What is the cutoff frequency of a low-pass filter?

The frequency at which the output signal amplitude drops to 70.7% (-3dB) of the input amplitude. Up to this frequency, signals can pass; around it, they start to become attenuated. From this frequency onwards, higher frequencies are increasingly attenuated at a pace of 20 dB per decade for 1st order filters, 40 db per decade for 2nd order and so on.

How does filter order affect performance?

Higher order filters have a steeper roll-off, meaning they attenuate frequencies beyond the cutoff more sharply (higher downwards slope), but they require more components.

Which filter topology should I use (RC, LC, LR)?

It depends on your application. RC filters are simple and small but cause voltage drop on the resistor, so they are only valid for low-current circuits. LC filters are great since there is no loss at DC at high currents, but the inductors are big and have undesired ressonances. LR filters are less common.

What is the difference between active and passive filters?

Passive filters use only resistors, capacitors, and inductors and cannot amplify signals. Active filters use op-amps, can provide gain, and avoid loading effects.

How do parasitic elements affect filter performance?

Parasitic capacitance, inductance, and resistance can alter the intended frequency response. In general, they diminish the filter performance at high frequencies as the signal "goes through" the parasitics instead of the intended components.

What are some common applications of low-pass filters?

Low-pass filters are used in audio processing to remove high-frequency noise, in power supplies to smooth out voltage and current fluctuations, and in communication systems to limit bandwidth and reduce interference.

What is the ressonance frequency in LC filters?

It is the frequency at which energy oscillates between the inductor and capacitor, leading to a peak in the frequency response. At this frequency, the filter exhibits amplification instead of attenuation. When filtering, this amplification is not desired, so damping networks are used to reduce it.

Low-pass filter graphic calculator

How to use the low-pass filter graphic calculator

To use the calculator use the selector to choose the filter topology you want to use. Then enter the values of the components and, optionally, their parasitic values. You can modify the units using the selectors. The response of the chosen filter will be plotted on the graph. You can add as many traces as you want to compare the different topologies. click on the names of the traces to hide them.

What is a low pass filter?

A low pass filter is a circuit that lets direct current and low frequencies pass, and attenuates or blocks high frequency. A key parameter of it's low pass filter is it's cutoff frequency. It is the frequency up to which a signal can pass. Signals of higher frequency than the cutoff will be rejected. Typically, cutoff frequency is divided when the amplitude of the signal at the output of the filter is half (-3dB) of what is available at the input. There are many types of filters, here we will see the simplest ones, which are also the most used. To understand how a filter works, we have to think of a voltage divider. A divider gives at the output a specific fraction of the voltage at the input, and this happens for all frequencies. A low pass filter does the same thing, except that the voltage fraction at the output changes as a function of frequency. How to do this? By using capacitors and/or inductors, which are elements whose impedance changes as a function of frequency. The filters, in addition to decreasing the amplitude of the wave, also modify its phase.

To know the filter response you can use the voltage divider equation and substitute the impedance of each resistor by the impedance of the capacitor or inductor that replaces it. In the figure we have seen three ways to replace resistors by capacitors or inductors. There are many others that result in other types of filters, but here we will focus on these three, which are those that are used to make a low pass filter.

The RC filter

An RC filter consists of a resistor and a capacitor. The capacitor gives a path to ground for the high frequency current. Since its impedance is very low at high frequencies, it is as if there is a short circuit. In this way, the low and high frequencies are 'separated'. An RC filter provides an attenuation of 20dBs per decade. The equations describing the response of this type of filter are as follows:

Gain $$ \bigg|\frac{V_o}{V_i}(f)\bigg| = \frac {1}{\sqrt {1+\left(2\pi fRC\right)^{2}}}$$

