Timchasov characteristics of linear lances. Timchasov characteristics of lanceugs

Transitional and impulse characteristics can be seen before the clock parameters.

Let's look at the linear electric lance, so as not to take revenge on the independent wires of the stream and voltage.

Let the ovnіshnіy vpliv on lansyug is a function of inclusion (single striving) x (t) \u003d 1 (t - t 0).

transition characteristic h (t - t 0) of a linear lance, so as not to avenge independent energy sources, it is called the reaction of a single lance to the influx of a single streak stream or a strain

The transitional characteristic's roaming characterizes the difference between the roaringness of the air and the roaringness of the ovnishny plethora, to which the transitional characteristic can be the mother of the roaming support, the conductivity, or be a non-roaming value.

Let's have a splendid infusion into the language, let's take the form of the -function

x (t) \u003d d (t - t 0).

impulse response g (t - t0) linear lancer, so as not to avenge independent energy sources, the lancer's reaction to the influx of the -function at zero cob minds is called

The freshness of the impulse characteristics is the same as the expansion of the freshness of the lancer to the creation of the freshness of the warm infusion for an hour.

Similar to the complex frequency and operator characteristics of the lancet, the transitional and impulse characteristics establish a connection between the original infusion on the lancet and її reaction, however, on the first characteristics of the first characteristics, the argument of the remaining hours t, not kutova w or complex p frequency. Since the characteristics of the lancet, the argument of which is є hour, are called timchas, and the characteristics, the argument of which are є frequency (including complex) - frequency, then the transitional and impulse characteristics are compensated for the assigned hourly parameters of the lance.

The skin operator characteristic of the lancet H k n (p) can be set to the transient and impulse characteristics.

(9.75)

at t0 = 0 operator images of transient and impulse responses may look simple

Virazi (9.75), (9.76) establish a connection between the frequency and hourly characteristics of the lancer. Knowing, for example, the impulse response can, with the help of the direct transformation of Laplace, know the operational characteristic of the lanciug

and for the second operator characteristic H k n (p) for the additional Laplace reversal transformation we take the Lantzug impulse characteristic

Vikoristovuyuchi virazi (9.75) and the theorem of differentiation (9.36), it does not matter to establish a link between the transitional and impulse responses

If at t = t 0 the function h (t - t 0) changes like a string, then the impulse response of the lancet is associated with it to the onset of

(9.78)

Viraz (9.78) seems to be the name of the elaborated formula. The first dodanok in this case is a similar transitional characteristic when t > t0, And another addendum is to avenge the d-function on the value of the transitional characteristic at the point t = t0.

If the function h 1 (t - t 0) does not recognize the difference at t \u003d t 0, i.e., the value of the transient characteristic at the point t \u003d t 0 is equal to zero, then it is necessary to change the value of the transient characteristic at the point t \u003d t 0 lansyuga is more expensive pershoї pokhіdnoї transitional characteristics by the hour

(9.77)

To determine the transitional (impulse) characteristics of a linear lancet, there are two main methods.

1) It is necessary to look at the transitional processes, as they appear in this case, when the struma is injected into it, or the voltage in the switched on function or the -function. Tse can be vikonan for the help of classical or operational methods in the analysis of transitional processes.

2) In practice, for timing characteristics linear lances manually vikoristovuvaty ways, foundations on zastosuvanni spіvvіdnoshen, scho establish a link between frequency and hour characteristics. The designation of the time characteristics in this way starts from the folding of the operator scheme of the replacement of the lancet for the zero cob minds. Further, vikoristovuyuchi tsyu scheme, know the operational characteristic of H k n (p), in the given pair of assignments: ovn_shnіy inflow on the lancet x n (t) - the response of the lancet y k (t). Knowing the operational characteristics of the lansyug and the stagnant spіvvіdnoshennia (6.109) or (6.110), one can determine the shukanі timchasі characteristics.

If you look at the reaction of the linear lancet to the injection of a single impulse into the struma, or the voltage, the transitional process in the lancet is subdivided into two stages. At the first stage (with tн] t 0-, t 0 + [) The lancer is known under the influx of a single impulse, which rouses the lancer's energy. Currents of inductances and voltages of capacitances in case of this stribkom change to values, which in turn are in the energy supply, in case of which switching laws are violated. At another stage (with t³t0 +) DIIA Applied to Lanzyuga Zovnіshnogo Fitting Zakіnchilosy (at the center of Vimknenі, t. E. is represented by internal supports), and in Lancetling Vinuni Vіlnі Procesum, Scho protesuet for Rahununi Energії, and reactors in the reactants of the Element. Also, the impulse response characterizes the free processes in a well-looked lancet.

