We continue our acquaintance with electronic components and in this article we will look at device and principle of operation of the transformer.
Transformers have found wide application in radio and electrical engineering and are used for the transmission and distribution of electrical energy in power supply networks, for powering radio equipment circuits, in converter devices, as welding transformers, etc.
Transformer designed to convert AC voltage one value into an alternating voltage of another value.
In most cases, a transformer consists of a closed magnetic circuit (core) with two electrically unconnected windings located on it. The magnetic core is made of ferromagnetic material, and the windings are wound with insulated copper wire and placed on the magnetic core.
One winding is connected to an alternating current source and is called primary(I), voltage is removed from the other winding to power the load and the winding is called secondary(II). A schematic diagram of a simple transformer with two windings is shown in the figure below.
1. The principle of operation of the transformer.
The operating principle of the transformer is based on phenomenon of electromagnetic induction.
If alternating voltage is applied to the primary winding U1, then alternating current will flow through the turns of the winding Io, which will create around the winding and in the magnetic core alternating magnetic field. Magnetic field produces magnetic flux Fo, which, passing along the magnetic circuit, crosses the turns of the primary and secondary windings and induces (induces) alternating EMF in them - e1 And e2. And if you connect a voltmeter to the terminals of the secondary winding, it will show the presence of output voltage U2, which will be approximately equal to the induced emf e2.
When a load, for example an incandescent lamp, is connected to the secondary winding, a current arises in the primary winding I1, forming an alternating magnetic flux in the magnetic circuit F1 varying at the same frequency as the current I1. Under the influence of an alternating magnetic flux, a current arises in the secondary winding circuit I2, which in turn creates a counteracting magnetic flux according to Lenz’s law F2, seeking to demagnetize the magnetic flux generating it.
As a result of the demagnetizing effect of the flow F2 Magnetic flux is established in the magnetic circuit Fo equal to the flux difference F1 And F2 and being part of the flow F1, i.e.
Resultant magnetic flux Fo ensures the transfer of magnetic energy from the primary winding to the secondary winding and induces an electromotive force in the secondary winding e2, under the influence of which current flows in the secondary circuit I2. It is due to the presence of magnetic flux Fo and there is a current I2, which will be the greater the more Fo. But at the same time, the greater the current I2, the greater the counterflow F2 and therefore less Fo.
From the above it follows that at certain values of the magnetic flux F1 and resistances secondary winding And loads the corresponding EMF values are set e2, current I2 and flow F2, ensuring the balance of magnetic fluxes in the magnetic circuit, expressed by the formula given above.
Thus, the flux difference F1 And F2 cannot be zero, since in this case there would be no main thread Fo, and without it the flow could not exist F2 and current I2. Therefore, the magnetic flux F1, created by the primary current I1, always more magnetic flux F2, created by the secondary current I2.
The magnitude of the magnetic flux depends on the current creating it and on the number of turns of the winding through which it passes.
The voltage of the secondary winding depends on ratio of the number of turns in the windings. With the same number of turns, the voltage on the secondary winding will be approximately equal to the voltage supplied to the primary winding, and such a transformer is called dividing.
If the secondary winding contains more turns than the primary, then the voltage developed in it will be greater than the voltage supplied to the primary winding, and such a transformer is called increasing.
If the secondary winding contains fewer turns than the primary, then its voltage will be less than the voltage supplied to the primary winding, and such a transformer is called downward.
Hence. By selecting the number of turns of windings at a given input voltage U1 get the desired output voltage U2. To do this, they use special methods for calculating the parameters of transformers, with the help of which the windings are calculated, the cross-section of the wires is selected, the number of turns is determined, as well as the thickness and type of the magnetic core.
The transformer can only operate in alternating current circuits. If its primary winding is connected to a direct current source, then a magnetic flux is formed in the magnetic circuit, constant in time, in magnitude and direction. In this case, an alternating voltage will not be induced in the primary and secondary windings, and therefore, electrical energy will not be transferred from the primary circuit to the secondary. However, if a pulsating current flows in the primary winding of the transformer, then an alternating voltage will be induced in the secondary winding, the frequency of which will be equal to the ripple frequency of the current in the primary winding.
