Butterworth filter

Butterworth Low Pass Filter Transfer Function n-th order is characterized by the expression:

The frequency response of a Butterworth filter has the following properties:

1) In any order n frequency response value

2) at the cutoff frequency u=u s

The frequency response of the low-pass filter decreases monotonically with increasing frequency. For this reason, Butterworth filters are called filters with the most flat characteristics. Figure 3 shows the graphs of the amplitude-frequency characteristics of the Butterworth low-pass filter of 1-5 orders. Obviously, the higher the order of the filter, the more accurately the frequency response of an ideal low-pass filter is approximated.

Figure 3 - Frequency response for a Butterworth low-pass filter of the order from 1 to 5

Figure 4 shows a schematic implementation of the Butterworth HPF.

Figure 4 - HPF-II Butterworth

The advantage of the Butterworth filter is the smoothest frequency response at passband frequencies and its reduction to almost zero at suppression band frequencies. The Butterworth filter is the only filter that preserves the shape of the frequency response for higher orders (with the exception of the steeper rolloff at the cutoff), while many other types of filters (Bessel filter, Chebyshev filter, elliptical filter) have different shape of the frequency response at different orders.

However, compared to Type I and II Chebyshev filters or an elliptical filter, the Butterworth filter has a flatter rolloff and therefore must be of higher order (which is more difficult to implement) in order to provide the desired performance at the cutoff frequencies.

Chebyshev filter

The square of the modulus of the transfer function of the Chebyshev filter is given by:

where is the Chebyshev polynomial. The module of the transfer function of the Chebyshev filter is equal to one at those frequencies where it vanishes.

Chebyshev filters are usually used where it is required to provide the required frequency response characteristics with a low-order filter, in particular, good frequency suppression from the suppression band, while the smoothness of the frequency response at passband and suppression frequencies is not so important.

There are Chebyshev filters I and II genera.

Chebyshev filter of the first kind. This is a more common modification of Chebyshev filters. In the passband of such a filter, ripples are visible, the amplitude of which is determined by the ripple index e. In the case of an analog electronic Chebyshev filter, its order is equal to the number of reactive components used in its implementation. A steeper decay of the characteristic can be obtained if ripples are allowed not only in the passband, but also in the suppression band, by adding zeros to the transfer function of the filter on the imaginary axis jsh in the complex plane. This, however, will result in less effective suppression in the suppression band. The resulting filter is an elliptic filter, also known as a Cauer filter.

The frequency response for the Chebyshev low-pass filter of the fourth order of the first kind is shown in Figure 5.

Figure 5 - Frequency response for the Chebyshev low-pass filter of the first kind of the fourth order

The Type II Chebyshev filter (inverted Chebyshev filter) is used less frequently than the Type I Chebyshev filter due to the less steep rolloff of the amplitude response, which leads to an increase in the number of components. It has no ripple in the passband, but is present in the suppression band.

The frequency response for the Chebyshev low-pass filter of the second kind of the fourth order is shown in Figure 6.

Figure 6 - Frequency response for the Chebyshev low-pass filter of the second kind

Figure 7 shows circuit implementations of the Chebyshev HPF of the I and II orders.

Figure 7 - Chebyshev HPF: a) I order; b) II order

Properties of the frequency characteristics of Chebyshev filters:

1) In the passband, the frequency response has an equal-wave character. On the interval (-1? u? 1) there is n points at which the function reaches a maximum value of 1 or a minimum value of . If n is odd, if n is even;

2) the value of the frequency response of the Chebyshev filter at the cutoff frequency is

3) For , the function decreases monotonically and tends to zero.

4) The parameter e determines the unevenness of the frequency response of the Chebyshev filter in the passband:

Comparison of the frequency response of Butterworth and Chebyshev filters shows that the Chebyshev filter provides more attenuation in the passband than the Butterworth filter of the same order. The disadvantage of Chebyshev filters is that their phase-frequency characteristics in the passband differ significantly from linear ones.

For Butterworth and Chebyshev filters, there are detailed tables that show the coordinates of the poles and the coefficients of the transfer functions of various orders.

