Goodness is where to lie. Shifting the Q circuit. Higher quality factor than the resonant curve

Golovna / Zakhist

Shifting the Q circuit
A. Partin, metro station Yekaterinburg

The main indicator of the effectiveness of the colival circuit is the quality factor (Q). The physical quality factor is the value of the energy stored in the circuit before it is dissipated. The quality factor lies in the energy losses in the circuit, such as the heating of the wires, the losses in the capacitor and the inductance coil, as well as the vibration of electromagnetic coils in the excess medium. Even though the infusion circuit is not ideally prepared, it must be an active support.
The active power of the coil increases with increasing frequency and can increase tenfold. This is due to the fact that the alternating high-frequency stream rises closer to the surface of the conductor (skin effect). Why, to increase the quality factor of the coils, they are wound with insulated high-conductor wire of the LESHO type. The quality factor of the contour coil QL is calculated as follows:

de
- Frequency circuit;
L – coil inductance;
RL – expend.
The quality factor of the capacitor Qc is calculated using the formula


de
C – capacitor capacity;
RC – expend.

The quality factor of the Q circuit is the higher quality factor of its elements and is indicated by:

; .

de
ρ - characteristic (hvylovy) support to the contour;
r=rC +rL - summary reference to the contour.

Don’t forget the basic formula that determines the resonant frequency fp of the coli- val circuit:

Also, if you try to change one parameter of the circuit, for example L, so that the frequency does not “lose”, the additional LC is liable to lose power. One and the same resonant frequency can be taken away at different values ​​of inductance and capacitance, just as one and the same rectangular area can be taken away at different ratios of its sides. In order to obtain a high quality factor for the circuit, the choice of the values ​​of L and Z is important for singing minds. When designing injector circuits with a high quality factor, the advantage is given to coils with higher inductance. Great inductance means a high number of turns, and for high quality of conductor the traces are compatible, which is not always possible.

The hardening of pheromagnetic cores allows you to change the size of the coil and increase its quality factor. In addition, with the help of adjusting cores it is easy to regulate the inductance of the coils. However, with ferromagnetic cores, the amount of inductance and, apparently, the quality factor of the coils depends on the size of the stream that flows. This deposit is particularly strong in closed magnetic circuits (toroids). With greater current there is a waste of the magnetic powers of the heart.

on Fig.1 readings of transistor resonant booster at a frequency of 503 kHz, and in table 1 indicated by L, This is the corresponding value of the enhancement factor.
on Fig.2 readings dry filter at low frequency (503 kHz), table 2- ratings of LC components and filter attenuation coefficient.

I'll give you a couple of practical tips To do this, you can simply adjust the incinerator circuit to the desired frequency. For this you need a standard signal generator (GSS-6, G4-18a, G4-42 etc.) and a low-frequency oscilloscope.
Method 1. We connect the coil and then graduate the capacitor with an exchangeable capacity into the last lancer (Fig.3). This lance is connected to the 1 V socket of the generator (GSS). All attenuators are installed as much as possible. Before the display, turn on the generator, set the required frequency and close the output of the generator (1) to the housing. If the attenuators are set to maximum, the needle of the internal voltmeter will move to zero.
We connect the lance and set it up. The arrow is placed on the last half of the scale, leaving the last circuit at a frequency that is equal to the resonant one, which can achieve great operability. By wrapping the handle of the standard capacitor, we record the moment when the voltmeter needle moves to the left (the circuit’s support at the resonant frequency changes). The sharper the needle's direction, the higher the quality factor of the circuit. The maximum value of the capacitor capacity is determined. If the capacity size is small and there is no arrow tension, then you need to wind a number of turns of the dart from the spool.
Method 2. Let's take the diagram from Fig. 3b. From resistor R1 a signal is taken to the oscilloscope. Wrapping a pen
The capacitor fixes the moment of the minimum signal on the oscilloscope.

The basis of any radio receiver is the principle of vibrating signal generation, modulated by a non-current frequency, which, in its turn, is indicated by the resonance of the colivary circuit, which is the main element of the receiver circuit. In addition, to the extent that the frequency is chosen correctly, the strength of the signal will be maintained.

The vibrancy or selectivity of the receiver is determined by the fact that the signals that are due to the current method will be weakened and the signals will be strengthened. The quality factor of the circuit is a value that objectively demonstrates in numerical terms the success of the highest task.

