High-pass filter
A high-pass filter passes what is above its corner frequency and cuts what is below, DC included. It takes the DC off a photodiode's signal to leave the modulation, as AC coupling does.
Ports
One input, in, and one output, out.
The model
The filter is the Butterworth low-pass of order \(n\) with \(s\) turned into \(1/s\):
\[H(s) = \prod_{k=1}^{n} \frac{-p_k}{1/s - p_k}, \qquad s = \frac{i f}{f_c},\]with the low-pass’s poles \(p_k\) (see Low-pass filter). So
\[\lvert H(f)\rvert = \frac{1}{\sqrt{1 + (f_c/f)^{2n}}},\]3 dB down at the corner, falling at \(6n\) dB an octave below it, and zero at DC. Tones are multiplied by \(H(f)\) and the noise density by \(\lvert H(f)\rvert^2\).
Settings
| Field | Default | Meaning |
|---|---|---|
fc | 100 | Corner (Hz) |
order | 1 | Order: 1 (1), 2 (2), 3 (3), 4 (4) |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Readouts
The panel gives its output in the steady state: the DC level, the five strongest tones (each one’s amplitude, rms and the phase of its cosine), and the noise, as a density at 1 kHz and in rms from 1 Hz to 1 GHz. Any notes, such as an input left unwired, are listed under it.
Assumptions
- An ideal Butterworth response, with no noise of its own.
- Steady state only: there is no settling after a step.
Related
- Low-pass filter and band-pass filter.
- Bias tee, whose RF path is a first-order high-pass.