1 Define the order of the filter. The filter order is the number of reactive elements in the LPF and HPF.

Where
- Butterworth function corresponding to the allowable frequency .

- allowable attenuation.

2 We draw the filter circuit of the received order. In practical implementation, circuits with fewer inductances are preferred.

3 Calculate the filter transformation constants.

, mH

, nF

4 For an ideal filter with oscillator resistance 1 ohm, load resistance 1 ohm,
a table of normalized Butterworth filter coefficients has been compiled. In each row of the table, the coefficients are symmetrical, increase towards the middle, and then decrease.

5 To find the elements of the circuit, it is necessary to multiply the constant transformations by the coefficient from the table.

Filter order	Filter sequence numbers m

Calculate the parameters of the Butterworth low-pass filter if PP=0.15 kHz, =25 kHz, =30 dB,
=75 Ohm. Find
for three points.

29.3 Butterworth Phv.

HPF filters are four-terminal networks, which have in the range (
) the attenuation is small, and in the range (
) is large, that is, the filter must pass high-frequency currents to the load.

Since the HPF must pass high-frequency currents, then in the path of the current going to the load, there must be a frequency-dependent element that passes high-frequency currents well and low-frequency currents poorly. This element is a capacitor.

F
HF T-shaped

HPF U-shaped

The capacitor is placed in series with the load
and with increasing frequency
decreases, therefore, high-frequency currents easily pass into the load through the capacitor. The inductor is placed in parallel with the load, since
and increases with increasing frequency.
, therefore, low-frequency currents are closed through inductances and will not enter the load.

The calculation of the Butterworth HPF is similar to the calculation of the Butterworth LPF, it is carried out according to the same formulas, only

.

Calculate the Butterworth high-pass filter if
Ohm
kHz,
db,
kHz. Find:
.

Lesson topic 30: Butterworth bandpass and notch filters.

Page 1 of 2

Let's determine the order of the filter based on the required conditions according to the schedule for attenuation in the stopband in the book by G. Lam "Analog and digital filters" ch.8.1 p.215.

It is clear that a filter of the 4th order is sufficient for the required attenuation. The graph is given for the case when w c \u003d 1 rad / s, and, accordingly, the frequency at which the necessary attenuation is needed is 2 rad / s (respectively 4 and 8 kHz). General plot for the Butterworth filter transfer function:

We define the circuit implementation of the filter:

active fourth-order low-pass filter with complex negative feedback:

In order for the desired circuit to have the desired frequency response, the elements included in it can be selected with not very high accuracy, which is a plus of this circuit.

active low-pass filter of the fourth order with positive feedback:

In this circuit, the gain of the operational amplifier must have a strictly defined value, and the gain of this circuit will be no more than 3. Therefore, this circuit can be discarded.

4th order active low-pass filter with ohmic negative feedback

This filter is built on four opamps, which increases the noise and the complexity of calculating this circuit, so we also discard it.

From the schemes considered, we choose a filter with complex negative feedback.

Filter calculation

Transfer function definition

We write the tabular values ​​of the coefficients for the Butterworth filter of the fourth order:

a 1 \u003d 1.8478 b 1 \u003d 1

a 2 \u003d 0.7654 b 2 \u003d 1

(see W. Titze, K. Schenk "Semiconductor circuitry" tab. 13.6 p. 195)

The general expression of the transfer function for the fourth-order low-pass filter:

(See W. Titze, K. Schenk "Semiconductor Circuitry" Table 13.2 p. 190 and Form 13.4 p. 186).

The transfer function of the first link has the form:

The transfer function of the second link has the form:

where w c is the circular frequency of the filter cutoff, w c =2pf c .

Calculation of denominations of parts

Equating the coefficients of expressions (2) and (3) with the coefficients of expression (1), we obtain:

Constant signal transmission coefficients for cascades, their product A 0 must be equal to 10 according to the assignment. They are negative, since these stages are inverting, but their product gives a positive gain.

To calculate the circuit, it is better to set the capacitances of capacitors, while in order for the value of R 2 to be valid, the condition must be met

and correspondingly

Based on these conditions, C 1 \u003d C 3 \u003d 1 nF, C 2 \u003d 10 nF, C 4 \u003d 33 nF are selected.

