Active audio frequency filters on the op-amp circuit. Active filters

tutorial

Short intro

I continue to write spam on the topic of operational paramedics. In this article I will try to give an overview of one of the most important topics related to the OU. Father, kindly please, active filters.

Looking around themes

Possibly, you have already stuck with models of RC-, LC- and RLC-filters. The stench is quite suitable for big days. But for other purposes it is even more important to have a filter with more flat characteristics and a smoother transmission with cool lines. The axis here is for us and we need active filters.
For refreshment in memory, I guess, how filters are used:
Low pass filter(LPF) - transmits a signal that is lower than the singing frequency (also called the frequency of the sound). Wikipedia
High Pass Filter(HPF) - transmits a signal higher than the frequency of sight. Wikipedia
Secondary Filter- skips less than the singing frequency range. Wikipedia
Notch filter- zatrimuє less singing frequency range. Wikipedia
More lyric poetry. Look at the amplitude-frequency characteristic (AFC) of the HPF. On this schedule, don’t joke about anything yet, but just call respect on the plots of those їх:

The most common applications of active filters can be looked through in the "Integrator and Differentiators" section. Ale at ts_y statti ts_ scheme chіpati will not be, tk. stinks are even more effective.

Choose a filter

Admittedly, you have already chosen the frequency, as you want to filter. Now it is necessary to select the type of filter. More precisely, it is necessary to choose this characteristic. In other words, how the filter will “behave”.
The main characteristics є:
Butterword filter- may have a very flat characteristic in smooth transmission, but may have a smooth decline.
Chebishev filter- may have the steepest decline, but in the new most important characteristics in the smooth transmission.
Bessel filter- May have a good phase response and a generally “decent” rolloff. It is important to choose the best choice, as there is no specific task.

Some more information

Admissible, and z zim zavdannyam you ran into. And now you can boldly rozrahunki.
Є kіlka sposobіv rozrahunku. We do not complicate and speed up in the simplest way. And the simplest is the “table” method. Tables can be found in the relevant literature. Sob Vidovgo didn’t joke, I’ll bring from Khorovitsya and Hilla “The Art of Circuitry”.
For LPF:

Let's put it this way, you could know and read it in the literature. Let's move on to the design of filters.

Rozrahunok

I'll try to briefly "test" on all types of filters.
Otzhe, task 1. Induce a low-pass filter of a different order with a frequency of 150 Hz beyond the Butterword characteristic.
Let's get started. If we can filter the n-th pair order, it means that there will be n/2 operators. Tshomu's manager has one.
LPF scheme:

For which type of rozrahunka is taken to respect, scho R1 = R2, C1=C2.
We look at the sign. Bachimo, what K = 1.586. Tse we need a little bit a year.
For the low-pass filter, the following is true:
, de, understood,
- Tse frequency zrіzu.
Zrobivshi pіdrahunok, otrimuєmo. Now let's deal with the selection of elements. Z OU were appointed - "ideal" for the quantity of 1 pc. From the frontal equivalence, we can allow, which is not important for us, some element to choose “first”. Let's start from the resistor. The best thing is that the support of the boules in the range between 2kOhm and 500kOhm. On the eye, let it out there will be 11 com. Apparently, the capacitance of the capacitor is more than 0.1 uF. For reverse link resistors R take enough. I take 10 com. Then, for the upper value, take from the tables. Otzhe, lower matima meaning support R= 10 room, and the top 5.8 room.
Choose and model the frequency response.

