High Pass Filter Calculator

What the high-pass filter calculator does

A high-pass filter lets high frequencies through and holds back low ones, and the frequency where it makes that switch is the cutoff. This calculator finds the cutoff frequency for four common designs: a passive RC filter, a passive RL filter, and two active op-amp versions, which also report the gain.

Below is what a high-pass filter is, how the passive and active types work, where the cutoff frequency and gain come from, and a worked example.

How to use it

1. Choose the filter type: RC, RL, non-inverting op-amp, or inverting op-amp.
2. Enter the component values for that type, choosing units from the menus.
3. Press Calculate for the cutoff frequency, and the gain for the active types, or Reset to clear it.

What a high-pass filter is

A high-pass filter is a circuit that passes signals above a certain frequency while weakening those below it. Picture a gate that swings open for fast-changing signals and stays mostly shut for slow ones. The frequency that divides the two, where the filter starts letting signals through, is called the cutoff frequency. Above it, signals pass with little loss; below it, they are increasingly cut down. The name says it plainly: high frequencies pass.

High-pass filters are everywhere in electronics. They block the slow drift and direct-current offset that would otherwise upset an amplifier, remove low rumble from audio, and form one half of the crossover networks that send treble to a tweeter. They come in two broad families. Passive filters use only resistors, capacitors, and inductors, and simply shape the signal. Active filters add an operational amplifier, which lets the filter boost the signal as well as shape it, and isolates it from whatever it drives. This calculator covers both families, finding the cutoff frequency that defines any of them.

The passive types: RC and RL

The simplest high-pass filters use just two components. An RC high-pass filter pairs a resistor and a capacitor: the capacitor blocks low frequencies, since its opposition to current rises as frequency falls, while letting high frequencies through to the output. An RL high-pass filter pairs a resistor and an inductor, with the inductor doing the frequency-dependent work. Both produce the same kind of high-pass response, and which you choose depends on the components and the rest of the circuit.

For the RC filter, the cutoff frequency depends on the resistance and the capacitance together, while for the RL filter it depends on the resistance and the inductance. In each case the two component values set where the filter makes its transition. These passive designs are simple, reliable, and need no power supply of their own, which makes them a common first choice. Their limitation is that they cannot amplify; the output is always a shaped version of the input, never a stronger one. When gain is needed, the active designs step in.

The active types: op-amp filters

An active high-pass filter takes a passive RC network and adds an operational amplifier, which brings two advantages: it can amplify the passband signal rather than only shaping it, and it presents a high input impedance and low output impedance, so the filter does not load down the source or sag under the load it drives. The calculator offers the two standard arrangements, which differ in how the amplifier is wired.

In the non-inverting version, the signal passes through the high-pass network into the amplifier's non-inverting input, and the output stays in step with the input. Its gain is always one or more. In the inverting version, the capacitor sits in series with an input resistor feeding the amplifier's inverting input, and the output is flipped, a mirror image of the input, which shows up as a minus sign on the gain. Both pass high frequencies and both let you set the amount of amplification with a pair of resistors, so the calculator reports the gain alongside the cutoff frequency for each.

The cutoff frequency

The cutoff frequency is the heart of any filter, the frequency at which it changes from blocking to passing. It is defined as the point where the output power has fallen to half its passband value, which corresponds to the output voltage dropping to about 71 percent. In decibels this is the well-known minus-three-decibel point, which is why the cutoff is often called the three-decibel frequency. Signals well above it pass almost untouched, signals well below it are strongly cut, and the cutoff marks the changeover.

For each filter type the calculator uses the standard relationship. For the RC filter and both op-amp filters, the cutoff depends on a resistance and a capacitance through f_c = 1 ÷ (2πRC). For the RL filter it depends on a resistance and an inductance through f_c = R ÷ (2πL). In every case, larger component values push the cutoff lower, and smaller ones push it higher. Below the cutoff the response rolls off at a steady rate of twenty decibels for every tenfold drop in frequency, the signature slope of a first-order filter. The cutoff frequency is the single number that tells you where a high-pass filter goes to work.

Gain in the active filters

What sets the active filters apart is gain, the factor by which they amplify signals in the passband. For both op-amp types, the gain is fixed by two resistors, separately from the components that set the cutoff frequency, so you can choose the amount of amplification and the cutoff point independently. The calculator reports the gain both as a plain multiplying factor and in decibels.

For the non-inverting filter, the passband gain is one plus the ratio of the feedback resistor to the ground resistor, so it is always at least one and the output keeps the same sign as the input. For the inverting filter, the gain is minus the ratio of the feedback resistor to the input resistor, and the minus sign reflects that the output is flipped relative to the input. The size of the gain is just the ratio of those two resistors, while the sign tells you the phase. A gain expressed in decibels is twenty times the logarithm of this factor, so a gain of two is about six decibels. The passive RC and RL filters have no gain to report, since they cannot amplify, which is why the calculator shows gain only for the two active types.

Units and precision

The calculator takes resistances in ohms, kilohms, or megohms, capacitances in farads down to picofarads, and inductances in henries down to microhenries, converting each to base units before calculating. It returns the cutoff frequency in hertz, kilohertz, or megahertz, whichever reads most naturally, and for the active filters it also returns the gain as a factor and in decibels. The formulas are the standard first-order relationships, exact for ideal components. Real components have tolerances, and a real op-amp filter's high-frequency reach is limited by the amplifier itself, so a built filter will sit close to these figures rather than exactly on them.

A worked example

Suppose you build an RC high-pass filter with a 1.6-kilohm resistor and a 10-nanofarad capacitor.

The cutoff frequency is f_c = 1 ÷ (2π × 1600 × 0.00000001) ≈ 9.9 kilohertz. Signals well above 10 kilohertz pass freely, while those below are cut, fading at twenty decibels per decade. If you built this as a non-inverting op-amp filter with equal feedback and ground resistors, the passband gain would be 1 + 1 = 2, or about 6 decibels, so the passed signal would also come out twice as strong.

Questions people ask

How do you calculate the cutoff frequency?

For RC and op-amp filters, use f_c = 1 ÷ (2πRC). For an RL filter, use f_c = R ÷ (2πL). Larger component values give a lower cutoff.

What does an op-amp add to a filter?

It lets the filter amplify the passband, not just shape it, and isolates the filter from the source and load. The two passive types cannot amplify.

How is the gain set in the active filters?

By two resistors. Non-inverting gain is 1 + Rf/Rg; inverting gain is minus Rf/Ri. The cutoff frequency is set separately by the R and C.

Why is the cutoff called the three-decibel point?

Because at the cutoff the output power has dropped to half its passband value, which is minus three decibels, with the output voltage at about 71 percent.

References

A quick note on where this comes from. The high-pass filter formulas, the cutoff frequency, and the active-filter gain relationships are standard electronics, set out in Electronics Tutorials and in analog design references. The links are worth a quick click to confirm they land where you expect.

1. Electronics Tutorials, Active High Pass Filter. https://www.electronics-tutorials.ws/filter/filter_6.html
2. Analog Circuit Design, High-Pass Filters. https://analogcircuitdesign.com/high-pass-filters/
3. Wikipedia, High-pass filter. https://en.wikipedia.org/wiki/High-pass_filter