Calculate the resistance values ​​for the first stage:

The resistance values ​​of the second stage:

OU selection

When choosing an op amp, it is necessary to take into account the frequency range of the filter: the unity gain frequency of the op amp (at which the gain is equal to unity) must be greater than the product of the cutoff frequency and the filter gain K y.

Since the maximum gain is 3.33, and the cutoff frequency is 4 kHz, almost all existing op-amps satisfy this condition.

Another important parameter of an op amp is its input impedance. It must be greater than ten times the maximum resistance of the circuit resistor.

The maximum resistance in the circuit is 99.6 kOhm, therefore the input resistance of the op-amp must be at least 996 kOhm.

It is also necessary to take into account the load capacity of the OS. For modern op amps, the minimum load resistance is 2 kOhm. Given that the resistances R1 and R4 are 33.2 and 3.09 kΩ, respectively, the output current of the operational amplifier will certainly be less than the maximum allowable.

In accordance with the above requirements, we select the OU K140UD601 with the following passport data (characteristics):

K min = 50,000

R in = 1 MΩ

MINISTRY OF EDUCATION AND SCIENCE OF UKRAINE

Kharkiv National University of Radio Electronics

Department of REU

COURSE WORK

SETTLEMENT AND EXPLANATORY NOTE

BUTTERWORTH HIGH PASS FILTER

Kharkiv 2008

Technical task

Design a high-pass filter (HPF) with approximation of the amplitude-frequency characteristic (AFC) by the Butterworth polynomial, determine the required filter order if the AFC parameters are set (Fig. 1): K 0 = 26dB

U m Vx \u003d 250mV

where is the maximum filter gain;

The minimum gain in the bandwidth;

Maximum filter gain in the delay band;

Cutoff frequency;

The frequency from which the filter gain is less than .

Figure 1 - Butterworth HPF template.

Provide a small sensitivity to deviations in the ratings of the elements.

ABSTRACT

Settlement and explanatory note: 26 p., 11 fig., 6 tab.

Purpose of the work: synthesis of an active high-pass RC filter circuit and calculation of its components.

Research method: approximation of the frequency response of the filter by the Butterworth polynomial.

The approximate transfer function is implemented using an active filter. The filter is built by cascading independent links. Active filters use finite-gain non-inverting amplifiers, which are implemented using operational amplifiers.

The results of the work can be used to synthesize filters for radio engineering and household equipment.

Introduction

1. Overview of similar schemes

3.1 Implementation of HPF normalization

3.2 Determining the required filter order

3.3 Definition of the Butterworth polynomial

3.4 Reverse transition from normalized to projected HPF

3.5 Transition from transfer function to circuit

3.6 Transition from transfer function to circuit

4. Calculation of circuit elements

5. Technique for adjusting the developed filter

Introduction

Until recently, the results of comparing digital and analog devices in radio equipment and technical means of telecommunications could not but cause a feeling of dissatisfaction. Digital nodes implemented with the widespread use of integrated circuits (ICs) favorably differed in their constructive and technological completeness. The situation was different with the nodes of analog signal processing, which, for example, in telecommunications accounted for 40 to 60% of the volume and mass of communication equipment. Bulky, containing a large number of unreliable and time-consuming winding elements, they looked so depressing against the background of large integrated circuits that they gave rise to an opinion among a number of experts about the need for “total digitalization” of electronic equipment.

The latter, however, like any other extreme, did not (and could not) lead to results adequate to those expected. The truth, as in all other cases, was somewhere in the middle. In a number of cases, equipment built on functional analog units, the elemental basis of which is adequate to the capabilities and limitations of microelectronics, turns out to be more efficient.

Adequacy in this case can be ensured by the transition to active RC circuits, the elemental basis of which does not include inductors and transformers, which are fundamentally not implemented by means of microelectronics.

The validity of such a transition is currently determined, on the one hand, by the achievements of the theory of active RC circuits, and, on the other hand, by the success of microelectronics, which has provided developers with high-quality linear integrated circuits, including integrated operational amplifiers (op-amps). These op amps, having great functionality, significantly enriched analog circuitry. This was especially evident in the circuitry of active filters.

