Good day, dear readers! Today we will talk about assembling a simple low-pass filter. But despite its simplicity, the quality of the filter is not inferior to store-bought analogues. So let's get started!
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Yuri Sadikov
Moscow
The article presents the results of work on creating a device that is a set of active filters for building high-quality three-band low-frequency amplifiers of the HiFi and HiEnd classes.
In the process of preliminary studies of the total frequency response of a three-band amplifier built using three second-order active filters, it turned out that this characteristic has a very high unevenness at any filter junction frequencies. At the same time, it is very critical to the accuracy of filter settings. Even with a small mismatch, the unevenness of the total frequency response can be 10...15 dB!
MASTER KIT produces a set NM2116, from which you can assemble a set of filters, built on the basis of two filters and a subtractive adder, which does not have the above disadvantages. The developed device is insensitive to the parameters of the cutoff frequencies of individual filters and at the same time provides a highly linear total frequency response.
The main elements of modern high-quality sound reproducing equipment are acoustic systems (AS).
The simplest and cheapest are single-way speakers that contain one loudspeaker. Such acoustic systems are not capable of operating with high quality in a wide frequency range due to the use of a single loudspeaker (loudspeaker head - GG). When reproducing different frequencies, different requirements are placed on the GG. At low frequencies (LF), the speaker must have a large and rigid cone, a low resonant frequency and have a long stroke (to pump a large volume of air). And at high frequencies (HF), on the contrary, you need a small, lightweight but solid diffuser with a small stroke. It is almost impossible to combine all these characteristics in one loudspeaker (despite numerous attempts), so a single loudspeaker has high frequency unevenness. In addition, in wideband loudspeakers there is an intermodulation effect, which manifests itself in the modulation of high-frequency components of an audio signal by low-frequency ones. As a result, the sound picture is disrupted. The traditional solution to this problem is to divide the reproduced frequency range into subranges and build acoustic systems based on several speakers for each selected frequency subrange.
Passive and active electrical isolation filters
To reduce the level of intermodulation distortion, electrical isolation filters are installed in front of the loudspeakers. These filters also perform the function of distributing the energy of the audio signal between the GG. They are designed for a specific crossover frequency, beyond which the filter provides a selected amount of attenuation, expressed in decibels per octave. The slope of the attenuation of the separating filter depends on the design of its construction. The first order filter provides an attenuation of 6 dB/oct, the second order - 12 dB/oct, and the third order - 18 dB/oct. Most often, second-order filters are used in speakers. Filters of higher orders are rarely used in speakers due to the complex implementation of the exact values of the elements and the lack of need to have higher attenuation slopes.
The filter separation frequency depends on the parameters of the GG used and on the properties of hearing. The best choice of crossover frequency is at which each GG speaker operates within the piston action area of the diffuser. However, in this case, the speaker must have many crossover frequencies (respectively, GG), which significantly increases its cost. It is technically justified that for high-quality sound reproduction it is enough to use three-band frequency separation. However, in practice there are 4, 5 and even 6-way speaker systems. The first (low) crossover frequency is selected in the range of 200...400 Hz, and the second (middle) crossover frequency in the range of 2500...4000 Hz.
Traditionally, filters are made using passive L, C, R elements, and are installed directly at the output of the final power amplifier (PA) in the speaker housing, according to Fig. 1.
Fig.1. Traditional performance of speakers.
However, this design has a number of disadvantages. Firstly, to ensure the required cutoff frequencies, you have to work with fairly large inductances, since two conditions must be met simultaneously - to provide the required cutoff frequency and to ensure that the filter is matched with the GG (in other words, it is impossible to reduce the inductance by increasing the capacitance included in the filter). It is advisable to wind inductors on frames without the use of ferromagnets due to the significant nonlinearity of their magnetization curve. Accordingly, air inductors are quite bulky. In addition, there is a winding error, which does not allow for an accurately calculated cutoff frequency.