2. Transformer design.
2.1. Magnetic core. Magnetic materials.
Purpose magnetic circuit consists in creating a closed path for the magnetic flux with minimal magnetic resistance. Therefore, magnetic cores for transformers are made of materials with high magnetic permeability in strong alternating magnetic fields. The materials must have low eddy current losses so as not to overheat the magnetic circuit at sufficiently high values of magnetic induction, be fairly cheap and not require complex mechanical and thermal treatment.
Magnetic materials, used for the manufacture of magnetic cores, are produced in the form of separate sheets, or in the form of long tapes of a certain thickness and width and are called electrical steels.
Sheet steels (GOST 802-58) are produced by hot and cold rolling, strip textured steels (GOST 9925-61) only by cold rolling.
Also used are iron-nickel alloys with high magnetic permeability, for example, permalloy, permindur, etc. (GOST 10160-62), and low-frequency soft magnetic ferrites.
For the manufacture of a variety of relatively inexpensive transformers, they are widely used electrical steels, which have a low cost and allow the transformer to operate both with and without constant magnetization of the magnetic circuit. The most widely used steels are cold-rolled steels with best characteristics compared to hot rolling steels.
Alloys with high magnetic permeability used for the manufacture of pulse transformers and transformers designed to operate at elevated and high frequencies 50 – 100 kHz.
The disadvantage of such alloys is their high cost. For example, the cost of permalloy is 10–20 times higher than the cost of electrical steel, and permendur is 150 times higher. However, in some cases their use can significantly reduce the weight, volume and even the total cost of the transformer.
Another disadvantage is the strong influence of permanent magnetization and alternating magnetic fields on the magnetic permeability, as well as low resistance to mechanical influences - shock, pressure, etc.
From soft magnetic low frequency ferrites manufactured with high initial permeability pressed magnetic cores, which are used for the manufacture of pulse transformers and transformers operating at high frequencies from 50 - 100 kHz. The advantage of ferrites is their low cost, but the disadvantage is low saturation induction (0.4 - 0.5 T) and strong temperature and amplitude instability of magnetic permeability. Therefore, they are used only in weak fields.
The choice of magnetic materials is made based on electromagnetic characteristics, taking into account the operating conditions and purpose of the transformer.
2.2. Types of magnetic circuits.
Magnetic cores of transformers are divided into laminated(stamped) and tape(twisted), made from sheet materials and pressed from ferrites.
Laminated Magnetic cores are assembled from flat stamped plates of the appropriate shape. Moreover, the plates can be made from almost any, even very fragile, materials, which is an advantage of these magnetic cores.
Tape Magnetic cores are made of a thin tape wound in the form of a spiral, the turns of which are firmly connected to each other. The advantage of strip magnetic cores is the full use of the properties of magnetic materials, which makes it possible to reduce the weight, size and cost of the transformer.
Depending on the type of magnetic circuit, transformers are divided into rod, armored And toroidal. Moreover, each of these types can be either rod or tape.
Rod.
In magnetic circuits rod type windings are located on two rods ( rod called the part of the magnetic circuit on which the windings are placed). This complicates the design of the transformer, but reduces the winding thickness, which helps reduce leakage inductance, wire consumption and increases the cooling surface.
Rod magnetic cores are used in output transformers with a low level of interference, since they are insensitive to the effects of external low-frequency magnetic fields. This is explained by the fact that, under the influence of an external magnetic field, voltages that are opposite in phase are induced in both coils, which, when the turns of the windings are equal, compensate each other. As a rule, transformers of high and medium power are made of rod type.
Armored.
In the magnetic circuit armor type the winding is located on the central rod. This simplifies the transformer design, allows for more complete use of the winding window, and also provides some mechanical protection for the winding. Therefore, such magnetic circuits are most widely used.
Some disadvantage of armored magnetic cores is their increased sensitivity to low-frequency magnetic fields, which makes them unsuitable for use as output transformers with low noise levels. Most often, medium-power transformers and microtransformers are armored.