Until the 60s, mainly passive elements were used to implement filters, i.e. inductors, capacitors and resistors. The main problem in the implementation of such filters is the size of the inductors (at low frequencies they become too bulky). With the development of integrated operational amplifiers in the 60s, a new direction in the design of active filters based on op-amps appeared. Active filters use resistors, capacitors, and op-amps (active components), but they don't have inductors. In the future, active filters almost completely replaced passive ones. Currently, passive filters are only used at high frequencies (above 1 MHz), outside the frequency range of most widely used op amps. But even in many high-frequency devices, such as radio transmitters and receivers, traditional RLC filters are being replaced by quartz and surface acoustic wave filters.

Now, in many cases, analog filters are being replaced by digital ones. The operation of digital filters is provided mainly by software, so they are much more flexible in use compared to analog ones. With the help of digital filters, it is possible to realize such transfer functions that are very difficult to obtain by conventional methods. However, digital filters cannot yet replace analog filters in all situations, so there remains a need for the most popular analog filters - active RC filters.

1. Overview of similar schemes

Filters are frequency-selective devices that pass or delay signals within certain frequency bands.

Filters can be classified according to their frequency response:

1. Low-pass filters (LPF) - pass all oscillations with frequencies not higher than a certain cutoff frequency and a constant component.

2. High-pass filters (LPF) - pass all vibrations not lower than a certain cutoff frequency.

3. Band-pass filters (BPF) - pass oscillations in a certain frequency band, which is determined by a certain level of frequency response.

4. Band-stop filters (BPF) - delay oscillations in a certain frequency band, which is determined by a certain level of frequency response.

5. Notch filters (RF) - a type of BPF that has a narrow delay band and is also called a stopper filter.

6. Phase filters (FF) - ideally have a constant transmission coefficient at all frequencies and are designed to change the phase of input signals (in particular, for the time delay of signals).

Figure 1.1 - The main types of filters

With active RC filters, it is impossible to achieve the ideal shape of the frequency response in the form of rectangles shown in Fig. 1.1 with a strictly constant gain in the passband, infinite attenuation in the suppression band, and infinite steepness of the roll-off from passband to suppression band. The design of an active filter is always a compromise between the ideal form of the characteristic and the complexity of its implementation. This is called the “approximation problem”. In many cases, the requirements for the quality of filtering make it possible to get by with the simplest filters of the first and second orders. Some schemes of such filters are presented below. Filter design in this case comes down to choosing a circuit with the most appropriate configuration and then calculating the element ratings for specific frequencies.

However, there are situations where the requirements for filtering can be much more stringent, and higher order schemes than the first and second ones may be required. Designing high-order filters is a more difficult task, which is the subject of this course work.

Below are some of the main schemes of the first second order with a description of the advantages and disadvantages of each of them.

1. LPF-I and HPF-I based on a non-inverting amplifier.

Figure 1.2 - Filters based on a non-inverting amplifier:

a) LPF-I, b) HPF-I.

The advantages of filter circuits include mainly the ease of implementation and tuning, the disadvantages are the low steepness of the frequency characteristics, and are not very resistant to self-excitation.

2. LPF-II and HPF-II with multi-loop feedback.

Figure 1.3 - Filters with multi-loop feedback:

a) LPF-II, b) HPF-II.

Table 2.1 - Advantages and disadvantages of LPF-II with multi-loop feedback

Table 2.2 - Advantages and disadvantages of HPF-II with multi-loop feedback

2. LPF-II and HPF-II Sallen-Key.

Figure 1.4 - Sallen-Kay filters:

a) LPF-II, b) HPF-II

Table 2.3 - Advantages and disadvantages of LPF-II Sallen-Kay.

Table 2.4 - Advantages and disadvantages of Sallen-Kay HPF-II.

3. LPF-II and HPF-II based on impedance converters.

Figure 1.5 - LPF II circuit based on impedance converters:

a) LPF-II, b) HPF-II.

Table 2.3 - Advantages and disadvantages of LPF-II and HPF-II based on impedance converters.