1. TASK

Scheme of the doslidzhuvano lanceug [Fig. 1] No. 22, up to option 22 - 13 - 5 - 4. Lance element parameters: L = 2 mH, R = 2 kOhm, C = 0.5 nF.

The outflowing inflow is given by the function:, de and is calculated according to formula (1)

Malyunok 1. The electrical circuit of a given Lanziug

It is necessary to indicate:

a) viraz for the primary parameters of the given chotiripole in the form of a function of frequency;

b) a complex coefficient of transmission by the voltage of the chotiripoleum in the idle mode on zatiskach;

c) amplitude-frequency and phase-frequency characteristics of the voltage transmission coefficient;

d) operator transmission coefficient for the voltage of the chotipole in idling mode on zatiskach;

e) the transitional characteristic of the Lanciug;

e) the impulse response of the lanceug;

g) lancer's feedback on the tasks of the input inflow with the switched-on navantage.

2. Rosrakhun's part

.1 Designation of the primary parameters in the chotiripole

For the designation of Z - the parameters of the chotipole, it is foldable that the electrical balance of the lancet is equal to the method of contour jets of vicorist and the complex scheme of replacing the lancet [Fig. 2]:

Malyunok 2. A complex substitution scheme for a given electric number

By choosing directly bypassing the contours, as indicated in [Fig. 2], and vrakhovuyuchi

let's write down the contour line of the lansyug:

Substitutes in otrimani equal value i:

(2)

Otrimani equalization (2) to remove more strumi and stress on the input and output clamps of the chotiripole and can be converted to a standard-looking record of the main rivnyan of the chotiripole in form Z:

(3)

Converting equal (2) to the form (3), we take:

Rivnyuyuchi otrimani rіvnyannya z іvnyanny (3), otrimuemo:

chotipole voltage idle amplitude

2.2 Designated voltage transfer coefficientin idle mode on exit

Comprehensive coefficient of transmission by voltage from zatiskachiv to zatiskachiv in idle mode () at the output we know, vicorist otrimani at the point 2.1 expression for the first parameters:

2.3 Designation of the amplitude-frequencyi phase frequencycharacteristics of the coefficient of transmission by pressure

Let's take a look at the viraz for the introduction of two complex numbers, we know the viraz for the AFC and PFC.

Frequency response matime looking:

From the formula (4) we can see that the PFC looked like:

de, glad / s to know s equal

Graphs of frequency response and phase response are directed to the front side. [Fig.3, Fig.4]

babes 3. Amplitude-frequency characteristic

Malyunok 4. Phase response

Boundary value at for control, calculate the cost of the value, without going into the rozrachunk formulas:

· Vrahovyuchi, that the opir of inductance with a steady stream is equal to zero, and the opir of capacity is infinitely large, in the scheme [see. ріс1] it is possible to open a gilt to avenge the capacitance, and replace the inductance with a jumper. In the otrimaniy scheme i, because the input voltage fluctuates in phase with the voltage on the clamps;

· At the infinitely great frequency of the needle, which can avenge the inductance, it is possible to break it, so that the inductance of the pragne is inexhaustible. Do not marvel at those who opir the capacity of the load to zero, you cannot replace it with a jumper, as the voltage on the capacity is the voltage. In the otrimaniy scheme [see. Fig.5], when,, the input strum is in phase with the input voltage, and the output voltage is fluctuating in phase with the voltage at the input, so .

Malyunok 5. The electrical circuit of a given lanceug with.

2.4 Designated operator transmission factor by voltagechotiripole in idle mode on the grips

The operational scheme for substituting the lancet behind the starry sight does not fit into the complex substitution scheme [Fig. 2], since the analysis of the electric stake is carried out at zero cob minds. In order to change the operating voltage transfer coefficient, add it to the expression for the complex transmission coefficient, replace it by the operator:

Let's remake the rest of the viraz so that the coefficients at the senior steps in the numeral and banner were equal to one:

The function can have two complex-coordinated poles:; and one speech zero: .

Malyunok 6. Pole-zero function diagram

The pole-zero diagram of the function is shown in Fig.6. Transitional processes in the lances may have a damped kolyvalny character.

2.5 Designation of transitionand pulselanceug characteristics

The operator window allows you to select the image of the transitional impulse response. The transition characteristic is manually assigned, vikoristovuyuchi links between images according to Laplace of the transition characteristic and operator transfer coefficient:

(5)

The impulse response of the lansyug can be otrimana z spіvvіdnoshen:

(6)

(7)

Vicorist formulas (5) and (6), we write down the expression of the impulse and transient characteristics:

We convert the image of the transient and impulse responses to a look that is easy for the designation of the original timing characteristics for the additional table of Laplace's transformation:

(8)

(9)

In this order, all the images are linked to the upcoming operational functions, the originals of which are shown in the tables of Laplace's transformation:

(12)

I’ll look at what is for a given vipadka, what is being looked at , , , We know the value of the post for the expression (11) and the value of the post for the expression (12).

