ANALYSIS OF THE BASIC DIAGRAM OF MAGNETIC-TRANSISTOR CONVERTERS Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

ANALYSIS OF THE BASIC DIAGRAM OF MAGNETIC-TRANSISTOR CONVERTERS

B. Abdullaev1, Kh.E. Kholbutaeva2, M.U. Idriskhodjaeva3, M.B. Peysenov4

1Candidate of technical sciences, Associate Professor, Department of Electrical Engineering 2Senior teacher Department of Electrical Engineering 3Associate Professor, Department of Electrical Engineering 4Senior teacher Department of Electrical Engineering 1,2,3,4Tashkent State Technical University https://doi.org/10.5281/zenodo.11093187

Abstract. The article provides an analysis of multiplying and dividing devices based on a magnetic transistor amplifier. We consider the amplification mode and the transient process of a magnetic transistor converter, and also provide a description of the operating states of the basic circuit. The proposed scheme is simple, economical, highly reliable, fast and stable. As a result of the research, based on the data obtained, characteristics were constructed on which it can be noted that the rate of change of induction during the operating half-cycle is constant and does not depend on the magnitude of the control signal. When designing functional converters with magnetic transistor pulse-width modulators, the one used in the analysis of one of the proposed circuits, taking into account the dynamic hysteresis loop, can serve as the basis for a preliminary assessment of the conversion accuracy in a given range of input values.

Keywords: converter, analysis, hysteresis loop, compensation, error, switching, generator, transient process, amplification mode, calculation, modulator, graphs, transistor, induction, magnetic permeability.

A large class of multiplier-dividing devices and other functional converters are based on magnetic transistor amplifiers (MTAs), which act as pulse-width modulators. Converters with MTA are therefore called magnetic transistor (MP). In the existing literature [3,4,5], a general approach to the design of MP has not yet been developed, since the basic scheme of MP has not been defined and, as a consequence, there is no theoretical analysis of it. The choice of such a scheme and its selective study would make it possible to develop a unified methodology for calculating the MP, to identify the components of the error in the functional transformation and ways to compensate for them. Let's consider one of the possible variants of the basic MTA circuit (Fig. 1) on two cores A and B with power from a direct current source and transistor switching of the control windings wy and working wp from transformator Tp with circular frequency ro master oscillator (MO). The circuit is simple, economical, highly reliable, fast and stable, its operating states are determined by switching transistors T1+T4 are given in the table.

Table 1

Characteristics of the operating states of the circuit

Elements State 1 State 2

Transistors T1 and T4 Open Open

Transistors T2 and T3 Close Close

Core A Working half-cycle Control half-cycle

Core B Control half-cycle Working half-cycle

Having accepted the known assumptions about the ideality of transistors and the rectangularity of the static hysteresis loop, we write the initial equations for the state 1:

* lpR,= U h

rlR

w * i, R, = U y,

ipwp= HAl ;

- iywy = HBl ;

(1)

(2) (3)

(4)

where BA, HA u BB, HB - magnetic induction and field strength in cores Aand B;

T

a)

U„

" V

Uy>Uym/

Rice. 1. Basic circuit of a magnetic transistor amplifier a); passage characteristic 6); self-saturation area e).

B)

'P

H

UH, i , R - supply voltage, current and total active resistance of the operating circuit; Uy, i , R

- voltage, current and active resistance of the control circuit; S, l - core cross-section and length of the average magnetic field line.

Boost mode. The magnetization reversal of the cores occurs according to a particular dynamic cycle of the hysteresis loop, for which the expressions [2, 3] are valid:

(5)

at n

0 <

uy < luyS\

(6)

0

1

where: ^ - equivalent magnetic permeability, determined from the dynamic demagnetization

curve (DDR);

Hc - static coercive force;

Sign "-" in formula (5) corresponds to an increase in induction in the core, "+" to its

decrease. Then from equations (2) and (5) we obtain the expression for the control current:

<7>

2 t

Where k = —, xэ = m ^3Wp5 - equivalent inductive reactance of the working winding.

