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How to determine 1.1 coefficient in this expression t = 1.1·R1·C1?

Latest Updated:01/01/2007

Question:

In the uPC1555 Data Sheet, there is an example of a monostable multivibrator. In this example, it says, "The output pulse width (delay) is determined by the expression t = 1.1·R1·C1." How is the coefficient 1.1 determined?

Answer:

The expression is calculated assuming inverse operation under the ideal conditions of a pin voltage of 0 V when the capacitor discharges and a threshold pin input voltage of 2/3 Vcc.
When a low level is input to the trigger pin, the internal latch inverts turning the discharge pin off. The capacitor's charge voltage then rises. When this voltage reaches 2/3 Vcc, the internal latch inverts back by 2/3 Vcc applied to the threshold pin, causing the discharge pin to revert to its original ON state. This process is known as a monostable operation.
The expression "capacitor pin voltage = (1-exp(-t/C1·R1))Vcc*" rises to 2/3 Vcc as follows:
1-exp(-t/C1·R1)=2/3
exp(-t/C1·R1)=1/3
t/C1·R1=ln3=1.09861...≈1.1
t=1.1·C1·R1

*Note   For more information on this expression, see the "Time constant" FAQ in the Background Knowledge section.

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