Toroidal.
Toroidal or ring transformers make it possible to make fuller use of the magnetic properties of the material, have low dissipation fluxes and create a very weak external magnetic field, which is especially important in high-frequency and pulse transformers. But due to the complexity of manufacturing the windings, they were not widely used. Most often they are made from ferrite.
To reduce losses due to eddy currents, laminated magnetic circuits are assembled from stamped plates 0.35 - 0.5 mm thick, which are coated on one side with a layer of varnish 0.01 mm thick or an oxide film.
The tape for tape magnetic cores has a thickness from a few hundredths to 0.35 mm and is also covered with an electrically insulating and at the same time adhesive suspension or oxide film. And the thinner the insulation layer, the denser the cross-section of the magnetic circuit is filled with magnetic material, the smaller the overall dimensions of the transformer.
Recently, along with the considered “traditional” types of magnetic cores, new forms have been used, which include “cable” type magnetic cores, “inverted torus”, coil type, etc.
Let's leave it at that for now. Let's continue in .
Good luck!
Literature:
1. V. A. Volgov - “Parts and components of radio-electronic equipment”, Energia, Moscow 1977
2. V. N. Vanin - “Current Transformers”, Publishing House “Energia” Moscow 1966 Leningrad.
3. I. I. Belopolsky - “Calculation of transformers and chokes of low power”, M-L, Gosenergoizdat, 1963.
4. G. N. Petrov - “Transformers. Volume 1. Fundamentals of Theory", State Energy Publishing House, Moscow 1934 Leningrad.
5. V. G. Borisov, “Young Radio Amateur”, Moscow, “Radio and Communications” 1992
Let's take a coil with a ferromagnetic core and take it out separate element ohmic resistance of the winding as shown in Fig. 2.8.
Figure 2.8 – To derive the formula for transformer EMF
When you turn on the alternating voltage e c in the coil, according to the law of electromagnetic induction, a self-induction emf e L appears.
(2.8)
where ψ is flux linkage,
W – number of turns in the winding,
Ф – main magnetic flux.
We neglect the scattering flux. The voltage applied to the coil and the induced emf are balanced. According to Kirchhoff's second law for input circuit can be written:
e c + e L = i * R exchange, (2.9)
where R rev is the active resistance of the winding.
Since e L >> i * R exchange, we neglect the voltage drop across the ohmic resistance, then e c ≈ – . If the network voltage is harmonic e c = E m cos ωt, then E m cos ωt = , whence 
. Let's find the magnetic flux. To do this, we take the indefinite integral of the right and left sides. We get
, (2.10)
but since we consider the magnetic circuit to be linear, only a harmonic current flows in the circuit and there is no permanent magnet or constant component, then the integration constant c = 0. Then the fraction in front of the harmonic factor is the amplitude of the magnetic flux, from which we express E m = Ф m * W * ω. Its effective value is
Or we get
where s is the cross-section of the magnetic circuit (core, steel).
Expression (2.11) is called the basic formula of transformer EMF, which is valid only for harmonic voltage. Usually it is modified and the so-called form factor is introduced, equal to the ratio of the effective value to the average:
. (2.12)
Let's find it for a harmonic signal, but find the average value on the interval
Then the form factor is 
and the basic formula of the transformer EMF takes its final form:
(2.13)
If the signal is a meander, then the amplitude, effective and average values for half the period are equal to each other and its . You can find the shape factor for other signals. The basic formula of transformer EMF will be valid.
Let's construct a vector diagram of a coil with a ferromagnetic core. With a sinusoidal voltage at the coil terminals, its magnetic flux is also sinusoidal and lags in phase from the voltage by an angle π/2 as shown in Fig. 2.9a.
Figure 2.9 – Vector diagram of a coil with ferromagnetic
core a) without losses; b) with losses
In a lossless coil, the magnetizing current - reactive current (I p) is in phase with the magnetic flux Ф m. If there are losses in the core (), then the angle is the angle of losses due to magnetization reversal of the core. The active component of the current Ia characterizes the losses in the magnetic circuit.
