RC Low-Pass Filter Step Response
Watch a square wave bend into an exponential curve through a single resistor and capacitor.
Difficulty: Breadboard. Estimated build time: about 20 minutes. Estimated parts cost: about US$0.75. 4-line bill of materials. Compare supplier offers when available. A teaching circuit that exists for one purpose: to make the famous V_out = V_in × (1 − e^(−t/RC)) curve visible on an oscilloscope.
Drive a square wave into the input
Set a function generator to a 0–5 V square wave at 1 kHz with a 50% duty cycle. If you don't have one, an Arduino digital pin running tone(pin, 1000) is good enough. Connect the source through one column of the breadboard.
Build the RC network
Place a 10 kΩ resistor in series with a 10 nF ceramic capacitor between the source and ground. The point between R and C is the output — that is the voltage you will probe.
Probe both signals
Put one scope channel on the input (across the source) and the other on V_out (across the capacitor). Use the same ground reference. You should see the square input on channel 1 and a curved exponential rise/fall on channel 2.
Measure the time constant
Turn on the scope's measurement cursors. The output should reach 63% of the final value (≈3.15 V if the input is 5 V) at exactly τ = R × C = 100 µs after the rising edge. Try swapping the capacitor to 100 nF — τ becomes 1 ms, the curve looks ten times slower, and the −3 dB cutoff drops from 1.6 kHz to 159 Hz.
Try the frequency-domain view
Switch the source to a 1 kHz sine wave, then sweep up. The output amplitude is unchanged at low frequencies, drops by 3 dB (a factor of 0.707) at f_c = 1/(2π × R × C), and falls off at 20 dB/decade above that. This is the same filter, just viewed from the other side.