Phase $$ \angle\frac{V_o}{V_i}(f) = \tan ^{-1}\left(-2\pi f RC\right)$$

The LR filter

An LR filter consists of a resistor and an inductor. The latter has a very high impedance at high frequencies. Therefore, a very high voltage falls on it, which 'leaves' very little for the output of the filter. For low frequencies, it is as if the inductor were not there, so all the input goes to the output. An LR filter provides an attenuation of 20dBs per decade. The equations describing the response of this type of filter are as follows:

Gain $$ \bigg|\frac{V_o}{V_i}(f)\bigg| = \frac {1}{\sqrt {1+\left(2\pi f\frac{L}{R}\right)^{2}}}$$

Phase $$ \angle\frac{V_o}{V_i}(f) = \tan ^{-1}\left(-2\pi f \frac{L}{R}\right)$$

The LC filter

An LC filter consists of an inductor and a capacitor. This type of filter combines the two previous ones producing a much higher high frequency rejection than the LR or RC. An LC filter provides an attenuation of 40dBs per decade. A peculiar feature of LC filters is that they exhibit a resonance at a certain frequency. At this resonance, the filter produces amplification instead of attenuation. The equation describing the gain of this type of filter is:

$$ \bigg|\frac{V_o}{V_i}(f)\bigg| = \frac{1}{\sqrt{\left(1 - (2\pi f)^2 LC\right)^2 + \left({2\pi f}\right)^2 LC}}$$

If you look closely at the above expression, you will see a particular case of the expression in which the denominator is 0. A 0 denominator implies that, for the frequency that causes it, we have infinite gain. In real life, this is impossible because there are parasitic elements that introduce losses and make it impossible to have infinite gain, although very high. The expression to calculate the resonance frequency is:

$$ f = \frac {1}{2\pi\sqrt{LC}}$$

From that frequency onwards the phase is shifted 180º.

Low Pass Filter LTSpice Simulation

Download this LTSpice simulation to analyze the frequency response and cutoff frequency of your low pass filter. With this simulation you can verify the results obtained with the calculator and tweak filter topologies to better suit your needs. Also, you can include real component models to see how parasitics affect filter performance. The simulation includes AC analysis to plot the frequency response, but it can be modified to observe transient response as well. In addition to voltage gain, you can also obtain input and output impedances to ensure proper matching with other circuit stages.

Download Low Pass Filter Simulation (.asc)

Frequently Asked Questions

What is the cutoff frequency of a low-pass filter?
The frequency at which the output signal amplitude drops to 70.7% (-3dB) of the input amplitude. Up to this frequency, signals can pass; around it, they start to become attenuated. From this frequency onwards, higher frequencies are increasingly attenuated at a pace of 20 dB per decade for 1st order filters, 40 db per decade for 2nd order and so on.
How does filter order affect performance?
Higher order filters have a steeper roll-off, meaning they attenuate frequencies beyond the cutoff more sharply (higher downwards slope), but they require more components.
Which filter topology should I use (RC, LC, LR)?
It depends on your application. RC filters are simple and small but cause voltage drop on the resistor, so they are only valid for low-current circuits. LC filters are great since there is no loss at DC at high currents, but the inductors are big and have undesired ressonances. LR filters are less common.
What is the difference between active and passive filters?
Passive filters use only resistors, capacitors, and inductors and cannot amplify signals. Active filters use op-amps, can provide gain, and avoid loading effects.
How do parasitic elements affect filter performance?
Parasitic capacitance, inductance, and resistance can alter the intended frequency response. In general, they diminish the filter performance at high frequencies as the signal "goes through" the parasitics instead of the intended components.
What are some common applications of low-pass filters?
Low-pass filters are used in audio processing to remove high-frequency noise, in power supplies to smooth out voltage and current fluctuations, and in communication systems to limit bandwidth and reduce interference.
What is the ressonance frequency in LC filters?
It is the frequency at which energy oscillates between the inductor and capacitor, leading to a peak in the frequency response. At this frequency, the filter exhibits amplification instead of attenuation. When filtering, this amplification is not desired, so damping networks are used to reduce it.