Manager #2. Induce a fourth-order high-frequency filter with a frequency of 800 Hz for the Bessel characteristic.
We see it. As a filter of the fourth order, then the scheme will have two operatives. Everything is easy here. We simply cascade two HPF circuits.
The filter itself looks like this:

The filter of the fourth order looks like:

Now it's a mess. Yak bachimo, for the fourth order filter we already have 2 values Before. It is logical that the first is assigned to the first cascade, the other - to the other. Value Before equal 1.432 and 1.606 apparently. Table bula low-frequency filters (!). For the rozrahunka of the HPF, it is necessary to change it. Coefficient Before zalishayutsya such well at be-like vipadku. For the Bessel and Chebishev characteristics, the parameter is changed
- Normalizing frequency. Won dorivnyuvatime now:

For Chebishev and Bessel filters, both for lower frequencies and for high frequencies, the same formula is valid:

Cheer up, what for the skin okremo cascade to happen to rahuvati okremo.
For the first cascade:

Come on W= 0.01 uF todi R= 28.5 kOhm. Resistor zvorotnoy zv'yazku: lower, as zavzhdi, 10 kOhm; top - 840 Ohm.
For another cascade:

The capacitance of the capacitor is too constant. Once Z = 0.01 uF, then R= 32 kOhm.
We will be frequency response.

For the creation of a smug or a cut-off type of filters, it is possible to combine a cascade low-pass filter and a high-pass filter. Ale, such types often do not corrode through filthy characteristics.
For dark and notch filters, it is also possible to use the “table method”, but also for other characteristics.
I’ll give you a sign and I’ll explain a little. Don't overdo it too much - the value is taken overnight for a fourth-order smog filter.

a1і b1- Rosrakhunkovі koefіtsієnti. Q- Kindness. Price parameter. The higher the Q factor is, the more “sharp” the decline will be. ∆f- the range of frequencies that are passed through, and the vibration is equal to -3 dB. Coefficient α - One more rozrahunkovy coefficient. You can know yoga, vicorist formulas, which are easy to know on the Internet.
Well, garazd, wiggle. Now it's work.
Manager #3. Induce a dark filter of the fourth order after the Butterword characteristic with a center frequency of 10 kHz, a frequency width that is passed 1 kHz and a gain factor at the point of the center frequency equal to 1.
Let's go. Fourth order filter. Otzhe two OS. I’ll introduce a typical scheme with rozrachunk’s elements.

For the first filter, the center frequency is set as:

For another filter:

Itself in our mood, I’m still familiar with the tables, it’s obvious that goodness Q\u003d 10. The quality factor of the filter is protected. Moreover, varto means that the goodness of both will be equal.

Power correction for the center frequency area:

The final stage is the development of components.
Bring the capacitor up to 10 nF. Todi for the first filter:

In the same order that i (1) is known R22=R5= 43.5 kOhm, R12 = R4= 15.4 kOhm, R32 = R6= 54.2 Ohm. Just lie, what is victorious for another filter
Well, finally, frequency response.

An advancing tooth is a strip-enclosing filter or a cutter.
There are some variations here. Without a doubt, the simplest one is the Wien-Robinson Filter (English Active Wien-Robinson Filter). Typical scheme - the same filter of the 4th order.

Our rest task.
Manager #4. Induce a notch filter with a central frequency of 90 Hz, quality factor Q\u003d 2 and the coefficient of strength in the smoothness of the transmission is equal to 1.
Nasampered, quite selectable capacitor capacitance. Permissible Z = 100 nF.
Significantly significant R6=R7=R:

It is logical that by "playing" with these resistors, we can change the frequency range of our filter.
They gave us the need to determine the intermediate coefficients. We know them through goodness.

We choose quite a resistor R2. In this particular situation, the best way is to add 30 kOhm.
Now we can know the resistors, how to regulate the coefficient of strength in the transmission smoothness.

І nasamkinets, it is necessary to choose enough R5=2R1. In my circuit, resistors may have a value of 40 kOhm and 20 kOhm, obviously.
Vlasne, frequency response:

Maizhe Kіnets

To whom it is better to know a little more, I can encourage you to read Horowitz and Hill "The Art of Circuitry".
Also, D. Johnson "A handbook of active filters".