The resonant frequency of the circuit is determined by Thompson's formula:

f=1/(2π√LC), for any

L – inductance value;

To understand how the vibrations in the circuit occur, consider how it operates.

Both amnesic and inductive impulses cross the vineyard of the electric current, rather than fail in antiphase. In this manner, the smells create the minds for the guilt of the colival process in much the same way as it happens on the goaders, when two people ride and move them in opposite directions alternately. Theoretically, by changing the value of the capacitor or coil capacitance, it is possible to ensure that the resonant frequency of the circuit approaches the frequency that is transmitted to the radio station. The more intense the stench, the less clear the signal. In practice, the trick is to adjust, change

All power depends on how much the guest will be on the frequency response graph of the appropriate device. You can visually understand how the red signal will be strengthened to the extent that it is suppressed. The quality factor of the circuit is this parameter, which indicates the selectivity of the reception.

It is indicated by the following formula:

Q=2πFW/P, de

F – resonant frequency of the circuit;

W - energy in the colival circuit;

P – tension of rose.

The quality factor of the circuit when a capacitor and inductance are connected in parallel is calculated using the following formula:

Everything is clear about the values ​​of the inductance and capacitance of the capacitor, and as far as R is concerned, you can guess that in addition to the coil there is an active storage tank. This circuit diagram is often depicted as including three elements: capacitance Z, inductance L and R.

The quality factor of the circuit is a value that is wrapped in a proportional fluidity of the extinguisher in the new kolivan. The greater the value, the greater the relaxation of the system.

In practice, the most important factor that affects the quality factor of the circuit is the quality of the coil, which is contained in the core, the number of turns, the level of insulation of the hole, the type of support, as well as the costs when passing the line. high frequency minds. Therefore, to regulate the frequency of the device, you need to install capacitors of variable size, which are two sets of plates that go in and out one after the other when wrapped. Almost all non-digital radio receivers have this system.

Moreover, digitally tuned receivers also have their own combustion circuits, but their resonant frequency changes differently.

When working with equalizers, we most often control only two parameters – Freq, which indicates the central frequency of the filter and Gain What does the gain coefficient at the center frequency of the filter mean? To this list you can add a choice of the type of equalizer filters, but in all modern software equalizers this choice is automatically selected and is stored at the primary location of the node in the frequency range. If you click the mouse in the region of 20-30 Hz, the high-pass filter will be activated; If you create a noise in the region of 60-70 Hz, then the low-frequency police will be responsible for everything; If you create a buzzer higher than 100 Hz, a jingle will be created, etc. Naturally, for a skin equalizer, the frequency values ​​assigned to the type of filters will be different, but the trend in the market is this - a daily equalizer is guilty of identifying types of curved equalizer filters automatically. Thus, we are deprived of two parameters (Freq, Gain) with which we can manipulate. What is missing from this list, or is it not so?

Along with the parameters of the central frequency and the coefficient of filter amplification, there is another extremely important parameter - the quality factor of the filters ( Q), which means the width of the amplified or attenuated range of frequencies and is defined as the ratio of the central frequency to the width of the range, which lies within 3 dB of the gain factor at the central frequency. Simply put, what is worth the value of the quality factor, then the range of frequencies, and what is the value of the lower value of the quality factor, then the range of frequencies is wider. All this, in front of us, is full of ringing-like filters. For high-pass and low-pass filters, the quality factor value indicates the steepness of the filter rolloff at the center frequency. Thus, in your hands you have a tool that can shape frequency landscapes - from gentle hills to steep cliffs.

How to determine the quality factor (Q) parameter in practice?

There are a number of important speeches that you can use when adjusting the quality factor:

1. By increasing the range of frequencies, changing the value of the quality factor

The main purpose of equalization is, first of all, to achieve an optimal balance of frequencies in the middle of other instruments, which results in balancing the entire mix. Coming from this, if the increase in frequencies may be soft and neat. Human hearing reacts very sensitively to very deep frequency ranges, so in order to preserve the sound balance at higher frequencies, it is important to select the widest ranges that indicate low quality factors.