Wv L

Wy 0

Substituting expression (4) into (7), we obtain for the magnetic field strength of core B:

Uywy X3HC

rl mrwK

2

h б (8)

-1

7ГТуГуК

Considering that the supply voltage of the MTA is

U = — R + rp )Hpm, (9)

wp

where Hpm- amplitude of the field strength in the operating half-cycle; from expressions (1), (5) and (9) we determine the strength of the core A:

H „

Hpm {Rh + rp )-

pm \RH + rp Xэ

HA =---n. (10)

^ + RH + rp n

Then the expression for the operating circuit current is:

L HpmPxHc

1P =--p-. (11)

P ^p 1 + Pxc

From expression (11) the current values in the operating circuit during magnetization intervals can be obtained (0 + a) and saturation (a + n). Really. When magnetized хэ >> Rzn,px ^ 0, hence:

ip ном (12)

Wp

In the saturation interval хэ ^ 0, px ^ m, in hence: J у 1 HpmPx + Hc 1 „

H = lim--ГГ- = -Hpm ■ (13)

Px Wp 1 + Px wp

From the point of view of the physics of processes, state 2 is not fundamentally different from state 1, cores A and B change roles, therefore we determine the average value of the load voltage over the period by integrating expressions (11) and (13):

HpmPx + HC

U = -RhL

U H. cp

ж wp

-a + H m(n - a)

(14)

1 + Ax P

On the other hand, as for a conventional MU with self-saturation [1], for the MTA we can

write:

Uhcp =vUebiXCp-v{u - 2fWpS\ABy I) (15)

where ] =

R

H

Rh + rp

; A8 - the absolute value of the change in induction in the core during the

control half-cycle.

Then, given that Un — 4fwpSBs From equations (14) and (15) we determine the MTA saturation angle:

Hpm-Hc | Pm

2f]SwP [2BS (1 + px |J

'S (1 + f xj

TJ

(16)

To calculate the current and final values of the core inductions for state 1, we obtain

B A =

I (RH + rp \Hpm - Hc )

w

>(1 +Px )

(T-0s ) + BS ,

B =

wysa

Uy +

u -xh-

y 7myk2

1 -

x„

wyk2

t + b„

(17)

(18)

where 0 <т < a; Uy < 0.

Passage characteristic of MTA. For DDR, we accept approximation by three straight segments (Fig. 1, b).

ABy =ABo, on (Hy > Hcd); Щ < 0 (site С-Д);

ABy =Мэ (Hy + Hcd), on (Нум < Hy < H^d ) (site В-С);

ABy = ABmax, on (Hy < Hym ) (участок А-В).

Approximation parameters H^ and Hcd can be determined directly from experimental DDR or theoretically. For example, H^ is determined from formula (8) taking into account the fact that at the point «В» Uym = 4fSwyBs;

H =

y.m.

4fSWyBs - t-JH

WyK

x„

лГуК2

L

w„

(19)

and the dynamic coercive force with a linear change in induction can be expressed as follows [3]

1213 (20)

Hcd = H + 0,125aöd2 Bs,

where S - specific electrical conductivity of a ferromagnet; d - thickness of the tape or plate.

To simplify, let' s assume Bmax — 2Bs u Bmax ^ 0. Then for the SD section of the DDR, the voltage at the load is equal to UHar — rUn, , for site ВС

UH.cp = tU„ - 2fwpS\^\\Hy - HHcp )

H .cp

And for site АВ

(21)

UHcp = RH" H

сд.

