High-pass filter

A high-pass filter (\HPF) is an electronic circuit, algorithm, or filter, allowing signals frequencies under a above a cutoff frequency (high frequency signals) to pass, but impedes/attenuating/blocking/reducing (attenuating) lower frequencies (low frequency signals), by increasing its amplitude. A filter's exact frequency response depends on its design. [1] It's sometimes called a low-cut filter, or bass-cut filter in audio applications. A high-pass filter is the complement of a low-pass filter, which has its components being switced in position.

impede: delay/stop one by obstructing them; hinder
attenuate: reduce the strength or intensity (often technical/scientific)

[3]

A HPF's capacitor's resistance changes in voltage overtime, so it suppresses slow signals (felow cutoff) and passes fast ones (above cutoff). The capacitor blocks DC signals and allows AC signals to pass. At electrons' scales, electrons pile up on plates and push others via the electric field, but never cross the gap. A HPF's capacitor acts as a gate that only reacts to change.

A capacitor's governing equation is:

If the voltage changes slowly → dV/dt is small → no current flow
If the voltage changes quickly → dV/dt is high → easy current flow
governing equation: main equation depicting how component behaves

[3]

RC high-pass filter

[2] An RC high-pass filter is comprised of a resistor and capacitor, wired like a voltage-divider circuit, with its opposite positions as an RC low-pass filter, as shown on the left.

Similarly as the RC low-filter (Vout = Vin(XC//Z) = XC/√(R2 + XC2)) and voltage divider's output voltage (Vout = Vin[R1/(R2+R1)]), an RC high-pass filter's Vout is Vout = Vin(XC//Z) = Vin[XC/√[R2 + (XL - XC)2]i].

capacitor reactance: XC = 1/(2fπC)

Thus as the frequency (f) increases, so will Vout, and XC decreases.

So as f decreases, so will Vout, and XC increases.

Note that Vout increases when f does, which is a crucial trait of high-pass filter, inversely like how Vout decreases as f increases.

But Vout has a limit, so it increases infinitely: As the f keeps increasing, Vout eventually reaches Vin, thus Vout can't be above Vin.

[3]

[2] An RC high filter is drawn oppositely as an RC low filter's, where there's also a -3dB drop at the cutoff frequency fC, defined as

fC = 1/(2πRC).

The gain is also calcluated like the RC low filter's: 20log(Vout/Vin)

RL high-pass filter

[2] An RL high-pass filter is comprised of a resistor and inductor, wired like a RC low filters and an RL low-pass filter but with switched positions.

Unlike RC high filter, RL high filter lets both high and low signals flow through the same resistor. But the inductor only lets low, but not high signals which instead flow to the output.

The RL high filter's graph is akin to the RL high filter's. But its fC is instead calculated as fC = R/(2πL)

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High-pass filter

RC high-pass filter

RL high-pass filter

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