2. By weakening the range of frequencies, increasing the value of the quality factor

Regardless of the weakening of frequencies, there is a tendency to change the internal balance of the instrument and its sound. In addition to weakening frequency distortions, you can choose a neutral diet, including suppression of noise, noise, humming, dampness, whistling and other unimportant sounds, but at the same time, if the quality factor of the filters is incorrectly adjusted, you can harm the instrument, causing its sound to be dark and thin . To eliminate these unacceptable speeches, it is enough to increase the quality factor of the filters and reduce the sensitivity to narrow frequency ranges. In this way, you will take away the signal, thereby depriving all the frequencies. With extremely high quality values ​​of the ringing filter, it is possible to create a notch filter that is ideally suited for suppressing a specific frequency or a narrow range of frequencies. This can be useful if you need to suppress even stronger resonances or remove static noise, for example, hum from an electrical cutoff at 50 or 60 Hz, depending on the region in which the recording was made.

3. Do not select too high slope values ​​for image filters

Now I'm trying to find such an equalizer, in which there will be a cut-off filter, designed to cut frequencies under 90 degrees, so that this is a kind of brickwall filter. If I knew such a filter in IZotope Ozone and having heard it, I realized that it would sound even unmusical. True, the reduction of frequencies below the central frequency of the filter was detrimental - the filter cut everything, but was it really necessary? I want to create a clean, neat, precise and acceptable image for the ear, and as a result, I want to remove a great picture for the eyes and a thirsty sound for the ears. Thus, I understand that when adjusting the quality factor (coolness) of cutoff filters, it is necessary to focus not on the level of frequency suppression, but rather on the tandem of suppression/musicality. Cutting filters with suppressions of 6 and 12 dB per octave sound the most musical. It is necessary to use filters with a bias of 24 dB per octave or, rather, to stagnate linear phase filters, as they do not interfere with phase interference. If you use high-speed filters on certain tracks, you may not encounter any special problems, but if you use such filters on subgroups or on the master channel, be prepared before you use the tools localization can be wasted, and the stereo image can be “flooded”.

4. Read the documentation before your equalizers

In many classic analog equalizers (for example, API 550), and their emulations, it is obvious that the value of the quality factor is not consistently determined in order to increase, but proportionally, so that the lower the gain factor, thus The greater the value of the quality factor, and, incidentally, the greater the enhancement factor, the greater the significance quality factor Insure such features from the behavior of other devices, so that the process of creation is understood, and not robotically. The significance of the Q parameter in Gain can also be found in many software equalizers - Type 3 and Type 4 in Sonnox Oxford EQ operate in an “analog” manner: the versatility of these modes lies in the fact that, at the same time, the width of the tone is increased when Low Gain values ​​for Type 3 will lower for Type 4, but at the maximum Gain value, the width of the dark for Type 3 will be the same as for Type 4.

5. The range of frequencies with low quality factor covers a small area near the central frequency of the filter

Have you ever wondered why, with a high-frequency frequency at 10 kHz, instruments begin to sound more mellow, and not just distorted? Everything on the right is that the stronger you emphasize the high-frequency police with a central frequency of 10 kHz, the stronger the lower frequencies, and the stronger the high frequencies, but also the high middle. Enhancing the very lowest frequencies, rather than the top 10 kHz, gives this effect of brightness and juiciness. The more shallow the filters are, the more frequencies will be stored away from the center frequency of the filter. Remember this and ask yourself again about those things that you want to strengthen or really weaken? Do you want to manipulate this entire large frequency range in the middle of the police, or really ask you about a specific frequency next to it?

Statistically, it is clear that this is a coli- val circuit. Sequential and parallel injection circuit.

Colival circuit a device or an electric lance that contains the necessary radio-electronic elements for the creation of electromagnetic signals. Divided into two types based on the elements combined: sequentialі parallel.

The main radio element base of the colivary circuit: Capacitor, main body and inductance coil.

The final piercing circuit is the simplest resonant (colving) lancet. A successive incineration circuit is formed, with the inductance coil and capacitor being successively turned on. When an alternating (harmonious) voltage is applied to such a circuit, an alternating current flows through the coil and capacitor, the value of which is calculated according to Ohm’s law:I = U / X Σ, de X Σ- a sum of reactive supports for sequentially switched on coils and capacitors (the module of the sum is determined).

To refresh your memory, let’s figure out how to place the reactive supports of the capacitor and the inductor depending on the frequency of the alternating voltage. For the inductance coil, this value looks like this:

The formula shows that with increasing frequency, the reactive support of the inductance coil increases. For a capacitor, the density of its reactive support versus frequency looks like this:

By replacing the inductance, the capacitor reacts with everything - as the frequency increases, the reactive support changes. On the little one's foot there is a graphic representation of the position of the cat's reaction supports XL that of the capacitor X C type of cyclic (circular) frequency ω , as well as a graph of occupation versus frequency ω Their algebraic sum X Σ. The graph, above, shows the frequency of the gas reactive support of the serial coli- val circuit.

