RC Time Constant

- Rising Voltage Graph -

RC Time Constant vs Voltage
RC Time Constant

ec= ET[1-e-(T/t)]

The rise time for a resistor, capacitor combination is shown in the graphic above.
1 Time constant [TC] equal R x C. Two TC's equals 2 x[RC], and so on.
The Time constant is the time it would take for the potential difference across the capacitor to increase to the same level as the applied voltage.
The capacitance voltage rises at an exponential rate. Keep in mind, the voltage over the capacitor falls at the same rate.
The Capacitor Falling voltage is shown on it's own page.
Additional Data which can be derived from the graph:
0.2 time constant equals 80% amplitude.
0.7 time constant equals 50% amplitude.
Also keep in mind that normal IC logic uses 10% and 90% as nominal Pulse rise time values.
That would be 10% of final value and 90% of the final voltage value. So in some cases you may need to worry about the 90 to 100% rise time.
Definition of values for the equation above:
T = Time [in seconds]
t = Time Constant
ec = Voltage over the capacitor at any instant
ET = Voltage applied to the circuit
R = Resistance in Ohms
C = Capacitance in Farads

RC Filter, 1st Order Resistor Capacitor Circuit
RC Circuit

The time it takes for a capacitor to increase to it's final value is determined by the capacitor value and the resistor value.
So the absolute time changes as either of the component values are changed.
Placing another capacitor in parallel will increase the capacitance [CT= C1+C2] and so increase the Time Constant.
Adding or increasing the series resistance [RT= R1+R2] will also increase the Time Constant.

Back to the Logic Design, the Capacitor Information, Passive Filter Definition or Capacitor Manufacturers.

Design Hint; Although the rising edge of a pulse will always take the shape of an exponential curve, it may not appear as such.
Depending on the rate of increase and the time scale that it's being viewed at, the wave may appear as something else.
Using a slow time scale or having a fast signal rise time may make the pulse rise time appear almost vertical.

Related pages on this site:
Cap Dictionary Logic Slew Rate Trace Termination Ground, Power Planes Passive Design IC Package Types

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Modified 2/27/12
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