(22)

The last expression indicates the horizontality of the left branch of the MTA pass characteristic, which is its feature compared to conventional self-saturation MU. This is explained

1

by the fact that when\Uy\>4fSwyBs the dynamic hysteresis loop becomes asymmetrical relative to the induction axis (fig.1,e), Moreover, no subsequent expansion of the loop is observed when the cores are magnetized, i.e. during the working half-cycle. Indeed, from equations (17) and (18) one can obtain the rate of change of induction for the working and control half-cycles:

dBrab _ LRs(Hpm-Hc

dr M2Sw(1+pX)'

(23)

dB,

ynp

d

WyS(

uy-

X3LHc

KWyK2

X3

KTyK2

-1

(24)

Expression (23) shows that the rate of change of induction during the operating half-cycle is constant and does not depend on the magnitude of the control signal. Due to transistor switching of the windings at the end of the control half-cycle, the operating point of the MTA always returns to point I, from which the operating half-cycle begins, and at the maximum supply voltage, magnetization reversal occurs along a full hysteresis loop, which determines the constancy of the load current, equal to the no-load current of the MTA . This circumstance creates good prerequisites for the development of contactless magnetic relays with adjustable loop width while maintaining the differential coefficient unchanged.

To operate in amplification mode, as is known, a section of the VS DDR is used, in which the MTA has a voltage gain Ku , determined from expressions (8) and (21):

(25)

Ku = 2fwpß3x

nwyk2 L(x3-nry)'

Transient processes in MTA. Keeping the previously accepted assumptions, we will assume that the control signal changes abruptly from the initial state Uy and satisfies condition (6). The most common case is when a control voltage jump occurs in the interval of a half-cycle of the master oscillator frequency, not coinciding with its end or beginning.

Let us assume that the moment of the jump t_0 occurs within the (n-1) half-cycle, which is the control one for core A and the working one for B. At this point in time, the induction is equal

BA

wy S (

XsLHcg

uy0 —

Jy0 uwyk2

1-

X3

nryk2

T0 + Bs

(26)

and the magnetic state of core A on the dynamic hysteresis loop is determined by point 1 (Fig. 2). Beginning with t0 , when

Uy = WyA > M

the operating point moves along section 1-2, core A is demagnetized along a wider private cycle, and its induction changes as follows:

BA/ t0 < t < (n — 1)n =

1

wySM

u

y1

_ IT

uy0 nwyk2

nryk2

1

BA

x[(n — 2)n + r0] +--.

to

By the end of the half-period at i = (n — V)n induction takes on the meaning:

X3LHcg

BA/(n — 1)n = —

A

wy S (

UyT +

nwyk2

X3 nryk2

-1

[Or — To)] + Br-

(27)

1

Next n the half-cycle is working for core A and controlling for B. Core B is immediately remagnetized according to a new steady-state cycle corresponding Uy, at the end of the half-cycle its induction takes on a new steady-state value:

X3LHcg

n / 1 u , KWyk2 n

BB/nn = —— U^r + x/ . n + B

WySte

Xs nryk2

s.

(28)

This is where the transient process for the voltage at the load ends. In the next (n+1) half-cycle, the representing point of the core A moves along the new steady cycle. The curves of the transition process in the MTA are shown in Figure 2. Thus, the duration of the transition process for average values is equal to:

xnn = (n - t0) + n = 2n - T0,

(29)

the time of the transient process lies within one frequency period of the master oscillator.

Uy

B

A a bU To i _

1 T

1 O

1 t

Fig. 2. Transition process A particular case is when the control voltage jump coincides with the beginning of the (n -1) half-cycle. Then the representing point of the core A, already during this half-cycle, will move along a new established cycle, and the induction will change according to a linear law:

[T-(n-2y]+Bs. (30)

BA =

WySte

Uyo +

Jy° nwyk2

Xs

nryk2

Then, already in the next half-cycle, the voltage at the load will take its new steady-state value, and the MTA will be a link of pure delay by half the frequency period of the master oscillator.

The results of the analysis of one of the MTA circuits presented in the article, taking into

account the dynamic hysteresis loop, can serve as the basis for the design of functional converters

with magnetic transistor pulse-width modulators, in particular, for a preliminary assessment of the

conversion accuracy in a given range of input values.

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