The graph shows that at a given frequency ω=ω р, when the reactive support of the coil and the capacitor are equal in modulus (equal by the values, or equal by the sign), the reactive support of the lance goes to zero. At this frequency in the lancus, a maximum flow is avoided, which is bounded by only the ohmic losses in the coil inductance (the active support of the coil winding of the coil) and the internal support of the jet flow (generator). Such a frequency, if you are careful to look at the phenomenon called resonance in physics, is called the resonant frequency or the power frequency of Lanzug. It is also clear from the graph that at frequencies lower than the resonance frequency, the reactive support of the serial collateral circuit is of an inductive nature, and at higher frequencies it is inductive. If there is a resonant frequency, then it can be calculated using Thomson’s formula, which can be derived from the formulas for the reactive supports of the inductor and capacitor, equating their reactive supports one to one:

The little one is right-handed, shows an equivalent diagram of a serial resonant circuit with ohmic losses R, connected to an ideal harmonic voltage generator with amplitude U. The final support (impedance) of such a lance is given by: Z = √(R 2 +X Σ 2), de X Σ = ω L-1/ωC. At the resonant frequency, if the size of the reactive supports of the coil XL = ωL that of the capacitor X C = 1/? levels behind the module, value X Σ goes to zero (also, the operation of the lancer is purely active), and the flow in the lancer is determined by the settings of the voltage amplitude of the generator to the support of the ohmic costs: I=U/R. When the voltage on the capacitor, which stores reactive electrical energy, is applied, the voltage drops U L = U C = IX L = IX C.

At any other frequency, such as the resonant one, the voltages on the coil and the capacitor are not the same - they are indicated by the amplitude of the stream in the lanyard and the values ​​of the modules of the reactive supports XLі X Z Therefore, the resonance in the sequential collateral circuit is usually called voltage resonance. The resonant frequency of a circuit is such a frequency that the circuit is based on an active (resistive) character. The mind of resonance is the consistency of the reactive supports of the coil, inductance and capacitance.

One of the most important parameters of the colival circuit (temperature, sensitivity, resonant frequency) is its characteristic (or hwylov) basis ρ and quality factor of the circuit Q. Characteristic (hvilovim) support to the contour ρ The value of the reactive support capacitance and inductance of the circuit at the resonant frequency is called: ρ = X L = X C at ω =ω р. The characteristic opir can be classified in the following rank: ρ = √(L/C). Characteristic reference ρ є in a series of estimates of the energy stored by the reactive elements of the circuit - the coil (magnetic field energy) W L = (LI 2)/2 and a capacitor (electric field energy) W C = (CU 2)/2. The ratio of energy stored by reactive elements of the circuit to the energy of ohmic (resistive) losses over a period is usually called quality factor Q contour, which literally means “yakness” when translated from English.

Quality factor of the colival circuit- A characteristic that indicates the amplitude and width of the frequency response of the resonance and shows how many times the energy reserves in the circuit are greater than the energy consumption in one oscillating period. The goodness of the insurance company is the manifestation of an active support for vantage R.

For a sequential RLC collateral circuit in which all three elements are included in series, the quality factor is calculated:

de R, Lі C

Magnitude, value of quality factor d = 1/Q call the faded circuit. To increase the quality factor, ask yourself to use the formula Q = ρ/R, de R- based on ohmic losses to the circuit, which characterizes the tightness of the resistive (active losses) to the circuit P = I 2 R. The quality factor of real oscillating circuits, mounted on discrete inductors and capacitors, ranges from one to a hundred or more. The quality factor of various injector systems based on the principle of piezoelectric and other effects (for example, quartz resonators) can reach thousands or more.

In technology, the frequency power of different lantsugs is usually assessed using additional amplitude-frequency characteristics (AFC), in which the lants themselves are considered to be similar poles. The figures below show two of the simplest polarity circuits to replace the next oscillating circuit and the frequency response of these lantzugs, as indicated (shown by circuit lines). The vertical axis of the frequency response graphs shows the value of the lancet transmission coefficient behind the voltage K, which shows the ratio of the lancet output voltage to the input voltage.

