**What are active filters?**

The **active filters** They are those that have controlled sources or active elements, such as operational amplifiers, transistors or vacuum tubes. Through an electronic circuit, a filter allows to comply with the modeling of a transfer function that changes the input signal and gives an output signal according to the design.

The configuration of an electronic filter is usually selective and the selection criteria is the frequency of the input signal. Due to the above, depending on the type of circuit (series or parallel) the filter will allow the passage of certain signals and will block the passage of the rest.

In this way, the output signal will be characterized by being purified according to the design parameters of the circuit that constitutes the filter.

**Active Filter Characteristics**

– Active filters are analog filters, which means that they modify an analog signal (input) as a function of frequency components.

– Thanks to the presence of active components (operational amplifiers, vacuum tubes, transistors, etc.), this type of filter increases a section or the entire output signal, with respect to the input signal.

This is due to power amplification by the use of operational amplifiers (OPAMS). This makes it easier to obtain resonance and a high quality factor, without the need to use inductors. For its part, the quality factor —also known as the Q factor— is a measure of the sharpness and efficiency of the resonance.

– Active filters can combine active and passive components. The latter are the basic components of circuits: resistors, capacitors, and inductors.

– Active filters allow cascade connections, are configured to amplify signals and allow integration between two or more circuits if necessary.

– In the event that the circuit has operational amplifiers, the output voltage of the circuit is limited by the saturation voltage of these elements.

– Depending on the type of circuit, and the ratings of the active and passive elements, the active filter can be designed to provide a high input impedance and a small output impedance.

– The manufacture of active filters is economical compared to other types of assemblies.

– To operate, active filters require a power supply, preferably symmetrical.

**first order filters**

First order filters are used to attenuate signals that are above or below the rejection degree, in multiples of 6 decibels each time the frequency is doubled. This type of assembly is usually represented by the following transfer function:

Breaking down the numerator and denominator of the expression, you have:

– N(jω) is a polynomial of degree ≤ 1

– t is the inverse of the angular frequency of the filter

– Wc is the angular frequency of the filter, and is given by the following equation:

In this expression, fc is the cutoff frequency of the filter.

The cutoff frequency is that limit frequency of the filter for which an attenuation of the signal is induced. Depending on the filter configuration (lowpass, highpass, bandpass, or bandstop), the effect of the filter design is presented precisely from the cutoff frequency.

In the particular case of first-order filters, these can only be low-pass or high-pass.

**low pass filters**

This type of filter allows the lowest frequencies to pass, and attenuates or suppresses the frequencies above the cutoff frequency.

The transfer function for the low pass filters is as follows:

The amplitude and phase response of this transfer function is:

An active low-pass filter can fulfill the design function using input and ground resistors, along with operational amplifiers and parallel resistor and capacitor configurations. Below is an example of an active low-pass inverter circuit:

The transfer function parameters for this circuit are:

**high pass filters**

On the other hand, high pass filters have the opposite effect, compared to low pass filters. That is, this type of filter attenuates low frequencies and lets high frequencies pass.

Even, depending on the configuration of the circuit, active high-pass filters can amplify signals if they have operational amplifiers specially arranged for that purpose. The transfer function of a first order active high pass filter is as follows:

The amplitude and phase response of the system is:

An active high-pass filter uses resistors and capacitors in series at the input of the circuit, as well as a resistance in the path from discharge to ground, to fulfill the function of feedback impedance. An example of an active high-pass inverting circuit is shown below:

The transfer function parameters for this circuit are:

**second order filters**

Second order filters are usually obtained by connecting first order filters in series, to obtain a more complex assembly that allows selectively tuning frequencies.

The general expression for the transfer function of a second order filter is:

Breaking down the numerator and denominator of the expression, you have:

– N(jω) is a polynomial of degree ≤ 2.

– Wo is the angular frequency of the filter, and is given by the following equation:

In this equation fo is the characteristic frequency of the filter. In case there is an RLC circuit (resistor, inductor and capacitor in series), the characteristic frequency of the filter coincides with the resonant frequency of the filter.

In turn, the resonant frequency is the frequency at which the system reaches its maximum degree of oscillation.

– ζ is the damping factor. This factor defines the ability of the system to dampen the input signal.

In turn, from the damping factor, the quality factor of the filter is obtained through the following expression:

Depending on the design of the circuit impedances, the second order active filters can be: low pass filters, high pass filters and band pass filters.

**Active Filter Applications**

Active filters are used in electrical networks in order to reduce disturbances in the network, due to the connection of non-linear loads.

These disturbances can be permeated through the combination of active and passive filters, and the variation of the input impedances and RC configurations throughout the assembly.

In electrical power networks, active filters are used to reduce current harmonics that circulate through the network between the active filter and the electric power generation node.

Likewise, active filters help to balance the return currents that circulate through the neutral, and the harmonics associated with this current circulation and the system voltage.

In addition, active filters fulfill an excellent function regarding the correction of the power factor of interconnected electrical systems.