Rozroblyayuchi "radiokerovane relay" I virіshiv vikoristati frequency method of coding control commands. With this filter, it was decided to induce the OS, since the building still does not have a block of the OS. But I haven’t finished fantasizing yet, having thought a little and having seen, it’s possible to save more on the details of the vicarious elements, like in reality. Tse led to the writing of the stati "rozrahunok smogovogo filter at the Shelter". Having rummaged through the books, collecting all the necessary information, having created an algorithm for filtering the filter with unipolar eating. Let's talk about this, but at the same time there is not enough theory.

These filters are subdivided into: active filters, which vicorist for shaping the frequency response of a given type, like passive (resistors and capacitors), and active (transistors, microcircuits) elements, and passive filters, which are more passive (resistors) for shaping the frequency response of a given type. and capacitors) elements. And now let's talk about smug filters.

The adjacent filter is so called to the one that passes only that frequency range, for some adjustment, at which frequency, which is beyond the boundaries of this range, they will be relaxed. Whether a smug filter may have the main parameters of the initial characteristics: smuga transmission (smog in a signal passing through the filter may be the least extinguished), smuga sgashannya (smuga in such a signal is weakened), coefficient of strength (filter characteristic, yak vіdpovіdaє once the signal will be amplified or attenuated in the smooth transmission).

The ideal smug filter can be passed through straight smug, but in practice it’s impossible to reach it, but it’s possible, as the world is, to get closer to such a form. The real filter is not limited to the frequencies beyond the limits of the limited frequency range, as a result, the area of the gap between the given range, de the signal is more often weakened. This region is called the steepness of the filter rolloff, and is reduced to "dB" by an octave.

The principle of operation of the smug filter is based on the change of the coefficient of strength of the fallow in the frequency of the input signal. The main filter has an RC-lancet, inclusions in the lancets have a serous link, which, when the frequency is changed, adds to the gain coefficient. Well, I think everything is finished with theory, let's move on to rozrakhunkiv.

Rozrahunok zrobimo for the lower-guided scheme. Elements R1-R3 and C1, C2 - determine the amount of bandwidth and strength coefficient. R4, R5 - shift of the working point, necessary for living in the form of a unipolar dzherel. The op-amp microcircuit controls the role of the active element and the connection, it is necessary to look at the Datasheet. Below the diagrams in the pictures, the layout of the smug filter on the OS is shown, but you can also download the files of the Mathcad 14 layout and models in .

The scheme of the smug filter at the OS

This filter can be used with light and music outbuildings, radio stations, and other sensors.

List of radio elements

Appointment	Type	Denomination	Kіlkіst	My notepad
A	Operational pidsiluvach	LM358	1	Do notepad
C1, C2	Capacitor	3300 pF	2	Do notepad
R1	Resistor	3.3 com	1	Do notepad
R2	Resistor	240 ohm	1	Do notepad
R3	Resistor	1.5 mΩ	1	Do notepad
R4	Resistor

When implementing filters of low frequencies, upper and band frequencies, the filter scheme of a different Sallen-Ki order should be widely installed. On fig. 1 pointed її variant for LPF.

Negative return link (voltage divider R 3+ (b-1) R 3) ensure the coefficient of strength, equal b. A positive return link is established behind the capacitor side W 2 .

Rice. one.

The transfer function of the filter may look like:

May the stars

Z tsikh equal for the coefficients of the transfer function of the filter b 0 , a 1 , a 2 You can expand the values of the elements of the scheme.

To forgive the rozrahunka, you can ask yourself some kind of additional minds, for example, choose the coefficient of strength b \u003d 1. b-1) R 3 \u003d 0 and the resistive voltage dilator in the negative winding loop can be turned off, also the op-amp appears to be switched on after the repeater circuit, which is not inverted.

Which way the filter function is best transferred

May the stars

Then you can set the value of the resistors R 1 ta R 3 and calculate the values R 2 , W 1 , W 2. For circuitry implementation, it is more convenient, however, to choose from the nominal range of capacitor capacities W 1 ta W 2 R 1 ta R 2 .

Having changed the support and capacitors at the circuit in fig. 1. Remove the high pass filter (Fig. 2).

Rice. 2.

