Frequency filters are the simplest electrical circuits whose frequency response is nonlinear. The resistance in such circuits changes as the signal frequency changes. Such a circuit may consist of one or more circuit elements.
Passive and active low pass filters
A passive filter consists of resistors or capacitors only. They do not require energy to perform their assigned tasks. Almost all passive filters have a linear response.
An active filter includes a transistor or operational amplifier in its design. The frequency response of such a filter is more favorable than that of a passive one.
The question is, why and where are they used? Filters operate on the following principle: the signal received by them is filtered, and only those signals that are necessary remain. One of the areas of application of such devices is electronic color music.
Characteristics of frequency filters
The frequency at which the amplitude of the output signal decreases to a value of 0.7 from the input is called the cutoff frequency.
The slope of the frequency response of the filter. It shows how dramatically the signal changes after it has passed the filter. The larger the angle, the better.
Types of frequency filters
- Single element;
- G, T, U-shaped;
- Multi-star. They are series-connected L-shaped.
This article will discuss the circuits and design of a low-pass filter.
The simplest do-it-yourself low-pass filter
It is quite possible to make this device at home and its quality will not be much inferior to its store-bought counterpart. In addition, the low cost and simplicity of the design will pay off all the efforts invested.
What will be the characteristics
- Cutoff frequency – 300 Hz. The transmitted signal will not be higher than this indicator;
- Required voltage –9/30 V;
- Electricity consumption – 7 mA.
What you need to make a low pass filter:
- DD1 BA4558;
- VD1 D814B;
- C1, C2 10 µF;
- C3 0.033 µF;
- C4 220 nf;
- C5 100 nf;
- C6 100 µF;
- C7 10 µF;
- C8 100 nf;
- R1, R2 15 kOhm;
- R3, R4 100 kOhm;
- R5 47 kOhm;
- R6, R7 10 kOhm;
- R8 1 kOhm;
- R9 100 kOhm - variable;
- R10 100 kOhm;
- R11 2 kOhm.
Instructions on how to make a simple filter correctly
In a circuit that includes resistor R11, capacitor C6, and stabilizer VD1, a unit is assembled that stabilizes the incoming voltage. If the supplied voltage is less than 15 V, the resistor must be removed from the circuit.
Elements R1, R2, C1, C2 are adders of incoming signals. If the filter is fed with a mono signal, the adder can be removed. After this, you need to connect the signal source directly to the next (second) contact.
DD1.1 is an amplifier of the incoming signal, and DD1.2 contains a device that does not transmit high signals.
PCB manufacturing
We have described the circuit that needs to be used, now we will manufacture the most important element, namely the printed circuit board.
You need to take fiberglass, the width of which should be 2 cm and the length 4 cm. First, degrease the surface and sand it thoroughly. Then, after printing the diagram below, transfer it to a piece of fiberglass, observing the dimensions. It is recommended to use the LUT method.
Note! 
The design should be completely imprinted on the surface of the workpiece; if you did not succeed in doing this the first time, you can finish drawing the interrupted paths by hand.
We prepare a solution in which we will etch fiberglass. You need to take 2 tablespoons of citric acid and 6 tablespoons of hydrogen peroxide and mix them thoroughly. To speed up the mixing process, add a pinch of salt to the alkaline solution. Salt does not participate in the dissolution process.
You need to place the prepared workpiece with the drawn paths directly into the resulting solution. Before diving, make sure that the track pattern is well drawn, otherwise you will ruin the surface.
After waiting a little, make sure that all the excess copper layer has dissolved. Then you need to remove the workpiece from the container and rinse it in running water. Using acetone, remove ink from the board.
Assembly
In order to avoid mistakes during soldering, it is advisable to use a diagram. Solder all elements sequentially and carefully.
Note! 
Conclusion
The scheme described above should work after the first turn on. The filter does not require any settings. The main problems that may arise during startup are associated with poor-quality assembly or soldering, and in rare cases, with a malfunction of the circuit elements used.
In some cases, there is no sound after turning on the filter. To fix the problem you need to turn the variable resistor knob. If this does not help, check all connections at the solder points.
Photos of low pass filters
Note! 
Active filters are called electronic amplifiers containing R.C.-circuits, with the help of which the amplifier is given certain selective properties.
The use of amplifying elements distinguishes active filters from filters based on passive elements.
The advantages of active filters primarily include:
The ability to amplify a signal lying in the filter passband;
The ability to refuse the use of such low-tech elements as inductors, the use of which is incompatible with the methods of integral technology;
Easy to set up;
Small mass and volume, which weakly depend on the bandwidth, which is especially important when developing devices operating in the low-frequency region;
Simplicity of cascade inclusion when constructing high-order filters.