Let's take a coil with a ferromagnetic core and take out the ohmic resistance of the winding as a separate element, as shown in Figure 1.
Figure 1. Inductor with ferromagnetic core
When an alternating voltage e c is applied to the coil, according to the law of electromagnetic induction, a self-induction emf e L appears.
(1) where ψ
— flux linkage, W- number of turns in the winding, F- main magnetic flux. We neglect the scattering flux. The voltage applied to the coil and the induced emf are balanced. According to Kirchhoff’s second law for the input circuit, we can write:
e c + e L = i × R exchange, (2)Where R obm - active resistance of the winding.
Since e L >> i × R exchange, then we neglect the voltage drop across the ohmic resistance, then e c ≈ −e L. If the mains voltage is harmonic, e c = E m cosω t, That:
(3)
Let us find the magnetic flux from this formula. To do this, we transfer the number of turns in the winding to the left side, and the magnetic flux Ф to the right:
(4)
Now let's take the indefinite integral of the right and left sides:
(5)Since we consider the magnetic circuit to be linear, only harmonic current flows in the circuit and there is no permanent magnet or constant component of the magnetic flux, then the integration constant c = 0. Then the fraction in front of the sine is the amplitude of the magnetic flux
(6)from where we express the amplitude of the input EMF
E m = F m × W × ω (7)Its effective value is
(8) (9)Expression (9) is called basic formula of transformer EMF, which is valid only for harmonic voltage. With a non-harmonic voltage, it is modified and the so-called form factor is introduced, equal to the ratio of the effective value to the average:
(10)
Let's find the shape factor for a harmonic signal, and find the average value in the interval from 0 to π/2
(11)
Then the form factor is 
and the basic formula of the transformer EMF takes its final form:
If the signal is a sequence of rectangular pulses of the same duration (meander), then the amplitude, effective and average values for half a period are equal to each other and its k f = 1. You can find the shape factor for other signals. The basic formula of transformer EMF will be valid.
Let's construct a vector diagram of a coil with a ferromagnetic core. With a sinusoidal voltage at the coil terminals, its magnetic flux is also sinusoidal and lags in phase from the voltage by an angle π/2 as shown in Figure 2.
PRACTICUM
ON ELECTRIC MACHINES
AND APPARATUS
Tutorial
For full-time and part-time students
in the field of instrument engineering and optics
as a teaching aid for higher education students
institutions studying in specialty 200101 (190100)
"Instrument making"
Kazan 2005
UDC 621.375+621.316.5
BBK 31.261+31.264
Prokhorov S.G., Khusnutdinov R.A. Workshop on electrical machines
and devices: Textbook: For full-time and part-time students. Kazan: Kazan Publishing House. state tech. Univ., 2005. 90 p.
ISBN 5-7579-0806-8
Designed for conducting practical classes and performing independent work in the discipline “Electrical machines and devices” in the direction of training of a certified specialist 653700 – “Instrument making”.
The manual may be useful for students studying the discipline
"Electrical engineering", "Electromechanical equipment in instrument making",
"Electrical machines in instrument devices", as well as students of all
engineering specialties, including electrical engineering.
Table Il. Bibliography: 11 titles.
Reviewers: Department of Electric Drive and Automation of Industrial Installations and Technological Complexes (Kazan State Energy University); professor, candidate physics and mathematics Sciences, Associate Professor V.A. Kirsanov (Kazan branch of the Chelyabinsk Tank Institute)
ISBN 5-7579-0806-8 © Kazan Publishing House. state tech. University, 2005
© Prokhorov S.G., Khusnutdinov R.A.,
The proposed tests in the discipline “Electrical machines and devices” are intended for practical training and independent work. The tests are compiled in the sections “Transformers”, “Asynchronous machines”, “ Synchronous machines", "DC commutator machines", " Electrical apparatus" The answers in table form are given at the end of the manual.
TRANSFORMERS
1. Why are the air gaps in the transformer kept to a minimum?
1) To increase the mechanical strength of the core.
3) To reduce the magnetic noise of the transformer.
4) To increase the mass of the core.
2.Why is the transformer core made of electrical steel?
