Compute cutoff frequency (–3 dB point), gain (dB) & phase shift for passive RC or RL high‑pass filters. Visualize magnitude Bode plot, design crossovers, or analyze signal conditioning circuits.
A high-pass filter (HPF) attenuates frequencies below the cutoff frequency \(f_c\) and passes frequencies above it. The simplest passive implementations are the RC and RL networks. These filters are fundamental in audio crossovers, signal conditioning, DC blocking, and biomedical instrumentation. The cutoff frequency is defined where the output power drops by half (−3 dB relative to the passband).
The voltage transfer function magnitude and phase are derived from the voltage divider principle:
\( H(j\omega) = \frac{j\omega RC}{1 + j\omega RC} \) (RC case). The magnitude in dB: \( |H|_{dB} = 20 \log_{10}\left( \frac{f/f_c}{\sqrt{1+(f/f_c)^2}} \right) \). Phase angle: \( \phi = 90^\circ - \arctan(f/f_c) \). Above \( f_c \), gain approaches 0 dB; below \( f_c \), roll‑off is +20 dB/decade.
For real‑world circuits, also consider the source and load impedances: the formulas above assume an ideal voltage source and infinite load. When the load impedance is comparable to R, the actual cutoff frequency shifts – our interactive plot helps you visualise the ideal response as a first approximation.
Our solver determines \(f_c\) from your R and C (or L). It then reconstructs the Bode magnitude plot over a frequency range spanning 0.01×\(f_c\) to 100×\(f_c\) on a logarithmic scale. This reveals the characteristic +20 dB/decade slope below cutoff and the flat passband. The –3 dB line crossing at \(f_c\) validates the design. Use the test frequency input to evaluate gain or phase at any specific point – ideal for checking attenuation at undesired harmonics.
Vinyl records may suffer from low-frequency rumble (below 20 Hz). Using R = 10 kΩ and C = 0.79 μF yields \(f_c \approx 20\) Hz. This filter attenuates rumble by –20 dB at 2 Hz without affecting audible spectrum. Our tool instantly verifies this design, giving engineers confidence before prototyping.