However, active filters have the following disadvantages that limit their scope of application:
Inability to use in power circuits, for example as filters in secondary power supplies;
The need to use an additional energy source intended to power the active elements of the amplifier;
Let's consider the general principles of using op-amps with frequency-dependent feedback loops to form devices with different frequency properties.
Low and High Pass Filters
The simplest active filters of low and high frequencies of the first order are, respectively, integrating (Figures 3.13, 3.14) and differentiating (Figures 3.16, 3.17) amplifiers. In them, the main element that determines the frequency response of the amplifier is a capacitor included in the feedback circuit.
The transfer functions of the simplest filters are first order equations, that's why filters are called first order filters. The slope of the logarithmic frequency response (LAFC) outside the passband for first-order filters is only -20 dB/dec, which indicates poor selective properties such filters.
To improve selectivity, it is necessary either to increase the order of the filter transfer function by introducing additional R.C.-circuits, or sequentially connect several identical active filters.
In practice, op-amps with feedback circuits are most often used as filters, the operation of which is described by second-order equations. If it is necessary to increase the selectivity of the system, several second-order filters are included sequentially(for example, to obtain a fourth-order low-pass filter, two second-order low-pass filters are connected sequentially, to obtain a sixth-order low-pass filter, three second-order low-pass filters are connected in series, etc.).
Active filters of low and high frequencies of the second order are shown in Figure 3.28, A, b. For them, with appropriate selection of resistor and capacitor values, the LFC decline outside the passband is 40 dB/dec. Moreover, as can be seen from Figure 3.28, the transition from a low-pass filter to a high-pass filter is carried out by replacing resistors with capacitors, and vice versa.
a b
Figure 3.28 - Low-pass filter ( A) and high-pass filter ( b) second order on an operational amplifier
The transfer function of a second-order low-pass filter is described by the expression
and the second-order high-pass filter - by the expression
The cutoff frequencies of second-order filters are respectively equal to:
; (3.40)
. (3.41)
Recently, active low-pass filters and second-order high-pass filters implemented on voltage followers have become widespread (the maximum value of the voltage gain for such filters within the passband is 1). The circuits of these filters are shown in Figure 3.29, A(LPF) and 3.29, b(HPF).
a b
Figure 3.29 - Low-pass filter ( A) and high-pass filter ( b) second order on voltage followers
The sequence of calculation of filter elements based on repeaters is as follows:
a) using the graphs (Figure 3.30), select the appropriate filter characteristic (taking into account the required selectivity) and determine the number of poles required to obtain the desired attenuation;
b) select a suitable filter circuit from the repeater circuits (Figure 3.29);
c) using the data in Table 3.2, perform the necessary recalculation of the parameters of the filter elements.
Table 3.2 gives the capacitance values (in farads) for the repeater circuit depending on the number of filter poles. In this case, to obtain a filter, for example, a fourth order, a cascade connection of two identical repeaters is used, but the elements of the first cascade are calculated as for a filter with two poles, and the elements of the second cascade as for a filter with four poles.
Figure 3.30 - Amplitude-frequency characteristics of low-pass filter (left) and high-pass filter (right) Butterworth
Table 3.2 - Capacitor values (farads)
| Number of poles | Bessel filter | Butterworth filter | ||
| C 1 | WITH 2 | C 1 | WITH 2 | |
| 0,9066 | 0,6799 | 1,414 | 0,7071 | |
| 0,7351 1,0120 | 0,6746 0,3900 | 1,082 2,613 | 0,9241 0,3825 | |
| 0,6352 0,7225 1,0730 | 0,6098 0,4835 0,2561 | 1,035 1,414 3,863 | 0,9660 0,7071 0,2588 | |
| 0,5673 0,6090 0,7257 1,1160 | 0,5539 0,4861 0,3590 0,1857 | 1,091 1,202 1,800 5,125 | 0,9809 0,8313 0,5557 0,1950 | |
| 0,5172 0,5412 0,5999 0,7326 1,1510 | 0,5092 0,4682 0,3896 0,2792 0,1437 | 1,012 1,122 1,414 2,202 6,389 | 0,9874 0,8908 0,7071 0,4540 0,1563 |
Figure 3.31 shows the procedure for calculating filter circuits using repeaters using the example of a two-pole low-pass filter (left) and a Butterworth high-pass filter (right) with a cutoff frequency f in= 1 kHz.