The wire used to wind the coils has a finite ohmic resistance, which in turn leads to a decrease in the efficiency of the system as a whole and the conversion of part of the useful power of the PA into heat. This is especially noticeable in car amplifiers, where the supply voltage is limited to 12 V. Therefore, to build car stereo systems, GGs with reduced winding resistance (~2...4 Ohms) are often used. In such a system, the introduction of additional filter resistance of the order of 0.5 Ohm can lead to a decrease in output power by 30%...40%.
When designing a high-quality power amplifier, they try to minimize its output impedance to increase the degree of damping of the GG. The use of passive filters significantly reduces the degree of damping of the GG, since additional filter reactance is connected in series with the amplifier output. For the listener, this manifests itself in the appearance of “booming” bass.
An effective solution is to use not passive, but active electronic filters, which do not have all the listed disadvantages. Unlike passive filters, active filters are installed before the PA as shown in Fig. 2.
Fig.2. Construction of a sound-reproducing path using active filters.
Active filters are RC filters on operational amplifiers (op amps). It is easy to build active audio filters of any order and with any cutoff frequency. Such filters are calculated using tabular coefficients with a pre-selected filter type, required order and cutoff frequency.
The use of modern electronic components makes it possible to produce filters with minimal intrinsic noise levels, low power consumption, dimensions and ease of execution/replication. As a result, the use of active filters leads to an increase in the degree of damping of the GG, reduces power losses, reduces distortion and increases the efficiency of the sound reproduction path as a whole.
The disadvantages of this architecture include the need to use several power amplifiers and several pairs of wires to connect speaker systems. However, this is not critical at this time. The level of modern technology has significantly reduced the price and size of the mind. In addition, quite a lot of powerful integrated amplifiers with excellent characteristics have appeared, even for professional use. Today, there are a number of ICs with several PAs in one case (Panasonic produces the RCN311W64A-P IC with 6 power amplifiers specifically for building three-way stereo systems). In addition, the PA can be placed inside the speakers and short, large-section wires can be used to connect the speakers, and the input signal can be supplied via a thin shielded cable. However, even if it is not possible to install the PA inside the speakers, the use of multi-core connecting cables does not pose a difficult problem.
Modeling and selection of the optimal structure of active filters
When constructing a block of active filters, it was decided to use a structure consisting of a high-pass filter (HPF), a medium-frequency filter (band-pass filter, PSF) and a low-pass filter (LPF).
This circuit solution was practically implemented. A block of active filters LF, HF and PF was built. A three-channel adder was chosen as a model of a three-way speaker, providing summation of frequency components, according to Fig. 3.
Fig.3. Model of a three-channel speaker with a set of active filters and a filter filter on the PF.
When measuring the frequency response of such a system, with optimally selected cutoff frequencies, it was expected to obtain a linear dependence. But the results were far from expected. At the junction points of the filter characteristics, dips/overshoots were observed depending on the ratio of the cutoff frequencies of neighboring filters. As a result, by selecting the cutoff frequency values, it was not possible to bring the pass-through frequency response of the system to a linear form. The nonlinearity of the pass-through characteristic indicates the presence of frequency distortions in the reproduced musical arrangement. The results of the experiment are presented in Fig. 4, Fig. 5 and Fig. 6. Fig. 4 illustrates the pairing of a low-pass filter and a high-pass filter at a standard level of 0.707. As can be seen from the figure, at the junction point the resulting frequency response (shown in red) has a significant dip. When expanding the characteristics, the depth and width of the gap increases, respectively. Fig. 5 illustrates the pairing of a low-pass filter and a high-pass filter at a level of 0.93 (shift in the frequency characteristics of the filters). This dependence illustrates the minimum achievable unevenness of the pass-through frequency response by selecting the cutoff frequencies of the filters. As can be seen from the figure, the dependence is clearly not linear. In this case, the cutoff frequencies of the filters can be considered optimal for a given system. With a further shift in the frequency characteristics of the filters (matching at a level of 0.97), an overshoot appears in the pass-through frequency response at the junction point of the filter characteristics. A similar situation is shown in Fig. 6.