2. Selection and justification of the filter scheme

Filter design methods differ in design features. The design of passive RC filters is largely determined by the block diagram

Active AF filters are mathematically described by a transfer function. Names of transfer function polynomials are given to frequency response types. Each type of frequency response is implemented with a certain number of poles (RC circuits) in accordance with the specified frequency response slope. The most famous are the approximations of Butterworth, Bessel, Chebyshev.

The Butterworth filter has the most flat frequency response, in the suppression band the slope of the transition section is 6 dB / oct per pole, but it has a non-linear phase response, the input impulse voltage causes oscillations at the output, therefore the filter is used for continuous signals.

The Bessel filter has a linear phase response, a small slope of the transition section of the frequency response. Signals of all frequencies in the passband have the same time delays, so it is suitable for filtering rectangular pulses that must be sent without distortion.

Chebyshev filter - filter of equal waves in the joint venture, the masses of a flat shape outside it, suitable for continuous signals in cases where caps must have a steep slope of the frequency response behind the cutoff frequency.

Simple filter schemes of the first and second orders are used only when there are no strict requirements for the quality of filtering.

The cascade connection of the filter links is carried out if the filter order is higher than the second, that is, when it is necessary to form a transfer characteristic with a very large attenuation of signals in the suppressed band and a large slope of the attenuation of the frequency response. The resulting transfer function is obtained by multiplying the partial transfer coefficients

Chains are built according to the same scheme, but the values ​​​​of the elements

R, C are different, and depend on the cutoff frequencies of the filter and its strips: f sp.f / f sp.l

However, it should be remembered that cascading, for example, two second-order Butterworth filters does not give a fourth-order Butterworth filter, since the resulting filter will have a different cutoff frequency and a different frequency response. Therefore, it is necessary to choose the coefficients of single links in such a way that the next product of the transfer functions corresponds to the chosen type of approximation. Therefore, the design of an AF will cause difficulties in terms of obtaining an ideal characteristic and the complexity of its implementation.

Due to the very large input and small output impedances of each link, there is no distortion of the given transfer function and the possibility of independent regulation of each link. The independence of the links makes it possible to widely regulate the properties of each link by changing its parameters.

It does not fundamentally matter in which order the partial filters are placed, since the resulting transfer function will always be the same. However, there are various practical recommendations regarding the order of connection of partial filters. For example, to protect against self-excitation, a sequence of links should be organized in ascending order of the partial limiting frequency. Another order can lead to self-excitation of the second link in the peak region of its frequency response, since filters with higher limiting frequencies usually have a higher quality factor in the region of the limiting frequency.

Another criterion is related to the requirements of minimization, the noise level at the input. In this case, the sequence of links is reversed, since the filter with the minimum cut-off frequency attenuates the noise level that arises from the previous links of the cascade.

3. Topological filter model and voltage transfer function

3.1 In this paragraph, the order of the Butterworth HPF will be selected and the type of its transfer function will be determined according to the parameters specified in the ToR:

Figure 2.1 - HPF template according to the terms of reference.

Topological filter model.

3.2 Implementation of HPF normalization

According to the assignment condition, we find the boundary conditions for the filter frequency that we need. And we normalize for the transmission coefficient and for the frequency.

Beyond the transfer ratio:

K max \u003d K 0 -K p \u003d 26-23 \u003d 3dB

K min \u003d K 0 -K s \u003d 26- (-5) \u003d 31 dB

By frequency:

3.3 Determining the required filter order

Rounding n to the nearest integer: n = 3.

Thus, to satisfy the requirements given by the template, a third-order filter is needed.

3.4 Definition of the Butterworth polynomial

According to the table of normalized transfer functions of Butterworth filters, we find the Butterworth polynomial of the third order:

3.5 Reverse transition from normalized to projected HPF

Let's carry out the reverse transition from the normalized HPF to the projected HPF.

scaling by transfer coefficient:

frequency scaling:

We make a replacement

As a result of scaling, we obtain the transfer function W(p) in the form:

Figure 2.2 - Frequency response of the designed HPF Butterworth.