For passive lances (so as not to interfere with the supporting elements and energy), the value Before I don’t overestimate one at all. The support of the alternating stream, shown on the small lancet, will be minimal at an influx frequency that is equal to the resonant frequency of the circuit. In this case, the coefficient of transmission of the lantzug is close to one (indicated by the significant losses in the circuit). At frequencies that strongly increase from the resonant one, the circuit's support for the exchangeable stream reaches a high value, and therefore the transmission coefficient of the lancer drops almost to zero.

When there is resonance in this circuit, the input signal terminal appears to be actually a short-circuited small support circuit, which is why the transmission coefficient of such a circuit at the resonant frequency drops practically to zero (this is due to the presence of the terminal support). However, at frequencies of the input influx, which significantly move away from the resonant one, the transmission coefficient of the Lantzug is found to be close to one. The power of the colival circuit to significantly change the transmission coefficient at frequencies close to resonant is widely used in practice if it is necessary to see a signal with a specific frequency without the presence of unnecessary signals dissipated on Other frequencies. So, any radio receiver will be tuned to the frequency of the required radio station with the help of ringing lancets. The power of the colival circuit is seen from multiple frequencies, one is usually called selectivity or vibrancy. In this case, the intensity of change in the transmission coefficient of the lancet when the frequency rises to resonance is usually assessed using an additional parameter called transmission. The range of frequencies in which the change (or increase is due to the type of lancer) of the transmission coefficient of the same value at the resonant frequency exceeds 0.7 (3 dB) is taken as the transmittance.

The dotted lines on the graphs show the frequency response of exactly the same lancets, the oscillating circuits of which have the same resonant frequencies as for the same type of device, but have a lower quality factor (for example, the inductor coil is wound with a wire, which has a great effect p stationary strum). As can be seen from the little ones, with this the range of lanjug’s access to power is expanding and the selective power is becoming more and more popular. Based on this, when developing and designing the injection circuits, it is necessary to improve their quality factor. However, in a number of switches, the quality factor of the circuit must be lowered (for example, by including a small support resistor in series with the inductance coil), which allows the interference of wide-range signals to be eliminated. Although, in practice, it is necessary to see a wide-range signal, selective lancets, as a rule, will not be on single piercing circuits, but on folding interconnected (multiple-contour) piercing systems, incl. rich-lank filters.

Parallel injection circuit

In various radio-technical devices, the order of successive injection circuits often (more often than not) involves parallel injection circuits. Here, two reactive elements with different reactivity patterns are connected in parallel. Apparently, when the elements are connected in parallel, their support cannot be folded - the conductivity can only be folded. The graphical distribution of the reactive conductivities of the inductance coil is shown on the baby B L = 1/ωL, capacitor C = -ωC, as well as total conductivity U Σ these two elements, which contribute to the reactive conductivity of the parallel colival circuit. Similarly, for a serial col- lative circuit, this frequency is called resonant, on which reactive support (and therefore conductivity) of the coil and capacitor. At this frequency, the total conductivity of the parallel colival circuit without loss is reduced to zero. This means that at this frequency the oscillating circuit provides infinitely great support to the alternating stream.

To ensure the presence of reactive support in the frequency circuit X Σ = 1/B Σ This is crooked, depicted on the step baby, exactly ω = ω р Matime rose from a different family. The operation of a real parallel collateral circuit (with expenses), obviously, is not equal to the inconsistencies - it is less than the greater ohmic operation of the circuit's expenses, so it changes directly in proportion to the changed quality factor of the circuit. In general, it is important to understand the quality factor characteristic of the support and resonant frequency of the collateral circuit, as well as their rotary formulas, which are valid for both the serial and parallel collateral circuits.

For a parallel collateral circuit, in which the inductance, capacitance and operation are connected in parallel, the quality factor is calculated:

de R, Lі C- Opera, inductance and capacitance of the resonant lancet, obviously.

Let's take a look at the lancet, which consists of a generator of harmonic colivas and a parallel colival circuit. Whenever the frequency of the generator's oscillation approaches the resonant frequency, the circuit of its inductive and reactive coils will provide equal support to the alternating flow, as a result of which the currents in the coils of the circuit will remain the same. In this case it seems that there is a resonance of strums in the Lancus. As soon as the sequential coli- val circuit, the reactivity of the coil and the capacitor compensates for one another, and the circuit relies on the stream that flows through it to become active (resistive). The magnitude of this support, which is often called equivalent in technology, is determined by the quality factor of the circuit for its characteristic support R eq = Q ρ. At frequencies that are different from the resonant one, the circuit support changes and becomes reactive in nature at lower frequencies - inductive (some of the reactive inductance support falls with a change in frequency), and at higher frequencies - inductive, emn Lower (t to reactive operation capacity decreases with increasing frequency.