1) To reduce the no-load current.
2) To reduce the magnetizing component of the no-load current
3) To reduce the active component of the no-load current.
4) To improve corrosion resistance.
3.Why are the transformer core plates held together with pins?
1) To increase mechanical strength.
2) For attaching the transformer to an object.
3) To reduce moisture inside the core.
4) To reduce magnetic noise.
4. Why is the transformer core made of electrical steel plates electrically insulated from each other?
1) To reduce the core mass.
2) To increase the electrical strength of the core.
3) To reduce eddy currents.
4) To simplify the design of the transformer.
5. How are the beginnings of the primary winding of a three-phase transformer designated?
1) a, b, c 2) x, y, z 3) A, B, C 4) X, Y, Z
6. How are the primary and secondary windings of a three-phase transformer connected if the transformer has group 11 (Y - star, Δ - triangle)?
1) Y/Δ 2) Δ/Y 3) Y/Y 4) Δ/Δ
7. How do the magnetic core and winding of a conventional transformer differ in weight from an autotransformer if the transformation ratios are the same? TO=1.95? The power and rated voltages of the devices are the same.
1) No difference.
2) The masses of the magnetic core and autotransformer windings are less than the masses
magnetic core and windings of a conventional transformer, respectively.
3) The mass of the magnetic circuit of an autotransformer is less than the mass of the magnetic circuit of a conventional transformer, and the masses of the windings are equal.
4) The masses of the magnetic core and windings of a conventional transformer are less than those of the corresponding values of an autotransformer.
5) The mass of the autotransformer winding is less than the mass of the windings of a conventional transformer, and the masses of the magnetic cores are equal.
8. What law of electrical engineering is the principle of operation of a transformer based on?
1) On the law of electromagnetic forces.
2) Based on Ohm's law.
3) On the law of electromagnetic induction.
4) Based on Kirchhoff’s first law.
5) Based on Kirchhoff’s second law.
9. What will happen to the transformer if it is connected to a DC network of the same magnitude?
1) Nothing will happen.
2) May burn.
3) The main magnetic flux will decrease.
4) The magnetic leakage flux of the primary winding will decrease.
10. What does a transformer transform?
1) The magnitude of the current.
2) The magnitude of the voltage.
3) Frequency.
4) Current and voltage values.
11. How is electrical energy transferred from the primary winding of an autotransformer to the secondary?
1) Electrically.
2) Electromagnetic way.
3) Electrically and electromagnetically.
4) As in a regular transformer.
12. What magnetic flux in a transformer carries electrical energy?
1) Magnetic leakage flux of the primary winding.
2) Magnetic leakage flux of the secondary winding.
3) Magnetic flux of the secondary winding.
4) Magnetic flux of the core.
13. What is affected by the self-inductive emf of the primary winding of a transformer?
1) Increases the active resistance of the primary winding.
2) Reduces the active resistance of the primary winding.
3) Reduces the current of the primary winding of the transformer.
4) Increases the current of the secondary winding of the transformer.
5) Increases the current of the primary winding of the transformer.
14. What is affected by the self-inductive emf of the secondary winding of a transformer?
1) Increases the active resistance of the secondary winding.
2) Reduces the active resistance of the secondary winding.
3) Reduces the current of the secondary winding of the transformer.
4) Increases the current of the primary winding of the transformer.
5) Reduces the inductive reactance of the secondary winding
transformer.
15. What is the role of the EMF of mutual induction of the secondary winding of a transformer?
1) It is a source of EMF for the secondary circuit.
2) Reduces the primary winding current.
3) Reduces the secondary winding current.
4) Increases the magnetic flux of the transformer.
16. Select the formula for the law of electromagnetic induction:
Select the correct spelling of the effective value of the EMF of the secondary winding of the transformer.
18. How do voltages compare in magnitude? short circuit U 1k and nominal U 1n in medium power transformers?
1) U 1k ≈ 0.05. U 1н 2) U 1k ≈ 0.5. U 1н 3) U 1k ≈ 0.6. U 1n
4) U 1k ≈ 0.75. U 1н 5) U 1k ≈ U 1n
19. What parameters of the T-shaped equivalent circuit of a transformer are determined from the no-load experience?
1) r 0 , r 1 2) X 0 , r 1 3) r' 2 , X' 2
How does a transformer work?