3.6 Transition from transfer function to circuit

Let us represent the transfer function of the third-order HPF being designed as the product of the transfer functions of two active HPFs of the first and second order, i.e. as

And ,

where is the transmission coefficient at an infinitely high frequency;

is the frequency of the pole;

– quality factor of the filter (the ratio of the gain at the frequency to the gain in the passband).

This transition is valid, since the total order of series-connected active filters will be equal to the sum of the orders of individual filters (1 + 2 = 3).

The overall filter gain (K0 = 19.952) will be determined by the product of the individual filter gains (K1, K2).

Expanding the transfer function into quadratic factors, we get:

In this expression

. (2.5.1)

It is easy to see that the frequencies of the poles and the quality factors of the transfer functions are different.

For the first transfer function:

pole frequency ;

the quality factor of HPF-I is constant and equal to .

For the second transfer function:

pole frequency ;

quality factor.

In order for the operational amplifiers in each stage to have approximately equal requirements for frequency properties, it is advisable to distribute the total transfer coefficient of the entire filter between each of the stages in inverse proportion to the quality factor of the corresponding stages, and select the characteristic frequency (unit gain frequency of the op amp) among all stages.

Since in this case the HPF consists of two stages, the above condition can be written as:

. (2.5.2)

Substituting expression (2.5.2) into (2.5.1), we obtain:

;

Let's check the correctness of the calculation of the transmission coefficients. The total filter gain in times will be determined by the product of the coefficients of the individual filters. Let's translate the coefficient izdB into times:

Those. calculations are correct.

Let's write the transfer characteristic taking into account the values ​​calculated above ():

.

3.7 Selecting a 3rd order active HPF circuit

Since, according to the task, it is necessary to ensure a small sensitivity to deviations of the elements, we will choose as the first stage of the HPF-I based on a non-inverting amplifier (Fig. 1.2, b), and the second - HPF-II based on impedance converters (CPS), the circuit of which is shown in Fig. 1.5, b.

For HPF-I based on a non-inverting amplifier, the dependence of the filter parameters on the ratings of the circuit elements is as follows:

For HPF-II based on CPS, the filter parameters depend on the element ratings as follows:

; (3.4)

;

4. Calculation of circuit elements

Calculation of the first stage (HPF I) with parameters

Let's choose R1 based on the requirements for the input resistance value (): R1 = 200 kOhm. Then it follows from (3.2) that

.

We choose R2 = 10 kOhm, then from (3.1) it follows that

· Calculation of the second cascade (HPF II) with parameters

. .

Then (the coefficient in the numerator is chosen so as to obtain the nominal capacity from the standard series E24). So C2 = 4.3 nF.

From (3.3) it follows that

From (3.1) it follows that

Let . So C1 = 36 nF.

Table 4.1 - Ratings of filter elements

From the data in Table 4.1, we can start modeling the filter circuit.

We do this with the help of a special program Workbench5.0.

The scheme and simulation results are shown in Figure 4.1. and Fig.4.2, a-b.

Figure 4.1 - Scheme of the Butterworth HPF of the third order.

Figure 4.2 - Resulting frequency response (a) and phase response (b) of the filter.

5. Technique for setting and regulating the developed filter

In order for a real filter to provide the desired frequency response, resistances and capacitances must be chosen with great accuracy.

This is very easy to do for resistors, if they are taken with a tolerance of no more than 1%, and harder for capacitor capacities, because they have tolerances in the region of 5-20%. Because of this, the capacitance is calculated first, and then the resistance of the resistors is calculated.

5.1 Selecting the type of capacitors

We will choose the low-frequency type of capacitors due to their lower cost.

Requires small dimensions and mass of capacitors

· It is necessary to choose capacitors with as little losses as possible (with a small dielectric loss tangent).

Some parameters of the K10-17 group (taken from):

Dimensions, mm

Weight, g0.5…2

Permissible capacity deviation, %

Loss tangent0.0015

Insulation resistance, MOm1000

Operating temperature range, – 60…+125

5.2 Choosing the type of resistors

· For the circuit of the designed filter, in order to ensure a low temperature dependence, it is necessary to choose resistors with a minimum TCR.

· Selected resistors must have a minimum intrinsic capacitance and inductance, so we will choose a non-wire type of resistors.