Fig.4. Low-pass frequency response (black), high-pass frequency response (black) and pass-through frequency response (red), matching at level 0.707.
Fig.5. Low-pass frequency response (black), high-pass frequency response (black) and pass-through frequency response (red), matching at level 0.93.
Fig.6. Low-pass frequency response (black), high-pass frequency response (black) and pass-through frequency response (red), matching at the level of 0.97 and the appearance of an overshoot.
The main reason for the nonlinearity of the pass-through frequency response is the presence of phase distortions at the boundaries of the filter cutoff frequencies.
A similar problem can be solved by constructing a mid-frequency filter not in the form of a bandpass filter, but using a subtractive adder on an op-amp. The characteristics of such a PSF are formed in accordance with the formula: Usch = Uin - Uns - Uss
The structure of such a system is shown in Fig. 7.
Fig.7. Model of a three-channel speaker with a set of active filters and a PSF on a subtractive adder.
With this method of forming a mid-frequency channel, there is no need to fine-tune adjacent filter cutoff frequencies, because The mid-frequency signal is formed by subtracting the high- and low-pass filter signals from the total signal. In addition to providing complementary frequency responses, the filters also produce complementary phase responses, which guarantees the absence of emissions and dips in the total frequency response of the entire system.
The frequency response of the mid-frequency section with cutoff frequencies Fav1 = 300 Hz and Fav2 = 3000 Hz is shown in Fig. 8. According to the fall in the frequency response, an attenuation of no more than 6 dB/oct is ensured, which, as practice shows, is quite sufficient for the practical implementation of the PSF and obtaining high-quality sound of the midrange GG.
Fig.8. Frequency response of the mid-pass filter.
The pass-through transmission coefficient of such a system with a low-pass filter, a high-pass filter and a high-pass filter on a subtracting adder turns out to be linear over the entire frequency range of 20 Hz...20 kHz, according to Fig. 9. Amplitude and phase distortions are completely absent, which ensures crystal purity of the reproduced sound signal.
Fig.9. Frequency response of a filter system with a frequency filter on a subtractive adder.
The disadvantages of such a solution include strict requirements for the accuracy of the values of resistors R1, R2, R3 (according to Fig. 10, which shows the electrical circuit of the subtracting adder) that ensure balancing of the adder. These resistors should be used within 1% accuracy tolerances. However, if problems arise with the acquisition of such resistors, you will need to balance the adder using trimming resistors instead of R1, R2.
Balancing the adder is performed using the following method. First, a low-frequency oscillation with a frequency much lower than the low-pass filter cutoff frequency, for example 100 Hz, must be applied to the input of the filter system. By changing the value of R1, it is necessary to set the minimum signal level at the output of the adder. Then an oscillation with a frequency obviously higher than the high-pass filter cutoff frequency, for example 15 kHz, is applied to the input of the filter system. By changing the value of R2, the minimum signal level at the output of the adder is again set. The setup is complete.
Fig. 10. Subtractive adder circuit.
Methodology for calculating active low-pass filters and high-pass filters
As theory shows, to filter the frequencies of the audio range, it is necessary to use Butterworth filters of no more than the second or third order, ensuring minimal unevenness in the passband.
The second-order low-pass filter circuit is shown in Fig. 11. Its calculation is made according to the formula:
where a1=1.4142 and b1=1.0 are tabular coefficients, and C1 and C2 are selected from the ratio C2/C1 greater than 4xb1/a12, and you should not choose the ratio C2/C1 much greater than the right side of the inequality.
Fig. 11. 2nd order Butterworth low pass filter circuit.
The second-order high-pass filter circuit is shown in Fig. 12. Its calculation is made using the formulas:
where C=C1=C2 (set before calculation), and a1=1.4142 and b1=1.0 are the same table coefficients.
Fig. 12. 2nd order Butterworth high-pass filter circuit.
