Quality factor for resonance. Colival circuit. Parallel injection circuit

Golovna / Setting up

Good quality- the power of the colivatal system, which indicates the degree of resonance and shows how many times the energy reserves in the system are greater than the energy consumption in one kolivaniye period.

The quality factor is proportional to the speed of extinguishing the moisture in the system. The higher the quality factor of the colival system, the less energy is wasted during the skin period and the more the coliva is extinguished.

The formula for the quality of any colivatal system is:

· - Resonance frequency kolivan

· - Energy stored in the coli-val system

· - Rose tension.

For example, in an electric resonant lancet, the energy is dissipated through the end oper of the lancet, in a quartz crystal, the damped vibration is caused by internal losses in the crystal, in volumetric electromagnetic resonators it is lost in the walls of the resonator, in this terials and in coupling elements, in optical resonators - on mirrors.

For the colival circuit in RLC Lanzugs:

de , i - op, inductance and capacitance of the resonant lancug, obviously.

6) The folding of harmonious collisions of one direct and the same frequency. Bittya

May there be two harmonious vibrations of one directly and the same frequency

(4.1)

Rivnyannya resultant kolivannya matime viglyad

Singing in this place, having praised the rank of the system (4.1)

Having established the cosine sum theorem and completed the transformation of algebra:

It is possible to know such values A and ?0, so that the equals are satisfied

(4.3)

Seeing (4.3) like two equals with two unknown A and φ0, we know by calling them in a square and clasping them, and then dividing them into each other:

Substituting (4.3) to (4.2), removing:

Otherwise, it remains necessary to use the cosine theorem to sum up:

The body, taking part in two harmonious vibrations of one direction and the same frequency, also creates a harmonious vibration in the same direction and with the same frequency that and the vibration that add up. The amplitude of the resulting hammering depends on the difference in phases (φ2-φ1) of the hammering, which is smoothed out.

Depending on the phase difference (φ2-φ1):

1) (φ2-φ1) = ±2mπ (m=0, 1, 2, …), then A= A1+A2, then the amplitude of the resulting vibration A is equal to the sum of the amplitudes of the vibration that add up;

2) (φ2-φ1) = ±(2m+1)π (m=0, 1, 2, …), then A= |A1-A2|, then the amplitude of the resulting vibration is the same as the differences in the amplitudes of the vibration, which add up

Bittya

Periodic changes in the amplitude of the vibration that occur when two harmonic vibrations of close frequencies are added are called beats.

May the two sounds vary little in frequency. Then the amplitudes of the vibrations that add up are equal to A, and the frequencies are equal to ω and ω+Δω, and Δω is much less than ω. We select the cob from side to side so that the cob phases of both cuttings are equal to zero.

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. To put it simply, the higher the value of the quality factor, the greater the range of frequencies, and the lower the value of the quality factor, the wider the range of frequencies. 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?

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.