For expression (11):

І for curvature (12):

Substituting the subtraction of the value of the virazi (11) and (12), we take:

After the change, we will take the remaining factors for watch characteristics:

The transitional process in this country will end after the commutation in an hour , de - it is shown as a reversible value to the absolute minimum value of the real part of the pole. so yak , Then the hour of extinction is one (6 - 10) μs. Vіdpovіdno, vybirаєmo іrval rozrahunku numerical values ​​timchasovyh characteristics . Graphs of the transient and impulse characteristics are shown in Fig. 7 and 8.

For a clear explanation of the type of transient and impulsive characteristics of the lancet, before the input zatiskachi, the voltage was not independent. The transitional characteristic of the lancet is numerically increased by the voltage on the outer clamps when the voltage is applied to the lancet of a single streak at zero cob pressures. At the beginning of the hour after switching, the voltage at the capacity is equal to zero, so because of the laws of commutation at the end value of the amplitude, the voltage at the capacity cannot change. Otzhe, tobto. When the voltage at the input can be entered with a constant and equal 1V, then. In the lances, apparently, only the constant streams can flow, so you can replace the inductance with a gap, and the inductance with a jumper, also in such a rank of the lances, tobto. The transition from the cob mill to the old one is carried out in the kolival mode, which is explained by the process of periodic energy exchange between inductance and capacity. Extinguishing the coliving comes through spending energy on the support R.

Baby 7. Transitional characteristic.

Malyunok 8. Impulse response.

The impulse response of the lancet numerically changes with the output voltage when a single voltage impulse is applied to the input . By stretching a single pulse, the capacity is charged to its maximum value, and the voltage at the capacity becomes equal

.

In the case of a voltage plug, it can be replaced by a short-circuited jumper, and in Lancuse it can be replaced by a damped oscillating process of energy exchange between inductance and mnistyu. At the cob stage, the capacitance is charged, the capacitance current smoothly changes to 0, and the inductance stream grows to its maximum value at. Then the inductance strum, smoothly changing, recharges the capacity in the opposite direction, etc. With the help of a rise in energy in the support, all streams and springs of the lansyug should drop to zero. In this way, the oscillating nature of the voltage on the container, which decays over a period of time, explains the type of impulse response, moreover і.

The correctness of the analysis of the impulse response is confirmed precisely by the fact that the graph in Fig. 8 goes through 0 y at that moment and hour, if the graph in Fig. 7 has local extremums, and the maxima coincide hourly with the points of the curve overshoot. And also the correctness of the analysis is confirmed by the fact that the graphs i, similar to the formula (7), are correct. To check the correctness of the value of the transitional characteristic of the lancet, we know the characteristic when the voltage is applied to the lancet of a single strib by the classical method:

We know the independent cob mind ():

We know the deposits of cob mind ():

For which animal we are moving up to Fig. 9, which shows the scheme of the Lanziug at the moment of the hour, then it is necessary:

Malyunok 9. Scheme of a lanceug at the moment of the hour

We know the vision of the warehouse notice:

For the first animal moving up to Fig. 10, on which the lancet diagram is shown for the next commutation. Todi otrimuemo that

Malyunok 10. Scheme of the Lanziug at.

storeable differential alignment:

For this row, we write down the balance of strums in the knots for the first Kirchhoff law and write down the number of equals on the basis of another Kirchhoff law:

Vikoristovuyuchi component rіvnyannja reversible before rіvnyannya:

We can see all the unknown voltages through:

Now differentiating and transforming, we take the differential equal to another order:

Substituting constants and taking into account:

5. Let's write down the characteristic equality and know its root:
down to zero. A constant hour and a quasi-period of coagulation of the timcha characteristics are taken into account by the results subtracted from the analysis of the operational transmission coefficient; The frequency response of a looked lancet is close to the frequency response of an ideal low-pass filter with a cutoff frequency .

List of victorious literature

1. Popov V.P. Fundamentals of the theory of kіl: A tutor for universities - 4th ed., Rev. - M .: Vishcha. school, 2003. - 575s .: il.

Korn G., Korn T., Mathematician for engineers and university students. M .: Nauka, 1973, 832 p.