MASTER KIT specialists have developed and studied the characteristics of such a filter unit, which has maximum functionality and minimal dimensions, which is essential when using the device in everyday life. The use of modern element base made it possible to ensure maximum quality of development.
Technical characteristics of the filter unit
The electrical circuit diagram of the active filter is shown in Fig. 13. The list of filter elements is given in the table.
The filter is made using four operational amplifiers. The op-amps are combined in one MC3403 (DA2) IC package. DA1 (LM78L09) contains a supply voltage stabilizer with corresponding filter capacitors: C1, C3 at the input and C4 at the output. An artificial midpoint is made on the resistive divider R2, R3 and capacitor C5.
The DA2.1 op amp has a buffer cascade for pairing the output and input impedances of the signal source and low-pass, high-pass and mid-range filters. A low-pass filter is assembled on op-amp DA2.2, and a high-pass filter is assembled on op-amp DA2.3. Op-amp DA2.4 performs the function of a bandpass midrange filter shaper.
The supply voltage is supplied to contacts X3 and X4, and the input signal is supplied to contacts X1, X2. The filtered output signal for the low-frequency path is removed from contacts X5, X9; with X6, X8 – HF and with X7, X10 – MF paths, respectively.
Fig. 13. Electrical circuit diagram of an active three-band filter
List of elements of an active three-band filter
| Position | Name | Note | Col. |
| C1, C4 | 0.1 µF | Designation 104 | 2 |
| C2, C10, C11, C12, C13, C14, C15 | 0.47 µF | Designation 474 | 7 |
| C3, C5 | 220 µF/16 V | Replacement 220 uF/25 V | 2 |
| C6, C8 | 1000 pF | Designation 102 | 2 |
| C7 | 22 nF | Designation 223 | 1 |
| C9 | 10 nF | Designation 103 | 1 |
| DA1 | 78L09 | 1 | |
| DA1 | MC3403 | Replacement LM324, LM2902 | 1 |
| R1…R3 | 10 kOhm | 3 | |
| R8…R12 | 10 kOhm | Tolerance no more than 1%* | 5 |
| R4…R6 | 39 kOhm | 3 | |
| R7 | 75 kOhm | - | 1 |
| DIP-14 block | 1 | ||
| Pin connector | 2 pin | 2 | |
| Pin connector | 3 pin | 2 |
The appearance of the filter is shown in Fig. 14, the printed circuit board is shown in Fig. 15, the location of the elements is shown in Fig. 16.
Structurally, the filter is made on a printed circuit board made of foil fiberglass. The design provides for installation of the board into a standard BOX-Z24A case; for this purpose, mounting holes are provided along the edges of the board with a diameter of 4 and 8 mm. The board is secured in the case with two self-tapping screws.
Fig. 14. External view of the active filter.
Fig. 15. Active filter printed circuit board.
Fig. 16. Arrangement of elements on the active filter printed circuit board.
When working with electrical signals, it is often necessary to isolate one frequency or frequency band from them (for example, to separate noise and useful signals). Electric filters are used for such separation. Active filters, unlike passive ones, include op-amps (or other active elements, for example, transistors, vacuum tubes) and have a number of advantages. They provide better separation of the transmission and attenuation bands; in them, it is relatively easy to adjust the unevenness of the frequency response in the transmission and attenuation regions. Also, active filter circuits typically do not use inductors. In active filter circuits, frequency characteristics are determined by frequency-dependent feedback.
The low pass filter circuit is shown in Fig. 12.
Rice. 12. Active low pass filter.
The transmission coefficient of such a filter can be written as
,
(5)
And 
. (6)
At TO 0 >>1
Transmission coefficient 
in (5) turns out to be the same as for a second-order passive filter containing all three elements ( R,
L,
C) (Fig. 13), for which:
Rice. 14. Frequency response and phase response of an active low-pass filter for differentQ .
If R 1 = R 3 = R And C 2 = C 4 = C(in Fig. 12), then the transmission coefficient can be written as
Amplitude and phase frequency characteristics of an active low-pass filter for different quality factors Q shown in Fig. 14 (the parameters of the electrical circuit are selected so that ω 0 = 200 rad/s). The figure shows that with increasing Q
The active low-pass filter of the first order is implemented by the circuit Fig. 15.
