RC Filter Response: Bode Plot & Time-Domain Scope (2D)

Filter Type

Component Values

Resistance R 1.00 kΩ

Capacitance C 1.00 µF

Bode Probe

Test frequency 1.00 kHz

Time-Domain Source

Square-wave frequency 50 Hz

Live Readout

Cutoff f_c

159.2 Hz

Time constant τ

1.00 ms

|H| at probe

-3.0 dB

Phase at probe

-45.0°

How it works

A resistor and capacitor in series form a first-order filter. Taking the output across the capacitor gives a low-pass network; taking it across the resistor gives high-pass. Both share the same cutoff (corner) frequency, where the reactance of C equals R:

f_c = 1 / (2·π·R·C)          τ = R·C

Low-pass:  |H(f)| = 1 / sqrt(1 + (f/f_c)²)      φ(f) = −atan(f/f_c)
High-pass: |H(f)| = (f/f_c) / sqrt(1 + (f/f_c)²) φ(f) = 90° − atan(f/f_c)

The oscilloscope pane drives the same RC network with a bipolar square wave and integrates the exact capacitor-voltage ODE dV_C/dt = (V_in − V_C)/τ (closed-form exponential update each sub-step, unconditionally stable regardless of the time step). The low-pass output is V_C itself — the familiar charge/discharge exponential; the high-pass output is V_in − V_C, i.e. the voltage across R, which is why it spikes at every edge and decays back to zero within a few τ.

Magnitude pane — 20·log₁₀|H(f)| on a log-frequency axis from 1 Hz to 100 kHz, with the −3 dB cutoff marked.
Phase pane — φ(f) in degrees over the same axis; the probe dot tracks the test-frequency slider on both.
Scope pane — input (dashed) vs. filtered output (solid) over a rolling window of three square-wave periods.

Magnitude |H(f)| Phase φ(f) Probe frequency