VIYSKOVA
ACADEMY
ZV'YAZKU
2 department
PRACTICAL ACTIVITY
from primary discipline
"Electronics, electrical engineering and circuitry"
Topic No. 4 Mode of non-harmonious injections
linear electric lances
Lesson No. 17 “Razrahunok of timcha characteristics
linear electric lines »
Saint Petersburg

INITIAL POWER:
1. Analysis of timcha characteristics of linear
electric lancers.
2. Control of the assimilation of the twisted material.
LITERATURE:
Babkova L.A., Kiselov O.N. Methodical recommendations before
practical to take i kerіvnitstvo to laboratory robіt on
discipline "Fundamentals of the theory of life": Textbook. - SPb .: VAS, 2011.
2. Ulakhovich D.A. Fundamentals of the theory of linear electric lines:
Study guide. - St. Petersburg: BHV-Petersburg 2009.
1.

task 1

1. Analysis of timcha characteristics of linear
electric lancers.
task 1
Know the impulse and transition characteristics of the electrical
low-pass filter with the most flat frequency response, as you know
transfer function:
1
H(p)2
.
p 2 p 1

1
h (p) H (p).
p
h(p)
1
p (p 2 p 1)
2
.

2. Significantly image of the impulse response:
g(p) H(p).
This order of the image of the impulse response will be
mother looked:
g(p)
1
p 2 p 1
2
.
Having speeded up the table of performances, it is shown more graphically
image of transient and impulse characteristics:

transient characteristic
h(p)
1
p (p 2 + 2 p 1)
Fig1. Graph f (t)
A
p (p 2 α1 p α2)

impulse response

g(p)
1
p2 2 p 1
A
p 2 α1 p α2

task manager 2

To know the momentum and transition characteristics of the lanzug, as you can see
її transfer function:
181.8p
H(p)2
p thousand ninety-one p 1.818 106
1. Significantly depicting the transition characteristics
1
h (p) H (p)
p
2. Significantly image of the impulse response:
g(p) H(p).
181.8p
g(p)2
p thousand ninety-one p 1.818 106

transient characteristic
181,1
h(p)2
p thousand ninety-one p 1.818 106
A
2
pα1 pα2

impulse response

181.8p
g(p)2
6
p thousand ninety-one p 1.818 10
Ap
p 2 α1 p α2

Task 3 Calculate the transient and impulsive characteristics of the lancer, which are added up from the sequentially added R and C elements.

1. We know the transfer functions of the lance for
representations of reactions:
uc(p)
H1 (p)
;
u1(p)
uR(p)
H 2 (p)
.
u1(p)

2. Know the significance of the reaction on the elements C and R.

1
u1(p)
1
u1(p)
uc(p)i(p)
;
pC R 1 pC pRC 1
PC
u1(p)
u1(p)pRC
uR (p) i (p) R
R
.
1
pRC
1
R
PC

3. Transfer function in operator form:

1
H1(p)
;
pRC1
pRC
H2(p)
.
pRC1
4. We know the image of the transitional characteristics:
H1(p)
1
hC(p)
p
p(pRC 1)
1
RC
1
pp
RC
H2(p)
RC
1
h R (p)
.
p
pRC 1 p 1
RC
;

4. The image of the impulse characteristics is known from the speed:

g(p) H(p)
1
1
g C (p) H1 (p)
RC;
pRC 1 p 1
RC
1
pRC
1
g R (p) H 2 (p)
1
1 R.C.
1
pRC1
pRC1
p
RC

For respect!

It is acceptable that a step-by-step inflow was reported to the Lanziug, the image of which is the function

It is acceptable that the lancegug was reported in stages
picture of which function A
p
x (t) A 1 (t)
.
x(t)
0 at t 0;
x(t)
A at t 0.
A
t
0
Mal. 1. Step by step injection
Then the operator transfer function looked like:
y (p) y (p)
y(p)
H(p)
p
.
A
x(p)
A
p
(10)
,

Let us know the L-image of the transient characteristic. By virtue of the power of the line

Let us know the L-image of the transient characteristic. By virtue of the power of the line
Laplace's transformation is acceptable:
1
h (p) T (p).
p
(11)
Tsey vislav zbіgaєtsya with another spіvplіnnik prіvіy partі (10)
i, also, between the operator transfer function i
to the image of the transient characteristic h (p) є advancing
relationship:
H(p)ph(p);
1
h (p) T (p).
p
(12)
(13)
Similarly, we can insert a link between H (p) and images
impulse response g (p):
y(t)
g(p)
;
Si

If a pulsed injection is sent to the lancet, the image of which is one, then the operational transfer function,

How is it that a pulse injection x (t) S and (t) is applied to the lance,
image of what x (p) is more beautiful
, then the operating transmission
і
a function that confirms this infusion, may look:
S
y (p) y (p)
H(p)
.
x(p)
Si
(14)
Tsej vislav zbіgaєtsya with the function of the image impulse
lanceug characteristics. otzhe,
g(p) H(p).
(15)