Rice. 15. Active low-pass filter of the first order.
The filter transmission coefficient is
.
The passive analogue of this filter is shown in Fig. 16.
Comparing these transmission coefficients, we see that for the same time constants τ’ 2 And τ the modulus of the gain of the first order active filter will be in TO 0 times more than the passive one.
Rice. 17.Simulink-active low pass filter model.
You can study the frequency response and phase response of the active filter under consideration, for example, in Simulink, using a transfer function block. For electrical circuit parameters TO R = 1, ω 0 = 200 rad/s and Q = 10 Simulink-the model with the transfer function block will look as shown in Fig. 17. Frequency response and phase response can be obtained using LTI- viewer. But in this case it is easier to use the command MATLAB freqs. Below is a listing for obtaining frequency response and phase response graphs.
w0=2e2; %natural frequency
Q=10; % quality factor
w=0:1:400; %frequency range
b=; %vector of the numerator of the transfer function:
a=; %vector of the denominator of the transfer function:
freqs(b,a,w); %calculation and construction of frequency response and phase response
Amplitude-frequency characteristics of an active low-pass filter (for τ = 1s and TO 0 = 1000) are shown in Fig. 18. The figure shows that with increasing Q the resonant nature of the amplitude-frequency characteristic is manifested.
Let's build a model of a low-pass filter in SimPowerSystems, using the op-amp block we created ( operationalamplifier), as shown in Figure 19. The operational amplifier block is nonlinear, so in the settings Simulation/ ConfigurationParametersSimulink to increase the calculation speed you need to use methods ode23tb or ode15s. It is also necessary to choose the time step wisely.
Rice. 18. Frequency response and phase response of the active low-pass filter (forτ = 1c).
Let R 1 = R 3 = R 6 = 100 Ohm, R 5 = 190 Ohm, C 2 = C 4 = 5*10 -5 F. For the case when the source frequency coincides with the natural frequency of the system ω 0 , the signal at the filter output reaches its maximum amplitude (shown in Fig. 20). The signal represents steady-state forced oscillations with the source frequency. The graph clearly shows the transient process caused by turning on the circuit at a moment in time t= 0. The graph also shows deviations of the signal from the sinusoidal shape near the extremes. In Fig. 21. An enlarged part of the previous graph is shown. These deviations can be explained by op-amp saturation (maximum permissible voltage values at the op-amp output ± 15 V). It is obvious that as the amplitude of the source signal increases, the area of signal distortion at the output also increases.
Rice. 19. Model of an active low-pass filter inSimPowerSystems.
Rice. 20. Signal at the output of an active low-pass filter.
Rice. 21. Fragment of the signal at the output of an active low-pass filter.
Hello, dear radio amateurs! Today I want to offer you a low-pass filter circuit for anyone. I have tried quite a few filter circuits, of which some either did not suit the sound, or were started dancing to a tambourine, or were started by throwing them against the wall! And then one fine day I was surfing around a forum and came across a post with a diagram. As they wrote, the circuit was found on some forum in a long-forgotten topic and he was very pleased with its repeatability and good bass sound. Many thanks to this man! I also decided to repeat this circuit, since I had been looking for a good low-pass filter for a long time and the required microcircuit was available.
Copy to enlarge
The heart of the circuit is the well-proven TL074 (084), one dual variable resistor, in such a non-standard connection for me, and a few passive components (resistors and capacitors). I decided that for power supply I would give up any extra stabilizers (7815 and 7915) - the circuit consumption is small, and therefore it was decided to power the circuit in a simple way - a pair of zener diodes (I used 1N4712), a pair of limiting resistors (1.5 kom for me), small electrolytes for power supply and shunt capacitors of 0.1 uF - all this to the main power supply of the ULF subwoofer (+-35 volts in my case).