Let's look at how to determine the transmission coefficient of quadripoles depending on the frequency when switching on not consecutive oscillating circuits, but parallel ones.

Chotiripole, images on the baby, at the resonant frequency of the circuit is a great support for the strum, while ω=ω р Its transfer coefficient will be close to zero (subject to the regulation of expenses). At frequencies that are different from the resonant one, the circuit support changes, and the transmission coefficient of the circuit increases.

For a multi-pole device aimed at a small body, the situation will be the opposite - at the resonant frequency the circuit will have a very large support and practically all the input voltage will be applied to the output terminals (then the transmission coefficient will be maximum and close to unity i). With a significant difference in the frequency of the input inflow from the resonant frequency of the circuit, the signal that is connected to the input terminals of the circuit breaker will appear short-circuited, and the transfer coefficient will be close to zero.

Any resonant circuit, including the last one, is usually characterized by its quality factor Q and its characteristic support.

It is clear that in this case there is a significant increase in the quality factor of the circuit when the frequency of the life source changes.

At resonance
.

The quality factor of the circuit means the multiplicity of the displacement of the voltage on the pressure of the inductive or emnestic element, the support at resonance above the voltage of the entire lancet U = U R.

In electrical and radio engineering installations, the quality factor can be of any order, up to tens of thousands. For great quality factors (50–500) U L 0 >> U R ,U R = U VX = U, That is, the voltage on the inductance (or on the capacitance) is often greater than the applied voltage.

There is a clear influx of quality factor at critical resonances when connected in series

R, L, Z. Strum u lanciuzia is ancient

Vidnosne meaning of the struma:
, then.
.

According to this formula, it was claimed that
.

How to introduce the concept of reference frequency
.

Then the previous formula would be written like this:

Let's look at the resonance curves for the leading (along the stream) units (Fig. 7.8) for three quality factors. Looking at three resonant curves, it is clear that the higher the quality factor, the better the resonant curve will be. The amount of transmission of the circuit is indicated by the difference in frequencies that are created when the resonant curve is crossed by a horizontal line on the level .

3 fig. 7.8 it is clear that the lower the quality factor, the wider the transmission. In radio receivers, the ring circuits have a high quality factor (500-1000), so the circuits can have a high bandwidth, which allows only one station to be received by the selected radio receiver.

7.6. The value of the quality factor is equal to the resonance curve

In practice, the resonant frequency characteristics of real circuits can be adjusted by changing the frequency of the generator in different intervals and taking the readings of a voltmeter connected in parallel to the resistor (div. Fig. 7.9 A). There will be an experimental resonance curve and a value curve indicating the amount of transmittance. We can see a simple formula for the expansion of the quality factor behind the resonance curve, determined experimentally.

3 fig. 7.9 b trace:

.

This jealousy has equal banners, to that

Zvidsi
.

Let's write two: when і ???
;
.

After folding, the remaining viruses are removed

or else

Zvidsi

Very important: goodness is proportional
.

For sequential circuit R, L, C caused by a resonant curved stream during change

Volumes Z(Mal. 7.10).

Corresponding to the curve, the quality factor of the circuit is significant. Viraz for strumu

Vikonaemo low conversion of the remaining formula

;

.

Let's carry out a horizontal straight line on the level
.

Significant value of capacity C 1 ta Z 2 .

Volumes Z 1 ta Z 2. Let's write it down

We know the amount and the difference in capacities

Let's write down the setting
.

It is clear that the quality factor of the circuit is determined by the displacement of the voltage on the inductive (or emis- sive) support during resonance above the voltage of the entire lance (or the voltage active support), then.

In such a manner

Based on this result, you can select the values ​​of the parameters of the inductor coil ( Lі R)

.

Stars
;
.

Stars
.

Capacity size Z 0 when resonance occurs, it is calculated as follows:

;
;
;
.

Stars
.

Voltage resonance can be avoided in the circuit shown in Fig. 7.11.

The input of such circuits

In case of resonance, the reactive storage input support must be brought to zero, then.

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