Let's look at the link between the transient and impulse characteristics
lanceug. It is not important to remember that their images are related to spivvids
g(p)ph(p).
Provіvshi the same transformation of the rest of the jealousy
(having changed
h (0) h (0))
g (p) ph (p) h (0) h (0).
ph(p)h(p)
oskolki
is an image
sufficient transitional characteristics, then the equanimity
you can imagine
g (p) h (0) L h / (t).
Moving on to the realm of originals, we take away the formula that allows
calculate the momentum characteristic of the lanceug for the house
її
transient characteristic, g (t) h (0) (t) h (t).
g
t
h
(T).
If h (0) 0, then
Zvorotne spіvvіdnoshennia mіzh zaznachenimi characteristics maє
t
view:
h (t) g (t) dt.
0
(15)

3. Call between timing and frequency
lanceug characteristics
e t
Designate an operation for this lancer
transfer function and know the expression
for її frequency characteristics
C
C
R
u1(t)R
u2(t)
i 2 (p)
H(p)
.
e(p)
Mal. 5. Schematic of the RC-Lanceug
The image of the reaction u2 (p) is significant from the system of node
equal, folded for L-image of nodal stresses
u1(p); u2(p):
(2 pC G) u1 (p) pCu2 (p) pCe (p);
pCu1 (p) (pC G) u2 (p) 0.

Zvіdsi

e (p) p 2
u2(p)
;
2
G G
2
p 3p 2
C C
2
p
H(p)2
2
p 3 p
de designation
G
.
C
For the significance of the complex transfer function, we put in
to the rest of the world p j. also
H(j)2
.
2
() J3
2

The frequency response is determined by the module of the taken function, and the phase response is known
yak argument
H(j).
H(j)
2
(2 2) 9 2 2
Hj
3
() Arctg 2
(2)
1
0
a
0
b
Mal. Fig. 6. Graphs of the frequency characteristics of the RC-lance: a - frequency response, b - phase response

VISNOVSKI:
1. Transmission function є L-images of the impulse response.
2. Transmission
function
є
dribno-rational
function
h
speech coefficients.
3. The poles of the stable transfer function lie in the left r-p-plane.
4. Steps of the polynomials of the numerators of the transfer function and the square of the frequency response NOT
change the steps of the polynomials of the signs; under nonvikonannі tsgogo
the power of the frequency response at infinitely large frequencies (ω → ∞) is guilty of taking
infinitely great value, shards of numbers grow in every way
more than a banner.
5. frequency characteristics lancers are charged for the transfer function when
p = jω.
6. The square of the frequency response is a paired rational function of the change
speech coefficients: H (jω) 2 = H (-jω) 2.
7. For the transfer function, you can depict the Lantzug scheme.

.
Nutrition number 1 a. Vіlni kolyvannya in
to the last kolivalny contour.
At the moment t = 0, commutation has become,
then the key (Kl.) from the position 1 transitions to
station 2.
Charged capacity appeared
connected to RL-lance.
Look at the processes in the minds of the Frenchman before switching
Before switching, the capacity C was connected
parallel to dzherel constant voltage E,
(Key (Kl.) Being in position 1).
The pressure on the containers increased E.
uC (+0) = uC (-0) = E;
iL (+0) = iL (-0) = 0.

Look at the processes in lanceuzia after switching
I’ll look at what the voltage is on the tank
You can’t change by a stream committee, but according to the law of commutation, you can:
uC (+0) = uC (-0) = E
Pochatkovi mind non-zero
Let's take a look at the lanceg substitution scheme for the moment
From Ohm's law in operator form,
significant reaction image:
E
p
E
E
L
L
i(p)
2
,
2
1
R
1
p 2 p 0
pL R
p2p
PC
L
LC
de:
0
R

2L
1
LC
-circular frequency of wet coliving to the contour without vtrat.

When analyzing large and transitional coliving in folding lancets
reaction image y (p) is a fractional-rational function
change p with speech coefficients, which can be written in
you can see the blue of two polynomials:
M (p) bm p m bm 1 p m 1 bm 2 p m 2 ... b0
y(p)
N(p)
p n a n 1 p n 1 a n 2 p n 2 ... a 0
After the basic theorem of algebra, a polynomial of degree n can be expanded on n
simple spellers, tobto .:
N (p) = (p-p1) (p-p2), ..., (p-pn),
where p1, p2, p3, ..., pn are the roots of the polynomial N (p) or the poles of the function y (p).
A polynomial can also be represented by looking at the addition of m sp_multipliers:
M (p) = (p-p01) (p-p02) (p-p03), ..., (p-p0m).
where p01, p02, p03, ..., p0m are roots of the polynomial M (p) or zero functions y (p).
Due to the speechness of the coefficients ai and bi, zeros and poles of the image y (p)
can be verbal and (or) complexly obtained.
It is clear that the dislocation of the poles y (p) determines the nature of the free і
transitional kolivans in the analyzed lansyug.