The transfer function is described by virase

Shchob prostiti rozrahunki, you can vibrati b \u003d 1 W 1 = W 2 = W. Todi

An adjacent filter of a different order, similar to the Sallen-Key scheme, is shown in Fig. 3. Transmission function of the filter can be seen:

Here - the resonant frequency of the PF, the lower and upper frequencies of the PF. Parameter b can be said through: . Razrahuvshi b i SCH R, you can virahuvati, further wondering W or R know the value of the component that is missing.

Rice. 3.

The advantage of filters over the Sallen-Ki scheme is the possibility of separate regulation of the quality factor of the poles and frequencies at a glance, not much - the high sensitivity of the filter parameters to changes in the parameters of the components, from which this scheme is formed.

Less sensitive to the parameters of the components - a scheme of a lanka of a different order with a rich looped negative turning point (Rauch's scheme). Lanka LPF of another order of such a filter is shown in fig. 4.

Rice. 4.

The transfer function of such a filter may look like this:

Demonstrating the coefficients of the transfer function, we take

Coefficient b 0 sets the filter strength factor at zero frequency. Asking him, you can know the spіvіdnoshennia mіzh R 1 ta R 2 Then we choose the capacities of the capacitors and check two equalities for two unknown ones, you can know the values of the resistors' supports.

Rice. five.

Remembering the places of the capacitors and resistors in the circuit in Fig. 4, we remove the high-pass filter with a loopy loopback sound (Fig. 5).

A richly looped negative return link can be twisted to induce smug filters. A visual scheme is shown in Fig. 6. The transfer function of this filter is determined by the virus

For the analysis of the parameters of the circuit, it is possible to speed up with a thin furnishing, which at the resonant frequency is the coefficient at s 2 at the banner of the transfer function can be added 1. Otzhe,. Submitting your viraz to H(s) and adding the gain coefficients to the coefficients of the transfer function of the design filter, we take away the formula for the flow rate of the smog transmission and the gain coefficient of the filter at the resonant frequency Select, for example, the values W you can know the formulas for smugha R 2 , then speeding up the formula for calculating R 1 i, narashti, z formulas for calculating R 3 .

Having added a resistive dilnik in the circuit in Fig. 6 between the input of the circuit and the non-inverting input of the op-amp, we remove the rejection (band-relevant) filter with a negative negative return signal.

Rice. 6.

The transfer function of which filter is good

Mindfulness of total smothering of the signal at the resonant frequency is equal to zero coefficient b 1 transfer function, it is necessary to choose the support of the resistors mind: . Opir resistor R 3 capacitor capacity W they are chosen as i for the well-glanced smog filter (Fig. 5).

The adjacent and notch filters can also be inspired by the combination of LPF and HPF bands (Fig. 7).

An adjacent filter can be used for cascaded LPF and HPF connections (Mal. 7a). The lower frequency of the PF view is determined by the frequency of the HPF view, and the upper frequency is the frequency of the LPF view. The rejection filter can be induced by the path of the parallel connection of the low-pass filter and high-pass filter (Fig. 7c).

a - smug filter; b - frequency response of a smug filter; c - notch filter; d - frequency response of the notch filter

Rice. 7. Structures of dark and notch filters based on LPF and HPF

Lanka of a different order of filter with the transfer function of a wild look

(This is the name of the bіkvadratna lanka) you can implement dekіlkom in ways. One of the options for the scheme of such a line of indications in fig. 8.

Rice. 8.

The transfer function of the LPF of the lanka of this filter is expressed through the parameters of the circuit in the following order:

How to win the mind R 1 R 3 =R 2 R 7 , then the filter will be elliptical, so choose R 7 =?, then there is another order of polynomial filters of Butterworth, Chebishev and Bessel.

Rozrahunok tsgogo filter can vikonati, for example, in this way. Given the filter transmission coefficient at zero frequency K 0 and values W 1 , W 2 , R 3 other parameters of the scheme are known:

Ring out to choose W 1 =W 2 , and R 3 =1/SCH c C one . The bi-square filter is not very sensitive to the inaccuracies of the elements and is easy to adjust.