The component values taken from Table 3.2 for the low-pass filter circuit are normalized for a frequency of 1 rad/s with a resistor resistance of 1 Ohm and capacitor capacity in farads. The capacitances of the filter capacitors are recalculated by frequency by dividing the capacitance values taken from the table by the cutoff frequency in radians (2p f in). The filter components are recalculated by multiplying the resistance values by a suitable coefficient (for example, 10 4) and dividing the capacitance values by the same coefficient. As a result, we obtain the following values for the parameters of the low-pass filter elements: WITH 1 = 0.0225 µF, WITH 2 = 0.0112 µF, R 1 = R 2 = 10 kOhm.
The component values taken from Table 3.2 for the high-pass filter circuit are normalized for a frequency of 1 rad/s with a capacitor capacity of 1 F and resistor resistance in ohms, the reciprocal of the capacitance values. The capacitances of the filter capacitors are recalculated by frequency by dividing the capacitance values by the cutoff frequency in radians (2p f n). The filter components are recalculated by multiplying the resistance values by a suitable coefficient (for example, 14.1 10 3) and dividing the capacitance values by the same coefficient. As a result, we obtain the following values for the parameters of the high-pass filter elements: WITH 1 = WITH 2 = 0.0113 µF, R 1 = 10 kOhm, R 2 = 20 kOhm.
Bandpass and notch filters
simplest band pass filter can be obtained by combining low-pass and high-pass filters (e.g., integrator and differentiator). An example of such a circuit is shown in Figure 3.32, A, and its logarithmic frequency response is in Figure 3.32, b.
The filter cutoff frequencies are determined from the expressions:
Figure 3.31 - Sequence of calculation of low-pass filter (left) and high-pass filter (right)
For measurement technology and signal processing technology, three types of PF circuits are of interest:
- multi-loop feedback filter- used for quality factors up to 10 and differs favorably from other circuits in that it has only one operational amplifier;
- biquad resonator- is a more complex electrical filter, performed on three op-amps and providing a quality factor of up to 200;
- switched filter- provides a quality factor of up to 1000, necessary for the selection of narrow-band signals.
A
Figure 3.32 - Circuit and logarithmic frequency response of a bandpass filter
Quality factor Q in all cases is determined by the following relation
Where f 0 - average frequency of the passband;
D f- bandwidth at -3 dB (that is, at 0.707 K U max).
Frequency response of bandpass filters for various values Q are shown in Figure 3.33.
 |
Figure 3.33 - Frequency response of bandpass filters at different Q values
Figure 3.34 shows the circuit of a bandpass filter with multi-loop feedback (MFMOS) and the type of its frequency response.
Figure 3.34 - Bandpass filter with multi-loop feedback
Resistor values R1, R2 And R3 PFMOS at a given capacitor capacity WITH= 1 µF, selected taking into account the required quality factor Q and mid frequency f 0 by formulas:
, (3.46)
To obtain maximum filter stability, the calculation is carried out for unity gain at frequency f 0 .
Second order bandpass filter can be performed according to the scheme shown in Figure 3.45.
Figure 3.45 - Second-order bandpass filter
The quasi-resonant frequency of the second order PF (at which the filter transmission coefficient is maximum) can be found from the expression
. (3.49)
Notch filter can be obtained based on the PFMOS circuit if a non-inverting adder is connected to its output (Figure 3.46). In such a scheme, allocated at frequency f 0, the signal from the output of the inverting PFMOS, the voltage gain of which is equal to unity, is supplied to one of the inputs of the non-inverting adder. The input broadband signal is fed to the second input of the adder also without amplification and without phase change. As a result of the addition of two signals in antiphase, the signal is suppressed in the region of the notch frequency f 0, that is, the required type of frequency response for the notch filter is provided.
Figure 3.46 - Notch filter based on the PFMOS circuit
It should be noted that only individual examples of constructing active filter circuits are considered above. In practice, circuits based on a Wien bridge or a double T-bridge are also widely used.
When assembling amplifiers for cars using TDA 7293 or TDA 7294 microcircuits, sometimes there is a need for a compact filter unit, preferably one that is simple and understandable, and also has normal characteristics and is also an adder. It is in this article that I provide such a craft and a diagram.
The circuit is assembled using just one bipolar, low-power transistor. You can, of course, use a passive filter for the subwoofer, for example, from just one LC filter, it could filter the sound to a frequency of 20-150 Hz, but this is not advisable, since at the output we will get the same thing as at the input. This is precisely why we need to filter the initial sound well.
Why do they use low-pass filters, because when filtering, so to speak, with each step, the sound rating at the input decreases hundreds of times, and when we apply this rating to the subwoofer, it is not enough or simply not enough for normal build-up.
In the circuit presented in this article, almost the same thing happens, but with the exception that there is one transistor on which the pre-amplifier is assembled, and which has already “filtered” the audio signal and amplified it to feed it to the final amplifier.
a signet for those who are going to etch a board.