The installation is carried out on a printed circuit board made of textolite - download the file. I slightly adjusted the signet to suit myself and added zener diodes. All elements are signed, hover the cursor over the elements - its denomination is shown. Variable resistors that regulate the cutoff frequency and volume control, in my version, are removed from the board on wiring.
The circuit works right away, I’ve already done this low-pass filter ten times - of course, if you don’t confuse the values and don’t leave nozzles between the tracks. I also want to say that the sensitivity of the filter is enough to connect portable sound sources such as a cell phone, mp3 player and similar devices.
Have you prepared the board? Then take a soldering iron, and first of all solder the zener diodes with limiting resistors and capacitors, the socket for the TL. Connect the board to the power source of your ULF (I have +-35 volts) - make sure that +-12 volts are supplied to the sockets at pins 4 and 11 of the microcircuit. If everything is correct, we solder capacitors and resistors.
Do not forget that film capacitors must be installed in such circuits, not counting electrolytes and power supply shunts.
A variable resistor for adjusting the frequency cutoff must be connected exactly as shown in the diagram. I repeat that the circuit does not need adjustments, correct installation and cleaning of the scarf from flux, if you used the one mentioned.
Now in my subwoofer designs, I always use this filter for its good bass quality and simple circuit. Also without unnecessary unnecessary bells and whistles. I recommend, as they say to repeat, I was with you Akplex.
Discuss the article LOW PASS FILTER FOR SUBWOOFER
Psychoacoustics (the science that studies sound and its effect on humans) has established that the human ear is capable of perceiving sound vibrations in the range from 16 to 20,000 Hz. Despite the fact that the range is 16-20 Hz (low frequencies), it is no longer perceived by the ear itself, but by the organs of touch.
Many music lovers are faced with the fact that most of the supplied speaker systems do not fully satisfy their needs. There are always minor flaws, unpleasant nuances, etc., which encourage you to assemble speakers and amplifiers with your own hands.
There may be other reasons for assembling a subwoofer (professional interest, hobby, etc.).
Subwoofer (from the English “subwoofer”) is a low-frequency speaker that can reproduce sound vibrations in the range of 5-200 Hz (depending on the type of design and model). It can be passive (uses the output signal from a separate amplifier) or active (equipped with a built-in signal amplifier).
Low frequencies (bass), in turn, can be divided into three main subtypes:
Frequency filters are used for both active and passive subwoofers.
The advantages of active woofers are as follows:
By implementation
Type
According to the steepness of the decline
Main characteristics of filters:
Additional parameters for evaluating acoustic signal filters:
Linear filters of electronic signals differ from each other in the type of frequency response curves (dependence of indicators).
Varieties of such filters are most often named after the names of the scientists who identified these patterns:
And others.
The simplest low-pass filter for a subwoofer the second order looks like this: an inductance (coil) connected in series to the speaker and a capacitance (capacitor) in parallel. This is the so-called LC filter (L is the designation for inductance on electrical circuits, and C is for capacitance).
The operating principle is as follows:
This type of filter is passive. More difficult to implement are active filters.
As mentioned above, the simplest ones in design are passive filters. They contain only a few elements (the number depends on the required filter order).
You can assemble your own low-pass filter using ready-made circuits online or using individual parameters after detailed calculations of the required characteristics (for convenience, you can find special calculators for filters of different orders, with which you can quickly calculate the parameters of the constituent elements - coils, capacitors, etc. ).
For active filters (crossovers), you can use specialized software, for example, “Crossover Elements Calculator”.
In some cases, a filter adder may be needed when designing a circuit.
Here, both sound channels (stereo), for example, after output from an amplifier, etc., must first be filtered (leaving only low frequencies), and then combined into one using a adder (since most often only one subwoofer is installed). Or vice versa, first sum and then filter out low frequencies.
As an example, let's take the simplest second-order passive low-pass filter.
If the speaker impedance is 4 Ohms, the expected cutoff frequency is 150 Hz, then Butterworth filtering will be needed.