Let's look at the alignment:
p 2 + 2 p 02
There are two roots, (the poles of the image):
p1.2 2 02
Due to the speechness of the coefficients of this equalization (δ, ω), the poles
can be speech and complex communication.
Therefore, in the analysis of large colivans in the last contour
There are three modes of coliving.

Korіnnya rivnyannya complex-zv'yazanі:
p1,2 j1
de:
1 02 2 .
such a character of the roots may be at 0
or R 2
L
.
C
Original for strumu in
what will be the point:
E t
i(t)
e sin 1t,
1L

The amplitude of the colivanation changes in hours according to the exponential law,
That is why the process is called quenching. Speed ​​decrease in amplitude
the free colivans are assigned to the values ​​of the extinction coefficient δ.
2
Frequency: 1 02 2 0 1
0
extinguishing the contour. Vaughn, as you can see from the formula, start less
frequency of wet undamped colivants to the contour w0 i lie not only in
the value of the inductance and capacity of the circuit, ale and the value of the resistive
support.
The period of fading colivans:
T
2
2
0
2
.
Extinguishing coefficient of interference with the quality factor of the spivvіdnoshennia circuit:
de:Q
R0
.
2L 2Q
0 L
- quality factor of the sequential circuit.
R
In this rank, the ringing in the contour changes to the same more, more than yogo
goodness.

2. Critical regime of harmonies.

p1 p2,
.e. 0; R2
T
L
.
C
Coiling mode in the contour, based on a multiple root
characteristic alignment (image poles), can
look like a boundary vapadok of the kolival regime,
if the frequency of wet fading colivans in the circuit
zero, and the period of coliving becomes
1 02 2 old
infinitely great.

may look:
E0 t
i(t)
te
L

Root equal speech multiples:
p1,2,
de 2 02; .
first
parameters
contour
guilty
to satisfy the nervousness:
L
R2
.
C
Original i (t)
may look:
E
E
i(t)
L (p1 p2)
e p1t
L (p1 p2)
e p2t

Meal №1 b. Transitional colivannya in the next
kolivalny contour.
Pochatkovі mind NULLOVІ
E
E
E
p
L
L
i(p)
2
;
2
1
R
1
p
2
p
0
pL R
p2 p C
PC
L
L
uC (p) i (p)
According to the table of characteristics:
uC (t) E Ee (cos 1t sin 1t).
1
t
Voltage on the capacity of the circuit
at t → ∞ pragne to the old value equal to
stress jerela. Also, the capacity at t → ∞ is charged up to the voltage E. The process
charge at complexly obtained poles of the image
may kolivalny character.
1
LC
.
2
2
pC p (p 2 p 0)

The value of uC (t) in the next moment and hour can change the value of the voltage at a great quality factor, it can be two times the EPC of the dzherel.
At t → ∞, the value of the struma in the circuit, the stress on resistive element and on
increase the inductance of the circuit to zero, and the voltage on the capacitance - to EPC
dzherela. Otze, lanceug switch to mode fast strumu. process
installed kolivan vіdbuvaєtsya more povіlnіsh, chim more good quality
contour. To evaluate the time of installation, you can speed up the
earlier by the formula:
ty
3 4, 6
,
which changes the time interval, after the end of some voltage amplitude uC (t) is changed from the old value not more than 0.05 or 0.01.
Catering №2
parallel kolivalnoy circuit.
2.1 Vіlnі colivannya in PrKK
Pochatkovi mind non-zero
iL (+0) = iL (-0) = I0
uC (+0) = uC (-0) = u0

I0
Cu0
p
I0
u0 p
c,
u(p)
2
2
1
p
2
p
0
pC G
pL
G
- coefficient of extinguishing the circuit;
2C
1
0
- the frequency of wet kolivani contour without vtrat.
LC
de:
1. The mode of fading harmonies.
The primary parameters of the contour in which case are to blame for the satisfaction of the unevenness:
G
2C
1
LC
The law of changing the voltage on the circuit is viable up to the table of voltages by viraz:
I0
u
0
t
C
u (t) e u0 cos 1t
sin 1t
1

The analysis of the taken solution shows that
colivanya to wear a fading character, moreover
amplitude
colivannya
ubuvaє
on
exponential law. What is more
extinction coefficient, tim svidshe extinguish
kolyvannya. Like in the sequence contour,
frequency of free colivans:
1 0 1
0
2
0
2
2
reduce the frequency of wet undamped loops to the contour
2. Critical regime of harmonies.
Such a nature of roots in the universe at δ = ω0, if between the primary parameters of the contour there is a relationship:
G
2C
1
LC
I0
t
u (t) u0 u0 t e
C

3. Aperiodic mode of harmonies.
Tsej vapadok kazlivy for the mind δ = ω0, scho
spіvvіdnoshenyu mіzh primary parameters of the contour:
G2
C
.
L
I0
I0
u 0 p1
u0 p2
u(t) C
e p1t C
e p2t
p 2 p1
p 2 p1
It should be noted that at G = 0 the heaving in the contour is of a non-fading character,
so the circuit is not energized.

