Difference between active and passive filters?

Imagine being an audio engineer who has just recorded a take of one of the best vocals of your entire career, but the recording has a ton of unwanted high-frequency noise that can’t seem to be eliminated, or an electrical engineer perplexed by the high-frequency distortions in the dc output of your latest rectifier. Both these situations, despite their differences, warrant the same solution, a filter. A filter is an electric circuit that affects the ac content of the electrical signal that is being fed through its input. In the case of the audio engineer, he’d employ a filter to remove the high-frequency noise from his recording, while the electrical engineer would employ a different filter to attenuate (reduce) the distortion in her output voltage. In order to be able to determine the type of filter to be used, it is important to discuss the types of filters that are commonly employed.

Thanks to the work of French mathematician Joseph Fourier, it is now known that any periodic signal can be expressed as a combination of sine and cosine waves, whose aptitudes can be determined by analyzing the signal. This implies that any given periodic signal can be demonstrated to consist of sine and cosine waves of certain frequencies and that these individual frequencies can be affected in order to change the characteristics of the entire signal. Hence, filters can be characterized by their effect on different frequency components of a signal. The most common types are– low-pass, high-pass, band-pass, and band-reject (or notch) filters.

Figure 1: Fourier Transform

Low-pass Filter

As the name suggests, a low-pass filter allows frequencies that are lower than a certain frequency to pass through attenuated. This point is called the cut-off frequency of the filter. Any frequency component of the signal above the cut-off frequency will be attenuated to a certain value determined by how the filter is constructed. A simple example of such a filter would be hard walls that attenuate high-frequency components of an audio wave. This is precisely the reason why low-frequency notes of any audio are more legible in the adjacent room.

Figure 2: An ideal low-pass filter

In the above figure, the pass band refers to the band of frequencies that are unattenuated, whereas the stop band refers to the frequencies that are attenuated. The frequency response curve is used to denote the response of the filter.

High-pass Filter

A high-pass filter allows high-frequency components to pass through while attenuating low-frequency components. 

Figure 3: An ideal high pass filter

Band-pass Filter

A Band-pass filter allows a band of frequencies to pass through while attenuating the rest of the signal. It can be imagined as a combination of high- and low-pass filters, with the cut-off frequency of the low-pass filter greater than that of the high-pass filter.

Figure 4: An ideal band-pass filter

Band-reject Filter

The band-reject filter is the opposite of a band-pass filter wherein it allows frequencies outside of a range to pass through while attenuating the frequencies within the range. Like the band-pass filter, it can also be imagined as a combination of low- and high-pass filters with the cut-off frequency for the low-pass filter being lower than that of the high-pass filter.

Figure 5: An ideal band-reject or notch filter

There are two aspects of a periodic signal, namely, gain and phase. Gain refers to the amplitude of a signal, which is measured in dB (or decibels). Phase, on the other hand, relates to the time delay of a signal with respect to its original waveform. This can be better explained via a diagram.

Figure 6: Phase of a sine wave

Although the language used to describe filters suggests that they only attenuate/boost the gain of a signal, they also affect the phase of the individual frequency components in a signal. For instance, a low-pass filter not only attenuated the frequencies above its cut-off but also inverts their phase. This is the reason why filters have gain as well as phase response plots. These are plots that show the relation between the input signal frequency and the change in their gain and phase due to the application of a filter.

Figure 7: The phase response of a low-pass filter

Active and Passive Filters

Passive filters

The simplest of all filters are the ones built using just resistors, capacitors and inductors. Such filters are called passive filters, as they are constructed from passive components. In electronics, passive components are those which do not produce energy of their own. They are only capable of dissipating energy (in the case of resistors) or storing energy (in the case of inductors and capacitors). Additionally, their output cannot be altered using a power supply. For example, the following is the construction of a simple RC high-pass filter:

Figure 8: A simple RC high-pass filter

A low-pass filter can be realized by simply changing the output connections, like so:

Figure 9: A simple RC low-pass filter

The following is a simple band-pass filter using an RC network:

Figure 10: A simple RC band-pass filter

Note how it is built by cascading high- and low-pass filters:

Figure 11: Combining high- and low-pass filters to construct a band-pass filter

The same filter circuits can be built using RL networks. For example, an RL low-pass filter:

Figure 12: A simple RL low-pass filter

RC networks are the preferred construction for filters, as the filters can be implemented within a much smaller footprint. Inductors are large in size, even for small capacities, and contribute to system losses, while also being more expensive.

Although they are simple to implement, passive filters have a few drawbacks. For example, the pass-band gain of passive filters is not zero. This means that the signal decreases in intensity after passing through a passive filter. Also, when we cascade passive filters to increase the slope, it causes a further loss in the amplitude, a phenomenon termed ‘interstage loading’. Additionally, the load connected to the filter can change its cut-off frequency. These drawbacks have led to the development of active filters.

Active Filters

Active filters are named so because they are constructed using active components, or components that add energy to the circuits. Examples of active components include amplifiers, transistors, oscillators, etc. In filters, the most commonly used active components are operational amplifiers or op-amps for short. Amplifiers are used in filter circuits to overcome the drawbacks of passive filters.

Shown below is an active low-pass filter:

Figure 13: An active low-pass filter

Active filters have a 0dB gain for the passband, meaning that they do not attenuate the signals in the passband. They have high input and low output impedances, which correspond to two advantages - one, the load impedance doesn't affect the performance of the filter, and two, cascading multiple filters do not cause a decrease in gain, or it mitigates interstage loading. These characteristics make them perfect for cascading. Since they are active devices, they can be configured to boost the signals in the pass band.

The difference between active and passive filters

• As discussed above, the key difference between active and passive filters is that passive filters are built from passive components like resistors, capacitors and inductors, whereas active filters are made from active components like amplifiers in addition to passive components.

• Active filters require a power source to operate, whereas passive filters don’t. 

• The output of passive filters changes with the load, whereas active filters maintain their performance irrespective of the load connected.

• Passive filters cannot apply additional gain to the signal, whereas active filters can. Even if no gain is applied, active filters maintain the signal amplitude, whereas passive filters attenuate the entire signal.

Key Takeaways

• A filter is an electric circuit that attenuates certain frequencies.

• A high-pass filter attenuates frequencies lower than the cutoff frequency.

• A low-pass filter attenuates frequencies higher than the cutoff frequency.

• A band-pass filter attenuates frequencies outside two cut-off frequencies.

• A band-reject filter attenuates frequencies in-between two cut-off frequencies.

• A passive filter is a filter built using passive components such as resistors, capacitors, and inductors.

• An active filter is built using active components such as amplifiers as well as passive components.

References

• https://www.electronics-tutorials.ws/filter/filter_4.html

• https://www.allaboutcircuits.com/technical-articles/understanding-linear-phase-filters/

• https://en.wikipedia.org/wiki/RC_circuit

• https://en.wikipedia.org/wiki/RL_circuit

• https://www.elprocus.com/what-is-a-high-pass-filter-circuit-diagram-characteristics-and-applications/

• https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electronics/Operational_Amplifiers_and_Linear_Integrated_Circuits_-_Theory_and_Application_(Fiore)/11%3A_Active_Filters/11.03%3A_Section_3-

• https://pgfplots.net/fourier-transform/