An RC circuit consists of a resistor and capacitor connected in series. When charged, a capacitor will discharge through the resistor over time. A resistor controls the rate of charging and discharging, with higher resistance leading to slower charging. RC circuits can be used as filters, with high-pass filters passing higher frequencies and low-pass filters passing lower frequencies. The transient response of an RC circuit depends on the relative time constant and input signal period, resulting in either a triangular output for an integrator or spiked output for a differentiator.

1. RC Circuits and its
Transient Response
Prepared By:
Syed Hamza Abbas 2354-2018
Course Teacher
Engr. Sara Hafeez

2. RC Circuits;
A capacitor store energy and resistor placed in series with it, will control
the rate at which it charges or discharges.
Simplest RC circuit is consists of a capacitor and resistor in series.

3. RC Circuits;
• When a circuit consists of a only a charged capacitor and a
resistor, the capacitor will discharge its stored energy through
the resistor.
• Resistor and uncharged capacitor, the capacitor will charge,
based on the current flowing through the resistor.
• Resistor is used to control the rate at which the capacitor
charges and discharges.
• With a higher resistances , the current in the circuit is
decreased, and the capacitor charges more slowly.
• And vice verse with low resistances.

4. RC Circuits Filters;
• RC circuits can be used to filter a signal by blocking certain
frequencies and passing g others. There are two most
common types of filters high pass and low pass filters.

5. High pass filters.
• A high-pass filter is a circuit that will pass signals with a
frequency above a certain cutoff frequency and decreased or
removed signals with a frequency below that cutoff.

6. Low pass filter
• A low-pass filter will pass signals with a lower frequency than
the cutoff and removed signals with higher frequency than the
cutoff.

7. Transient response of RC circuit;
• One common use for an RC circuits is the RC Integrator. The
integrator is a low-pass Filter circuit that converts a square
wave input signal into a triangular waveform output.
• If the time constant is long compared to the time period of the
input RC waveform, then the resultant output will be
triangular in space.
• While the square wave is positive the capacitor is charging,
and the triangle wave is increasing. When the square wave
goes negative, the capacitor starts to discharges, and the
triangle wave starts decreasing,

8. low-pass Filter

9. RC Differentiator;
• The differentiator is the high pass filter that can convert a
square wave input signal into high frequency spikes at its
output

10. RC Differentiator;
• If the time constant is short compared to the time period of
the input waveform, then the capacitor will become fully
charged more quickly before the next change in the input
cycle.
• When the capacitor is fully charged , the output voltage across
the resistor is zero.
• The arrival of the falling edge of the input waveform causes
the capacitor reverse charge giving a negative output spike,
the as the square wave input changes during each cycle the
output spike changes from + to -.