2.2 Transitional colication in the PrKK
Vikoristovuyuchi Ohm's law in operator form, we know the image for all
reactions:
I
p
I
I
C
u(p)
2C
;
2
1
G
1
p 2 p 0
pC G
p2p
LC
C
LC
I
G
C
iG (p) u (p) G 2
;
2
p 2 p 0
I
u(p)
LC
iL(p)
;
2
2
pL
p (p 2 p 0)
iC (p) u (p) pC
IP
.
2
2
p 2 p 0

The law of change of voltage in parallel
colival
contours
similar
law
change the struma in the last contour.
Significantly, the Timchasian accumulation of struma iC (t).
iC (t) Ie
p
(Cos 1t sin 1t).
1
Since at t = 0 the voltage on the capacity reached zero, then for this moment
next hour to keep the fasteners short-circuited. otzhe,
at the moment t = + 0, the entire strum I passed through the container (iC (+0)) = I. As t → ∞, the lance
switch to the constant stream mode, for which u (∞) = 0, iL (∞) = I, iG (∞) = iC (∞) = 0.
The lower the quality factor (more extinguished) to the contour, the more quickly it will end
transitional process.

Alone functions and their powers. An important place in the theory of linear lances is occupied by the subsequent reaction of lances to the idealization of zonnish ings, described by the so-called single functions.

Single step function (Heavyside function) the function is called

Function schedule 1 (7 - (0) may look like a gathering or a streak, the height of some kind of a lonely one (Fig. 6.16, a). A stribok of this type will be called solitary. at t 0 = Q for a single step-frequency function, the value 1 (0 (Fig. 6.16, b).

At the link with tim, scho tver be-a fringe function of the hour f(t) Pa 1 (T - t0) equals zero at t i one / (0 at t>t0:

Heaviside function l (f - t0) manually wink for an analytical presentation of various external influences

Mal. 6.16.

When connecting the lancet to the dzherel of the standing strum, or the tension of the outward injection on the lancet

de to- switching moment.

Zovnishniy inflow of this kind is called non-lonely streak. The Heaviside function, viraz (6.95), can be represented by looking at

how t=? About the lancet, the cord of the harmonic struma or the voltage is turned on

then you can imagine the evocative influx on the lancers

Yakshcho zovnіy vpriv on lansyug at the moment of the hour t = t§ string-like change as one fixed value X ( to the next x 2, then

Zovnіshnіy vpriv on lansyug, scho maє the form of a rectangular impulse height X and trivality t u(Figure 6.17, a), You can imagine two identical strips

zsunutih in the hour on? i (Fig. 6.17, b, v):

Mal. 6.17.

Mal. 6.18.

Clearly rectilinear impulse to trivality At and height X / At(Figure 6.18, a). It is obvious that the area of ​​\u200b\u200bthe impulse is good alone and cannot lie in At. With a change in the trivality of the yogo impulse, the height grows, moreover, with At- *? 0 won straight to infinity, but the area of ​​the impulse is filled with equal unity. Impulse of infinitely small trivality, infinitely great height, the area of ​​some ancient one, we will call single impulse.

The function that represents a single pulse is set to 5 (T-to) and is called the 5-function or Dirac function ". in such a manner,

At? 0 = 0 for the 5-function, the value 5 (T). When prompted by time diagrams of the function b (T-to)і 8(t) we will show the vertical arrows with the sign 00 close to the wind (Fig. 6.18, b, c).

To establish a link between a 5-function and a single step function, it is accelerated by virase (6.96). respectfully X= 1 /At and directly At to zero, acceptable

in such a manner, The 8-function is similar to a single step function, and a single step function - integral of the 8-function.

A generalization of operations on single functions, including operations of differentiation of a single step function, is given in the theory of generalized functions. For a simple binding of such operations, functions 1 (7: - / 0) and 6 (7 - t0) visualize, in the form of boundary values, some more simple functions, for some other operations, they are simple. Let's look at, for example, the function.gDG) (Fig. 6.19, a), satisfies minds

Other functions X(t) by the hour (Fig. 6.19, b) may look like a straight-cut impulse to trivality At and height 1 / D t:

at At-*? 0 function X(t) evolve into a single stage function, and the function dx ((t) / dt- in b-function:

the stars are screaming

Mal. 6.19.