At the input of the filter, an adder is assembled that sums both channels, and subsequently the signal enters a passive filter with a cutoff frequency of 150 Hz. The second channel filter has an output amplifier. There is also a peculiarity of this circuit in that you can adjust the cutoff from 15 to 30 Hz.
The circuit does not require any adjustments or adjustments. The only adjustment is the cutoff frequency, which can be adjusted to suit your taste, since the circuit has a dual 100 kOhm regulator (you can take a nominal value from 47 to 2200 kOhm).
The circuit works perfectly with any audio frequency power amplifiers, both low-power 12-Volts and powerful bipolar ones.
Domestic or imported transistors feel great in this circuit, so the choice is yours.
And I also want to note one point: if you have a situation that requires you to contact a car dealership, then first find out about it by reading reviews. It's better to go when you know where you're going...
The proposed schemes are designed just for such cases. Most of them were developed at the request of workers. Therefore, by the way, there are few drawings of printed circuit boards - this is a purely individual matter, depending on the details and the layout as a whole. But a lot depends on the board, including the number of rake that the radio amateur will step on when repeating, so all additions are welcome. For now, I’m designing boards only for designs for personal use, I don’t have time for everything...
During development, two conditions were set:
- make do with only a unipolar 12 volt power supply, so as not to deal with the manufacture of converters and not to go inside the amplifier for increased voltage
- the scheme should be extremely simple and not require special qualifications to repeat
The first diagram is intended for the simplest installations. Therefore, its characteristics are far from ideal, but the capabilities are quite sufficient. The wide range of frequency tuning of the cutoff frequency allows the subwoofer to be used with almost any acoustic system. If the radio does not have linear outputs, it doesn’t matter. The circuit can also work from the speaker outputs of the radio. To do this, you only need to increase the resistance of resistors R1, R2 to 33...100 kOhm.
List of radioelements
| Designation | Type | Denomination | Quantity | Note | Shop | My notepad |
|---|---|---|---|---|---|---|
| VT1 | Bipolar transistor | KT3102 | 1 | BC546 | To notepad | |
| C1 | 1 µF 10V | 1 | To notepad | |||
| C2 | Capacitor | 100 nF | 1 | To notepad | ||
| C3 | Capacitor | 68 nF | 1 | To notepad | ||
| C4 | Capacitor | 33 nF | 1 | To notepad | ||
| C5 | Electrolytic capacitor | 100 µF 16V | 1 | To notepad | ||
| C6 | Electrolytic capacitor | 100 µF 10V | 1 | To notepad | ||
| VR1 | Variable resistor | 100 kOhm | 1 | Double | To notepad | |
| R1-R5 | Resistor | 10 kOhm | 5 | To notepad | ||
| R6 | Resistor | 200 kOhm | 1 | To notepad | ||
| R7 | Resistor | 240 kOhm | 1 |
This filter was made for a powerful car subwoofer. The presented scheme is one that cuts off all unnecessary bands, leaving only low ones. The signal is then amplified and fed to the input of the subwoofer amplifier. It is thanks to this low-pass filter that the head plays at low frequencies (commonly called BASS).
Active subwoofer circuit
In addition to the low-pass filter, the board also contains a adder, which is designed to sum the signal of both channels. A signal from two channels (stereophonic) is supplied to the input of this block; when it enters the adder, the signal turns into one single one, this makes it possible to obtain additional amplification. After summation, the signal is filtered and frequencies below 16Hz and above 300Hz are cut off. The control filter cuts the signal from 35Hz - 150Hz.
Thus, we receive a low-frequency signal with the ability to adjust within the specified limits. There is also a phase control, which makes it possible to match the subwoofer with the car's acoustics.
In the low-pass filter circuit I used only film capacitors; they say they are better than ceramics in amplifiers, but they also work very well with ceramic ones, the difference is not too big.
The installation is carried out on a printed circuit board, which was created using the LUT method.
LPF.lay
Such a subwoofer is powered by a bipolar power source (+/-15V), since it works in conjunction with a powerful one. If you have only one power source to power the amplifier and filter unit (as in my case), then the low-pass filter unit requires a bipolar voltage regulator.
Such a combiner and low-pass filter unit can work with literally any power amplifiers. Three controls, one of them is designed to adjust the volume, the other is for cutting low frequencies, the third is a smooth phase control (as mentioned above).
In my case, only microcircuits were purchased; all other passive components were removed from old boards. The film capacitors at the low-pass filter input were soldered off from an old TV, in a word, the costs for such a unit are minimal, no more than $3, in return you can be proud that a similar filter unit is used in modern car amplifiers, the price of which is about $400.
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