Low-pass filter

A low-pass filter (LPF), high-cut filter, or treble-cut filter, is an electronic circuit, algorithm, or filter, allowing signals frequencies under a a cutoff frequency (low frequency signals) to pass, but impedes/attenuating/blocking/reducing (attenuating) higher frequencies (high frequency signals), by reducing its amplitude. A filter's exact frequency response depends on its design. A low-pass filter is the complement of a high-pass filter.

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

Low-pass filter

RC low-pass filter

RL low-pass filter

References

Tools

[2]

[2] This drawing shows how if low signals enter the low-pass filter, its amplitude stays the same.

But for higher signals, their amplitude are greatly reduced.

[3]

RC low-pass filter

[2] An RC low-pass filter is comprised of a resistor and capacitor, wired like a voltage-divider circuit.

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

frequency = f
capacitance reactance: XC = 1/(2πfC)
total impedance: Z or ZT = √(R2 + XC2) =
Note: The total impedance often has the inductor's reactance (XL) included: √[R2 + (XL + XC2)], but since no inductor is used here, XL = 0.

As the f increases, XC decreases (since the f is the denominator in XC's formula) and Vout as well (since XC is the numerator of Vout's formula).

And as the f decreases, XC and Vout increases.

Note: All low-pass filter's output voltage decrease as frequency increases or vice versa.
Note: High f easily pass through capacitors. Low f easily pass through inductors.

[3]

[2] An RC low-pass filter's frequency response on the left, where the dashed lines are the cutoff frequencies (fC), where both gains are -3dB, calculated as 20log(Vout/Vin) and where Vout is 70.7% of the Vin (Vout = 0.707 ⋅ Vin), thus 20log(0.707) = -3.01 dB (since Vout = 0.707 ⋅ Vin → 0.707 = Vout/Vin).

RL low-pass filter

[2] An RC low-pass filter is comprised of a resistor and inductor, wired like a RC low filters.

[3]

[2] Similarly, an RL low-pass filter's Vout is Vout = Vin(XC//Z) = XC/√(R + (XL - XC)2]. But here unlike RC low filter, here, if f increases, so will XC (both are directly related) (since R is the denominator IO impedance X) and Vout decreases.

And if f decreases, so will XC, and Vout increases.

Another reason why RL low filter is a low-pass filter is due to high f being greatly impeded to be turned into low f as inputs.

An RL low filter has an akin graph as RC low filter.

The circuit resistance is directly proportional to fC: As the circuit's resistance R increases, so will fC.

But its inductance is inversely proportional to fC: inductance L increases, fC decreases.

References

Tools

[1] Low-pass filter calculator - Circuitspedia

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Low-pass filter

RC low-pass filter

RL low-pass filter

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