voltage
L=Low Voltage Level (initial value on charge and target value on discharge)
H=High Voltage Level (target value on charge and initial value on discharge)
R=Resistor Ohms
C=Total Capacitor Farads if Fully Charged
S=Seconds To Charge from Zero to Reach the Target Voltage (the Charge Time)
D=Seconds to Discharge from Target Voltage to Zero (the Discharge Time)
S=R*C*LN(1/(1-((H-L)/(L-V))))
D=R*C*LN(1/((H-L)/(L-V)))
If the Low Voltage Level (L) is going to be Zero, then the formula can be simplified to:
S=R*C*LN(1/(1-(H/V)))
D=R*C*LN(1/(H/V))
Using the source voltage (V), charging from Zero volts for (S) seconds, the voltage level of the capacitor will be (X) volts; here is the formula that I used to determine what the X volts would be (and I used it to confirm my formulas above:
X=V*(1-EXP(-S/(C*R)))
For discharging, starting from full capacity (C), and discharging for (S) seconds, I used this formula to determine what the (X) volts would be after the discharge:
X=V*EXP(-S/(C*R))
If anyone spots an error in my formulas let me know, but I believe these look good. I just wasn't finding something written down in a format that I could easily transfer to Microsoft Excel.
This link was a big help to me.
http://www.allaboutcircuits.com/vol_1/chpt_16/4.html
I've enjoyed this forum and just wanted to contribute.
I was not able to find something that laid this out easily and so I came up with this:
**Note: "LN" in the formula represents the Excel Function "LN", which returns the Natural Logarithm of a number; it's the inverse of the EXP function that is used for calculating e raised to an exponent--which is used in the Universal Time Constant Formula that we often see
V=Source Voltage
L=Low Voltage Level (initial value on charge and target value on discharge)
H=High Voltage Level (target value on charge and initial value on discharge)
R=Resistor Ohms
C=Total Capacitor Farads if Fully Charged
S=Seconds To Charge from Zero to Reach the Target Voltage (the Charge Time)
D=Seconds to Discharge from Target Voltage to Zero (the Discharge Time)
S=R*C*LN(1/(1-((H-L)/(L-V))))
D=R*C*LN(1/((H-L)/(L-V)))
If the Low Voltage Level (L) is going to be Zero, then the formula can be simplified to:
S=R*C*LN(1/(1-(H/V)))
D=R*C*LN(1/(H/V))
Using the source voltage (V), charging from Zero volts for (S) seconds, the voltage level of the capacitor will be (X) volts; here is the formula that I used to determine what the X volts would be (and I used it to confirm my formulas above:
X=V*(1-EXP(-S/(C*R)))
For discharging, starting from full capacity (C), and discharging for (S) seconds, I used this formula to determine what the (X) volts would be after the discharge:
X=V*EXP(-S/(C*R))
If anyone spots an error in my formulas let me know, but I believe these look good. I just wasn't finding something written down in a format that I could easily transfer to Microsoft Excel.
This link was a big help to me.
http://www.allaboutcircuits.com/vol_1/chpt_16/4.html
I've enjoyed this forum and just wanted to contribute.