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5.1 Definition of the filter
Generally the electronic filter element is a device which can transmit and split into parts, one constrains the range of frequencies, ie a specific set of frequencies. The range can be either continuous or intermittent, or discrete (linear).
Among the most common uses of filters is the separation of signal from noise. Mark is a finite set of frequency data of interest. Noise is an unwanted diatarrachon total signal, covering a range of frequencies. With the appropriate electronic filtering can remove the other unwanted signals thoryvikes these disorders, eg cutting range of noise when possible and letting pass only the desired signal spectrum.
The main feature is the size of a filter transfer function H (s) thereof. This complex is defined as the quotient (ratio) of the output voltage, Vo (s) corresponding to the input voltage, Vi (s), ie
H (s) = V4 (5.1.1)
where s =] oh, oh with pf = 2 the angular frequency signal and f is the (linear) frequency of this, while j represents the unit Complex (j = 1.
In practice the measure of great interest, | H (jo) |, the transfer function, which expresses the level of support or voltage gain (in dB) which gives the filter. The curve depicting the dependence of the measure, the frequency, h or f, is the frequency response curve of the filter.
Passive and active filters
Electronic filters are divided into two main groups, passive and active filtra.Ta passive filters consisting only of passive components, ie resistors, capacitors and inductors. In practice they have one serious drawback, namely that at low frequencies require large inductive resistors, thus require bulky coils. Also, it is not
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linear and cause degradation of the signal, with a large loss factor. Finally, create strong electromagnetic fields are peskiness cause electromagnetic interference. For these reasons, their use is usually avoided and takes place only in areas where active filters disadvantage, ie at high frequencies and large inputs of.
Active filters are composed of active components (transistors, operational amplifiers, etc.) combined with passive components (capacitors and resistors). These filters are free of the drawbacks of passive filters mentioned above, are efficient and cost little. So we are widely used, especially at low frequencies and low inputs of. Therefore, it is what will concern us in further.
Note
Today with the technological developments of operational amplifiers can build active filters in the range of MHz, but the cost is high.
5.2 Boxes
Depending on the frequency range in which authorize or prohibit the passage, active filters are divided into the following categories:
5.2.1 Low Pass Filters (FTT)
These filters permit the passage of only low frequency signals and inhibit the signals of higher frequency Sch.5.1. The pass band of them start from zero frequency (ie
signals from dc) and reaches a frequency called the cutoff frequency, f1 and fc. From it, then it shall be reduced drastically and the filter passes the stopband, the frequency of which extends to infinite frequency.
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0 db FTT-response curve
signal noise
frequency (logarithmic scale) Figure 5.1. Low frequency response filter (FSF)
If the filter is used to separate signal from noise (high frequency), taking care that the passband while covering the spectrum of the signal and the stopband range of noise, thus depicting the Sch.5.1 .
5.2.2 High Frequency Filters (PHY)
These filters inhibit the low-frequency signals and allow passage of only high frequency signals, Sch.5.2. The stopband of them start from zero frequency (ie signals from dc) and reaches a frequency of which is beyond help them grow quickly. Then, from a frequency f2 and then, called the cutoff frequency, passband begins, which extends up to infinite frequency.
PHY-response curve
frequency (logarithmic scale) Figure 5.2. High frequency response filter (FSF)
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If the filter is used to separate signal from noise (low frequency), taking care that the stopband while covering the spectrum of the noise and the passband range of the signal, thus depicting the Sch.5.2 .
5.2.3 Zone Pass Filters (FZD)
These filters allow the passage of only signals in the frequency contained in a band and frustrate all other frequencies, Sch.5.3. These filters have a first stopband from zero frequency (ie the dc) to a (lower) cutoff frequency f1, then follows the passband, the frequency / up to one (or more) cutoff frequency f2, and finally appears the second stopband, the frequency f2 to the infinite frequency.
If the FZD is used to separate the signal from the low noise and high frequency is taken care of, so that the passband covering the spectrum of the signal and the two bands cut the noise spectrum in a manner that shows Sch.5.3.
FZD-response curve
frequency (logarithmic scale)
Figure 5.3. Response filter pass band (FSD)
5.2.4 Filters stopband (FZA)
These filters only signals that inhibit their frequency include
taken in a band and not allow the passage of all other frequencies, Sch.5.4. These filters have a first passband from zero frequency (ie the dc) to a (lower) cutoff frequency f1, then follows the stopband, the frequency f1 to a (higher) cutoff frequency f2, and finally appears the second passband, the frequency f2 to the infinite frequency.
Figure 5.4. Response filter stopband (FZA)
In the same figure depicts the correlation of band pass cutoff filter and the range signal and the noise spectrum, in case the filter is used to separate signal from noise.
The FZA can also occur if you combine a FTT with a PHY and the drive signals to an analog adder.
5.2.5 Narrow Band Pass Filters (FSZD)
These filters allow the passage of only a narrow frequency band, focused around a center frequency / 0, and cut out all other frequencies, Sch.5.5.
Active Filters
response curve FSZD / noise
frequency (logarithmic scale) Figure 5.5. Narrowband filter response transit (FSSD)
It is obvious that these filters are particularly useful when the signal spectrum is concentrated within a narrow band around a center frequency f0.
5.2.6 Narrow Band Filters Cut (FSZA)
These filters, called filters and tooth cut out a narrow frequency band, rejecting only the frequencies
located in a narrow range around a center frequency f0, while allowing the passage of all other frequencies, Sch.5.6.
0 db response curve FSZD
isima (i \ / lthoryvos
frequency (logarithmic scale) Figure 5.6. Response narrowband rejection filter
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Obviously, these filters are particularly useful when we want to free the signal from noise strongly localized and concentrated around a frequency.
These filters are useful to cut the 50 Hz network which is often undesirable in electronic medical devices.
5.3 Ideal and real filters
Sometimes, for reasons of standardization and simplification, it is convenient to treat the active filters to approximate way, upgrading to the idealized and simplified theoretical models which are called ideal filters. In still other cases, the use of these standards are insufficient leads to remarkable errors then the filter should be treated based on accurate real behavior, ie as a real filter.
5.3.1 Ideal Filters
Ideal is a filter that meets the following 4 key terms:
• A gain (amplification) unit, ie not create or strengthen or demotion of the input signal to the full extent of the zone or passing.
• Creates a complete degradation (100%) of the input signal across the bands, or ex.
• The transition of response from one zone to another is quite abrupt.
• Does not create any distortion to signals passing through the transit zones.
The above lead to the Sch.5.7 response curves for the four main categories of ideal filter, ie FTT (a), PHY (b), FZD (c) and FZA (d). As observed, all these ideal curves are orthogonal and the voltage gain in the passband is unique.
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Figure 5.7. Response curves of ideal filters: FTT (a), PHY (b), FZA (c), FZA (d)
In the ideal FTT, the passband extends from zero frequency to the cutoff frequency / 1. In an ideal PHY, the band dilelefsis extends from the cutoff frequency f2 to the infinite frequency. In the ideal FZD, the transit zone covers the area / 1 <f </ 2. Finally, the ideal FZA, the passband extends from zero frequency up to f 1 and f2 by up to infinite frequency