· However, non-wire resistors have a higher level of current noise, so the parameter of the self-noise level of the resistors must also be taken into account.

Precision resistors of type C2-29V meet the specified requirements (parameters are taken from):

Rated power, W 0.125;

Nominal resistance range, Ohm;

TCS (in the temperature range ),

TCS (in the temperature range ),

Self-noise level, µV/V1…5

Limit operating voltage DC

and alternating current, V200

5.3 Selecting the type of operational amplifiers

· The main criterion for choosing an op amp is its frequency properties, since real op amps have a finite bandwidth. In order for the frequency properties of the op-amp not to affect the characteristic of the designed filter, it is necessary that for the unity gain frequency of the op-amp in the i-th stage, the relation is fulfilled:

For the first cascade: .

For the second cascade: .

Choosing a larger value, we obtain that the unity gain frequency of the op amp should not be less than 100 kHz.

The gain of the op-amp must be large enough.

· The supply voltage of the op amp must match the voltage of the power supplies, if known. Otherwise, it is desirable to choose an op-amp with a wide range of supply voltages.

· When choosing an op-amp for a multi-stage high-pass filter, it is better to choose an op-amp with the lowest possible bias voltage.

According to the reference book, we will choose an OS of type 140UD6A, structurally designed in a case of type 301.8-2. Op-amps of this type are general-purpose op-amps with internal frequency correction and output protection in case of load short circuits and have the following parameters:

Supply voltage, V

Supply voltage, V

Consumption current, mA

Bias voltage, mV

Op-amp voltage gain

Unity gain frequency, MHz1

5.4 Technique for setting and adjusting the developed filter

Setting up this filter is not very difficult. The frequency response parameters are “adjusted” with the help of resistors, both of the first and second stages, independently of each other, and the setting of one filter parameter does not affect the values ​​of other parameters.

The setting is carried out as follows:

1. The gain is set by resistors R2 of the first and R5 of the second stage.

2. The frequency of the pole of the first stage is adjusted by resistor R1, the frequency of the pole of the second stage is adjusted by resistor R4.

3. The quality factor of the second stage is regulated by the resistor R8, and the quality factor of the first stage is not regulated (it is constant for any rating of the elements).

The result of this course work is to obtain and calculate the scheme of a given filter. HPF with approximation of frequency characteristics by Butterworth polynomial with the parameters given in the terms of reference, has the third order and is a two-stage - connected HPF of the first order (based on a non-inverting amplifier) ​​and second order (based on impedance converters). The circuit contains three operational amplifiers, eight resistors and three capacitances. This circuit uses two power supplies of 15 V each.

The choice of circuit for each stage of the common filter was carried out on the basis of the technical task (to ensure low sensitivity to deviations in the values ​​of the elements), taking into account the advantages and disadvantages of each type of filter circuits used as the stages of the common filter.

The ratings of the circuit elements were selected and calculated in such a way as to bring them as close as possible to the standard nominal series E24, and also to obtain the largest possible input impedance of each filter stage.

After modeling the filter circuit using the ElectronicsWorkbench5.0 package (Fig. 5.1), frequency responses were obtained (Fig. 5.2), having the required parameters given in the terms of reference (Fig. 2.2).

The advantages of this scheme include the ease of setting all filter parameters, the independent setting of each stage separately, and low sensitivity to deviations from the element ratings.

The disadvantages are the use of three operational amplifiers in the filter circuit and, accordingly, its increased cost, as well as a relatively low input impedance (about 50 kOhm).

List of used literature

1. Zelenin A.N., Kostromitsky A.I., Bondar D.V. – Active filters on operational amplifiers. - Kh .: Teletekh, 2001. ed. second, correct. and additional - 150 p.: ill.

2. Resistors, capacitors, transformers, chokes, REA switching devices: Ref./N.N. Akimov, E.P. Vashchukov, V.A. Prokhorenko, Yu.P. Khodorenok. - Minsk: Belarus, 2004. - 591 p.: ill.

Analog integrated circuits: Ref./A.L. Bulychev, V.I. Galkin, 382 p.: V.A. Prokhorenko. - 2nd ed., revised. and additional - Minsk: Belarus, 1993. - hell.