Analog and Digital Frequency Filters

Analog and digital frequency filters – (in electronics) are a part of electrical circuit (quadripole), which are “put between” the power source and the receiver. They are designed to pass signals of a desired frequency range or containing specific harmonics of the signal and attenuate signals outside of this range. These are called frequency electrical filters or shortly, filters. They consist of RLC components (resistor, capacitor, coil) that can be combined in different configurations to achieve desired results.

Often in practice there is a need to pass (with the lowest possible loss) signals in the desired frequency range, and strong signal attenuation in a different frequency range. As an example, one can receive the only one desired telephone conversation broadcast by means of a modulated carrier wave, from among many calls sent by the same line. As another example, anti-interference devices may be used to prevent interference with radio reception by electric consumers prone to generating high frequency oscillations.

Filters can be divided due to the shape of the amplitude-frequency characteristics (frequencies of the signals passed), such as:

High-Pass Filters

High-Pass Filter (HPF) is an electronic system that transmits sine and spectral signals of complex signals with frequencies above a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency.

Ideal High-Pass Filter amplitude-frequency characteristics:

Fig. 1. High-pass filter

Low-Pass Filters

Low-Pass Filter (LPF) is an electronic system that transmits sine and spectral signals of complex signals with frequencies below a certain cutoff frequency and attenuates signals with frequencies above the cutoff frequency.

Ideal Low-Pass Filter amplitude-frequency characteristics:

Fig. 2. Low-pass filter

Band-Pass Filters

Band-Pass Filter (BPF) is an electronic system that transmits sine and spectral signals of complex signals with frequencies within a certain range and attenuates frequencies outside that range to very low levels.

Ideal Band-Pass Filter amplitude-frequency characteristics:

Fig. 3. Band-pass filter

Band-Stop Filters

Band-Stop Filter (BSF) is an electronic system that transmits most of the sine and spectral signals of complex signals unaltered and attenuates frequencies in a specific range to very low levels.

Ideal Band-Stop Filter amplitude-frequency characteristics:

Fig. 4. Band-stop filter

Active Filters – General Information

Active filters, as the name suggests, are electronic systems, which contain the combination of active electronic components (such as operational amplifiers and external power supplies) and passive ones (R – resistor, L – inductor, C – capacitor). Active filter is usually the quadripole used to extract the desired frequency band from the many signals fed to the input of that quadripole. The exceptions are bandpass filters for suppressing unwanted frequency or unwanted bands. Active analog filters can be found in almost every electronic device.

Audio systems use analog filters to limit the signal bandwidth and for graphic correction of the signal. Designers of communication systems use filters to tune the signal frequency to specific bands and eliminate other, undesired ones. Analog filters are also used to suppress high frequency signals in data acquisition systems. Such systems have implemented anti-aliasing filters (placed “before” the ADC converter input) or anti-imaging filters (placed “after” the DAC transducer output). Such filtering allows to remove the desired high frequency noise from the signal, which is included in the signal, before it reaches the ADC converter or after exiting the DAC. If the input signal given to the ADC input is characterized by a frequency greater than half of the sampling frequency, then if the amplitude is correctly converted into a digital form, the frequency will be aliased and may be incorrect.

We distinguish active filters due to their approximation of the, as an example we will mention the most popular ones:

• Bessel filters,
• Butterworth filters,
• Chebyshev filters,
• Butterworth-Thompson filters.

Due to the principle of operation, active filters are divided into:

• Continuous time filters,
• Switched capacitor filters.

Active filters are also divided due to their order:

• First order,
• Second order,
• Third order,
• n-order.

Active Filters – Tasks for students

If you are a student or simply want to learn how to solve Active Filter tasks, please visit this section of our website where you can find a wide variety of electronic tasks.

Examples of simple active filters:

Fig. 5. High-pass filter – passes signals of frequencies higher than a certain cutoff frequency and attenuates lower ones

Fig. 6. Low-pass filter – passes signals of frequencies lower than a certain cutoff frequency and attenuates higher ones

Fig. 7. Band-pass filter – passes only a limited range of frequencies and attenuates frequencies outside of that range

Fig. 8. Band-stop filter (2nd order) – attenuates signals in desired frequency range and passes only frequencies above and below that frequency range. The one presented in the picture is called notch filter

Passive Filters – General Information

Passive filters are built from passive (RLC) electronic components and do not contain amplifying and power supplying components in the circuit (like active filters do). The number of inductors and capacitors (not resistors or amplifiers) in circuit determines the order of the filter. It affects the shape of the filter’s frequency response.

Inductors are used for conducting low-frequency signals and blocking high-frequency ones. However, capacitors are used for conducting high-frequency signals and blocking low-frequency ones. Resistors are used for determining the circuit’s time constants, so it influences the frequencies to which it responds.

Examples of simple passive filters:

Fig. 9. High-pass RC filter

Fig. 10. Low-pass filter as an RC circuit

Fig. 11. Band-pass RC filter

Fig. 12. Band-stop RLC filter

Differences between Active and Passive Filters

Active filters, compared to RLC passive filters, have the following advantages:

• high stability of operation,
• better accuracy,
• ease of frequency tuning,
• no attenuation of the useful signal and even the possibility of its strengthening,
• elimination of the expensive and bulky inductive components due to their large dimensions.

Active RC filters can also operate in a wide range of frequencies, starting from single kHz to several dozen or even several hundred kHz. The active filter’s upper operating frequency is limited by the Op-Amp transfer bandwidth.

Digital Filters

The operation and design of analog and digital filter’s circuits is essentially identical. Small differences can only occur during construction processes. Even the operation of fully digital filters used in Digital Signal Processing (DSP) is based on the same rights and relations as used in traditional filters. The difference lies only in the type of signal being processed – in case of DSP, the processing is performed on numerical strings of sampled (discrete) signals by the ADC (Analog-to-Digital Converter) that represents the given continuous-time signal. Filters used in DSP have a wide variety of uses and are inexpensive, although there may be problems with noise accompanied to the signal conversions, but it can be negated with the usage of other filters.

The separation of digital filters (FIR and IIR filters) is as follows:

• FIR digital filter (Finite Impulse Response) – the main feature of this filter is that the current sample and the previous input signal are used to obtain the current output sample. For this reason, it is also sometimes called as non-recursive filters.
• IIR digital filter (Infinite Impulse Response) – the main factor distinguishing IIR filters from FIR filters is the need of feedback loop. Each output sample depends on the previous samples of the input AND output signal. It is called a recursive filter.