Transmitting functions of high-frequency filters, dark-skinned and notch filters can be eliminated by changing the changeover s in virase for the transfer function, similar to how to work when converting a normalized low-frequency prototype into a necessary filter.

Active filters are available from various ICs by companies, for example AFI00/150 chips (National Semiconductor), LTC1562 (Linear Technology), MAX270/271 or MAX274/275 (Maxim). The frequency of the filters is changed up to a few hundred kHz, the order is changed up to the eighth and the sound is transferred to program the filter type. As a butt, you can put the IMC MAX270, which will replace the two programming sections of the Chebishev low-pass filter in a different order after the Salen-Ki scheme (Fig. 9).

Rice. nine.

The frequency of the skin section is set by a parallel 7-bit double code from 1 to 25 kHz.

Visnovki and results

1. When implementing filters, the principle of stimulating filters with a path of cascade planting of a different order is widely victorious. How to zastosovut lanok filters in a different order after the Sallen-Ki scheme, filter lanks with a loopy negative turn signal (Rauh's scheme) and so called b_kvadratny lanka.

2. The advantage of the filter lines for the Sallen-Ki scheme is the possibility of separate regulation of the quality factor of the poles and frequencies in a short time, not much - the high sensitivity of the filter parameters to the change of the parameters of the components, from which this scheme is formed. Less sensitive to the parameters of the components of the scheme of a lanka of a different order with a loopy negative turning point (Rauch's scheme).

3. In science and technology literature, as a rule, there is a combination of transfer functions and rozrahunkovі spіvvіdnoshennia for the elements of a hundred-fold low-frequency filter. Necessary characteristics for high-frequency filters, dark and notch filters can be removed s in virase for the transfer function, similar to how to work when converting a normalized low-pass filter prototype into a required filter.

filter scheme operational pidsiluvach

List of literature.

1. Volovich G.I. Circuitry of analog and analog-digital electronic devices. 2nd view. – M.: DODEKA-XXI, 2007. – 528 p.: il.

2. Polonnikov D.Y. Operational subsidiaries: plant ambush, theory, circuitry. - M: Energoatomizdat, 1983. - 216s.

3. Peyton A. J., Walsh U. Analog electronics on operating devices. M: BINOM, 1994. - 352p.

4. Lem G. Analogue and digital filters: development and implementation / G. Lem; prov. from English Levina V.L. [that in.]. - M: Mir, 1982. - 592 p.

To the increasing order of the filter yogo, the filtering authorities will be broken. On one OS, it is easy to implement a filter of a different order. For the implementation of low-frequency filters, higher frequencies, and dark-skinned filters, a filter scheme of another Sallen-Ki order was widely used. On fig. 17 pointed її variant for LPF. Negative return link R 3 , (a - 1) R 3 secure coefficient of strength, equal a . Positive return link of the condenser's presence W 2. The transfer function of the filter may look like:

(21)

Fig.17. Active low-pass filter of a different order

The rozrahunok of the scheme is meaningfully simple, as if on the cob of the cob, ask for deeds of dodatkovі mind. You can choose the strength factor a = 1. Todi (a - 1) R 3 \u003d 0, and the negative winding resistance switch can be turned off. The op-amp appears to be switched on after the repeater circuit, which is not inverted. In the simplest way, the wines can be replaced by an em-terminal repeater on a warehouse transistor. When a = 1, the transfer function of the filter looks like:

Importantly, what are the capacitances of capacitors W 1 ta W 2 selectable values but 1 ta b 1 (div. (13)):

Schob value R 1 ta R 2 boules deisnimi, maє vykonuvatisya mind

Rozrakhunki can be forgiven by swearing R 1 =R 2 =Rі W 1 =W 2 =W. In this case, for the implementation of filters of a different type, it is necessary to change the value of the coefficient a. Transfer function of the filter matime look

Values for formulas (13) are taken

From the rest of the spin, it can be seen that the coefficient a indicates the quality factor of the pole and does not affect the frequency in sight. The value a in time determines the type of filter.

