Passive RC/RL Filter

In this article, the aim is to examine several filter configurations made with passive discrete components used for managing electrical signals. The term passive filter refers to a system that makes it possible to modify a signal by blocking certain frequencies and allowing others to pass, without providing gain; in other words, the output voltage will be less than or equal to the input voltage, never greater.

Electrical information, such as an audio signal, is often made up of a combination of several waveforms at different frequencies superimposed on one another. Over the years, this phenomenon has led to the development of configurations that make it possible to clean the original information by removing unwanted frequency components.

For example, in an audio signal, frequencies below 20 Hz or above 20 kHz are of little interest to us because they cannot be heard by the human ear. Therefore, our ear behaves exactly like a filter, detecting only the frequencies between 20 Hz and 20 kHz.

Passive filters can be made either with resistors and capacitors, or with properly sized resistors and inductors. There are several configurations depending on the final effect:

• Low-pass filter: allows only the signal components below a predefined frequency to pass,
• High-pass filter: allows only the signal components above a certain predefined frequency to pass,
• Band-pass filter: allows only the signal components between two predefined frequency thresholds to pass.

Passive RC low-pass filter

This type of filter is designed to allow only waves with a frequency lower than the cutoff frequency, Fc, to pass. In an audio circuit, for example, if I want to reduce the high frequencies coming out of the speaker, I can use this filter set to a cutoff frequency of approximately 12 kHz.

To size the circuit correctly, the following relationship is used: by setting the cutoff frequency and the capacitance, the value of the resistor to be used can be obtained.

Cutoff frequency:

In the following diagram, the intention was to create a low-pass filter with an Fc of 2 kHz and a capacitance of 100 nF. Using the formula above, the resulting resistance is approximately 800 Ω.

Passive RL low-pass filter

This type of filter is designed to allow only waves with a frequency lower than the cutoff frequency, Fc, to pass. This type of passive filter is typically used to eliminate any high-frequency disturbances present on the line being examined.

To size the circuit correctly, the following relationship is used: by setting the cutoff frequency and the inductance, the value of the resistor to be used can be obtained.

Cutoff frequency:

In the following diagram, the intention was to create a low-pass filter with an Fc of 1.2 kHz and an inductance of 15 mH. Using the formula above, the resulting resistance is approximately 112 Ω.

Passive RC high-pass filter

This type of filter is designed to allow only waves with a frequency higher than the cutoff frequency, Fc, to pass. This type of passive filter is typically used, for example, in audio systems to reduce the bass frequencies coming out of the speaker.

To size the circuit correctly, the following relationship is used: by setting the cutoff frequency and the capacitance, the value of the resistor to be used can be obtained.

Cutoff frequency:

In the following diagram, the intention was to create a high-pass filter with an Fc of 2 kHz and a capacitance of 100 nF. Using the formula above, the resulting resistance is approximately 800 Ω.

Passive RL high-pass filter

This type of filter is designed to allow only waves with a frequency higher than the cutoff frequency, Fc, to pass. This type of passive filter is typically used to clean the line of any disturbances with frequencies lower than Fc.

To size the circuit correctly, the following relationship is used: by setting the cutoff frequency and the inductance, the value of the resistor to be used can be obtained.

Cutoff frequency:

In the following diagram, the intention was to create a low-pass filter with an Fc of 1.2 kHz and an inductance of 15 mH. Using the formula above, the resulting resistance is approximately 112 Ω.

Passive RC band-pass filter

This type of filter is designed to allow only waves with frequencies within a given range to pass; as a result, it will have two cutoff frequencies. Physically, it is made from a high-pass filter, which sets the lower cutoff frequency Fc1, connected in series with a low-pass filter, which sets the upper cutoff frequency Fc2. The allowed frequencies are those between Fc1 and Fc2.

To calculate the cutoff frequencies, the following relationship is used by setting the frequency and the capacitance.

Cutoff frequency:

In the example, the first filter, the high-pass filter, is set to a cutoff frequency of approximately 100 Hz, and the second filter, the low-pass filter, is set to approximately 100 kHz.