High Pass Filter Calculator

Welcome to the high pass filter calculator. If you want to remove some low-frequency noise or you're trying to get more treble, you've come to the right place. Together, we'll learn:

• What a high-pass filter is;
• The different types of high-pass filter circuits;
• Passive high-pass filters and active high-pass filters;
• How to tell high-pass and low-pass filters apart; and
• How capacitors can be used in high-pass filters.

Using the high-pass filter calculator is easy! Here's how:

1. Select the filter type you're designing. The high-pass filter calculator covers the following filter types:

   • RC high-pass filter;

   • RL high-pass filter;

   • Non-inverting op-amp high-pass filter; and

   • Inverting op-amp high-pass filter.

2. Input the values for which you are designing. The passive RC and RL filters (both RLC circuits) let you fine-tune the component values and the desired cutoff frequency, while the active (op-amp) filters also let you adjust the gain on your output.

Keep reading if you want to learn how they work!

A high-pass filter is an electronic circuit that removes low-frequency components from a given AC signal. In other words, it blocks low frequencies and lets high frequencies pass through it. That's why we call it a "high-pass filter".

What does this mean in practice? Take a look at the Bode plot for high-pass filters below.

A Bode plot (like the one above) illustrates a circuit's frequency response, which is another word for how it amplifies signals of certain frequencies and damps others. A high-pass filter's frequency response suppresses low-frequency signals, which we can see all the way up to $f = f_c$. That frequency is called the cutoff frequency, and it's what defines any high-pass filter:

• Frequencies below $f_c$ are damped; and
• Frequencies above $f_c$ are left untouched.

The slope at which the frequency response drops for increasingly low frequencies is $-20\ \text{dB}/\text{decade}$. This means that every time the frequency is reduced by a factor of 10, the amplitude is reduced by 20 decibels. This slope is made even steeper if the order of the filter is increased: first-order filters have a 20-decibel slope, second-order filters slope at 40 decibels, third-order descends at 60, etc.

Real-world signals rarely consist of just one frequency, and that's partly why we need high-pass filters in signal-handling circuits. Here's how a high-pass filter affects signals comprised of more than one frequency:

There are two main categories of high-pass filters:

• Passive high-pass filters exclusively use passive components (which are resistors, capacitors and inductors). The two common passive high-pass filters are RC high-pass filters and RL high-pass filters.
• Active high-pass filters use some active component, typically an operational amplifier (or "op-amp"). Thanks to their adjustable gains, they can be modified more than passive filters.

The RC high-pass filter consists of a resistor and a capacitor in the configuration shown below.

It's probably the most well-known yet basic high-pass filter, partly thanks to the easy formula for its cutoff frequency:

The RC high-pass filter works thanks to its capacitor. A capacitor's impedance $Z_c$ decreases with frequency, making it act like a short-circuit for high-frequency signals. Inversely, a capacitor acts as an open circuit for low frequencies.

Thanks to this frequency-dependent impedance, we can use capacitors for high-pass filters.

The RL high-pass filter uses an inductor and a resistor in the configuration below:

Its cutoff frequency is also very simple to calculate:

An inductor $L$ acts the opposite way a capacitor does: An inductor becomes a short-circuit for low-frequency signals and an open circuit for high frequencies. Because of this, any low-frequency components of $v_\text{in}$ pass through the inductor, but high-frequency components are blocked. Instead, high-frequency components must travel through the load at $v_\text{out}$ instead. Here is the equation for the impedance of an inductor:

The inverting op-amp high-pass filter is an active filter that incorporates an operational amplifier (op-amp). The op-amp feeds back into itself with the feedback resistor $R_f$, with the high-pass filtering performed by the capacitor $C$. It's designed as follows:

Its cutoff frequency is calculated much like the RC filter's but with the feedback resistor $R_f$.

And the gain $G$ introduced by the op-amp is calculated with

See that minus sign in the equation for $G$? It means that we're flipping the signal around the time-axis, or in more technical terms, we're introducing a 180° phase shift. If this behavior is undesirable, then head on over to the next section on NON-inverting op-amp high-pass filters.

The non-inverting op-amp high-pass filter is more complicated than its inverting sibling, but it has the useful property of not inverting the input. We connect an RC high-pass filter to the negative input of the op-amp and create a feedback loop between the op-amp's output $v_\text{out}$ and the op-amp's positive input. See its circuit diagram below:

Because the only filtering is done by the passive RC circuit at $v_\text{in}$, we can calculate the filter's cutoff frequency by:

And we can calculate $G$ (the gain from $v_\text{in}$ to $v_\text{out}$) with:

Note that $G$ is positive, but also that $G \ge 1$, as resistance can never be negative.