After remembering the support and capacitors, we take away high pass filter(Fig. 18). The transfer function may look like this:

Rice. 18. Active high-pass filter of a different order

For the forgiveness of rozrakhunkiv, we put a \u003d 1 W 1 =W 2 =W. When we take the following formulas:

K besk = 1,R 1 = 2/wc Ca 1 , R 2 =a 1/2wc Cb 1 .

If the frequency response of a filter of a different order is not cool enough, then stop the filter of a higher order. For whom it is necessary to add Lanks in sequence, which are filters of the first and other order. And here the frequency response of the filter bars are multiplied (at a logarithmic scale they are added). However, the next mother on the vase, which the last day, for example, two Butterworth filters of a different order, did not produce the fourth order of the Butterworth filter before the removal. The resulting filter is designed to have a higher frequency over time and a lower frequency response. Therefore, it is necessary to set such coefficients of the filter parameters, so that the result of multiplying the frequency characteristics will match the bag type of the filter.

Bandpass filter another order can be implemented with the Sallen-Key scheme, as shown in fig. 19. The transfer function of the filter can be seen:

(22)

Rice. 19. Scheme of a smug filter of a different order

When comparing the coefficients of the virase to the coefficients of the transfer function (18), we take the formula for the analysis of the parameters of the filter:

f p = 1/2p RC; K p = a / (3 - a); Q= 1/(3 – a).

Nestacha circuits are responsible for the fact that the gain coefficient at the resonant frequency K p i quality factor Qє independent of each other. The efficiency of the scheme - the quality factor changes in the fallowness in a, but the resonant frequency in the coefficient a does not lie.

An active filter, which is behind the city, can be implemented on the basis of a suspended T-like bridge. If you want a lower T-like place by itself - a filter, which is fenced off, then the quality factor becomes only 0.25. Її you can move, yakscho mist uvimknut in lansyug zvorotnogo link OU. One of the options for such a scheme is shown in Fig. 20. Signals of high and low frequencies pass through the T-like subway without change. For them, the filter voltage is high a U input At the resonant frequency, the voltage is equal to zero. The transfer function of the circuit in fig. May 20 looked.

The filters are used for vibrating vision of the core signal from the sum of the noises, switching over to the same signal. The filters are characterized by a smog of transmission, a resonant frequency, the efficiency of seeing / attenuating the core / respectful signal.

Filters are one of the widest and most important nodes in radioelectronic equipment. Von allow:

♦ see the necessary cortical information from the noisy signal;

♦ improve the signal/noise ratio;

♦ increase signal strength.

For recognition of the following filters:

♦ high (upper) frequencies;

♦ low (lower) frequencies;

♦ smugovі;

♦ higher education;

♦ wide range;

♦ rector (zagorodzhuyuch) and in.

OU.

On fig. 38.1, a typical low frequency is induced and the frequency response is low.

Let's take a look at the main types of filters

As it turns out, the transmission coefficient of the OS included behind the circuit, fig. 38.2 is assigned as 1+R3/R4. For the implementation of a typical low-pass filter, it is necessary to use minds:

Rice. 38.2. An example of practical implementation of low frequencies

C1 = C2 = C, R1 = R2, Todi

the frequency of the filter can be determined from the approximate frequency: DHz]=10/C[μF], fig. 38.3. An analogous visnovok can be used for raising the high frequency filters.

The last filter of low and high frequencies in sequence can be selected, as shown in fig. 38.9.

Rice. 38.7. An example of practical implementation of high frequencies

Note.

Depending on the ratings of precision filter elements according to recommendations (rozrachunkovyh) the value can be overestimated by 7%. It is significant that for the filter it is possible to select precision elements ( , resistors) equal to the nominal value, switched on for the removal of the value of R / 2 and 2C in parallel.