(b, c) W x. W 2 connects to the load.
U 1 i 1 F. This flow induces an emf e 1 And e 2 in the windings of the transformer:
EMF e 1 U 1, emf e 2 creates tension U 2
· Step-down transformer – a transformer that reduces the voltage (K>1).
What is the transformation ratio?
Transformation ratio is the ratio of the effective voltages at the ends of the primary and secondary windings when the secondary windings are open circuit (no-load of the transformer). K=W 1 /W 2 =e 1 /e 2.
For a transformer operating in no-load mode, we can assume with sufficient accuracy for practice that .
What nominal parameters of the transformer do you know and what do they determine?
Rated power is the rated power of each of the transformer windings. Rated current, voltage of windings. The external characteristic is the dependence of the voltage at the terminals of the transformer on the current flowing through the load connected to these terminals, i.e. dependence U2=f(I2) at U1=const. The load is determined by the load factor Kn=I2/I2nom ≈ I1/I1nom, efficiency - η = P2/P1
How to determine the rated currents of the transformer windings if the rated power of the transformer is known?
The rated power of a two-winding transformer is the rated power of each of the transformer windings.
Rated power equation: S H =U1 * I1 ≈ U2 * I2
I1 = S H /U1 ; I2 = S H /U2
What is called the external characteristic of a transformer and how to obtain it?
The external characteristic is the dependence of the voltage at the terminals of the transformer on the current flowing through the load connected to these terminals, i.e. dependence U 2 =f(I 2) at U 1 =const. When the load (current I 2) changes, the secondary voltage of the transformer changes. This is explained by a change in the voltage drop across the resistance of the secondary winding I 2 " z 2 and a change in EMF E 2 "=E 1 due to a change in the voltage drop across the resistance of the primary winding.
The EMF and voltage equilibrium equations take the form:
Ù 1 = –È 1 + Ì 1 " z 1, Ù 2 "=È 2 – Ì 2 " z 2 " (1)
The load value in transformers is determined by the load factor:
K n =I 2 /I 2 nom ≈ I 1 /I 1 nom;
The nature of the load is the phase shift angle of the secondary voltage and current. In practice, the formula is often used
U 2 = U 20 (1 - Δu/100),
Δu=K n (u ka cosφ 2 + u cr sinφ 2)
u ka = 100% I 1nom (R 1 - R 2 ")/U 1nom
u ka = 100% I 1nom (X 1 - X 2 ")/U 1nom
How to find the percentage change in transformer secondary voltage for a given load?
The percentage change in secondary voltage ∆U 2% at variable load is determined as follows: , where are the secondary voltages at no-load and at a given load, respectively.
What transformer equivalent circuits do you know and how are their parameters determined?
T-shaped transformer equivalent circuit:
How does a transformer work?
A transformer is a static electromagnetic device designed to convert, through a magnetic flux, alternating current electrical energy of one voltage into alternating current electrical energy of another voltage at a constant frequency.
Electromagnetic circuit of the transformer (a) and symbolic graphic symbols of the transformer (b, c) are shown in Fig. 1. There are two windings located on a closed magnetic circuit made of sheets of electrical steel. Primary winding with number of turns W x connects to a source of electrical energy with voltage U . Secondary winding with number of turns W 2 connects to the load.
What determines the EMF of the transformer windings and what is their purpose?
Under the influence of supplied alternating voltage U 1 current appears in the primary winding i 1 and a changing magnetic flux appears F. This flow induces an emf e 1 And e 2 in the windings of the transformer:
EMF e 1 balances the bulk of the source voltage U 1, emf e 2 creates tension U 2 at the output terminals of the transformer.
3. In what cases is a transformer called a step-up transformer and in what cases is it called a step-down transformer?
· Step-down transformer – a transformer that reduces the voltage (K>1).
Step-up transformer - a transformer that increases the voltage (K<1).