When vikonannі different operations on single functions, the moment of commutation t Q manually divide into three different moments:? 0 _-moment to the hour, what without interrupting the commutation,? 0 - vlasne switching moment i? () + - the moment of the hour, coming without delay after switching. Looking at the mind (6.98) you can see

Have a sizzling glare

Tvіr suffices for the exchanged function for an hour / (?) At 8 (? -? 0)

Minds (6.103) are also satisfied with tvir f (t 0) 6 (t-? O)> already,

Z virazіv (6.102) and (6.104) are obvious, scho іntegral vіd dvor sufficiently subdivided function / (?) On 6(1: - tg) is more expensive or the values ​​of the function at t = to(as a point to lie within the interval of integration), or zero (as a point? 0 do not lie within the interval of integration):

In this way, after the help of the 5-function, you can see the value of the function / (?) At a certain moment and hour? 0 - Qiu singularity 8-function call name filtering power.

In order to determine the reaction of linear electric lances to the outer influx of a single hairline or a single impulse, it is necessary to know the image of single Laplace functions. Vikoristovuyuchi looked at the power of single functions, otrimuєmo

at t 0 = 0 operator images of single functions may look especially simple:

• More suvore designation of the 5-function div., For example, in robots.

linear lansyuga

Test #3

Nutrition for self-verification

1. Perekhuyte the main power of the width of the ymovirnosti of the magnitude of the fall.

2. How does the intensity of imovirnosti and the characteristic function of the volatility value relate to each other?

3. Recalculate the main laws of the subdivision of the magnitude of the fall.

4. What is the physical difference between the dispersion of the ergodic vypadkovy process?

5. Point out a few examples of linear and non-linear, stationary and non-stationary systems.

1. Vipadkovym process is called:

a. Be-yaké vipadkove zm_na deykoї physical value in hours;

b. The succession of functions to the hour, which is rooted in the actual statistical regularity for them;

c. Sukupnіst vipadkovyh numbers, scho pіdkoryayutsya deyakіy zagalnіy for them statistical patterns;

d. The succession of the vipadical functions of the hour.

2. The stationarity of the vypadkovy process means that by stretching the horns for an hour:

a. Mathematical spodіvannya and variance are constant, and the autocorrelation function is only deposited depending on the value of the hour t 1 i t 2 ;

b. Mathematical spodіvannya and variance are imminent, and the autocorrelation function is to fall only at the hour of the cob and the end of the process;

c. Mathematically, it is invariable, and the variance is deposited only depending on the value of the hour t 1 i t 2 ;

d. The dispersion is unchangeable, and it is mathematically accurate to deposit only at the hour of the cob and the end of the process.

3. Yergodic process means that the parameters of the vertical process can be determined by:

a. Kіlkom kіtsevim realіzatsіy;

b. One final implementation;

with One unfinished implementation;

d. Kіlkom neskіchennim realіzatsіy.

4. spectral width tightness of the ergodic process - tse:

a. Between the spectral width of the reduced implementation, subdivisions per hour T;

b. Spectral span of the last realization of trivality T, Submitted by an hour T;

c. Between the spectral width of the reduced implementation;

d. Spectral span of the last realization of trivality T.

5. The theorem of Wiener - Khinchin є spіvіdnoshnja mіzh:

a. Energy spectrum i mathematical refinement vipadic process;

b. Energy spectrum and dispersion of the vertical process;

c. Correlation function and dispersion of the vertical process;

d. Energy spectrum i correlation function vypadkovy process.

Electrically, there are a number of alternating signals that need to be on the її entrance. To that in the most extreme way mathematical model lansyug can be asked at the sight S in (t) and vyhіdny reaction S vortex (t) :

S in (t) = TS in (t),

de T is the Lanzug operator.

On the basis of the fundamental powers of the operator, one can make vysnovki about the most important sources of power of the Lantsyugs.

1. Just like the Lanciug operator T not lie in the amplitude of the inflow, then the lancet is called linear. For such a lancer, the principle of superposition is fair, which ensures the independence of diversified inputs:

T = TS in1 (t) + TS in2 (t) + ... + TS inn (t).

Obviously, with a linear conversion of signals in the spectrum of the input, there is no doubt about the frequencies that depend on the frequencies of the spectrum of the splashes.

The class of linear lances is made up as passive lances, which are composed of resistors, capacitors, inductances, and active lances, which include more transistors, lamps, etc. .

2. How should the sound of the input signal in the hour be brought up to the same sound of the output signal, i.e.

S in (t t 0) = TS in (t t 0),

then the lansyug is called stationary. The power of stationarity does not extend to the lansy, but to replace the elements with changing parameters (inductance, capacitors, etc.).