Why is a transformer not turning?

Ideal single-phase transformer

If electrical current flows through a wire, a magnetic field is created vertically around the conductor. The detection can be made visible with a compass (magnetic) needle aligned with the earth's magnetic field. In the vicinity of the current-carrying wire, the magnetic needle realigns itself in order to return to its original position after the current has been switched off. A wire wound in adjacent concentric turns forms a coil. If electrical current flows through it, the magnetic field lines overlap and the coil generates a magnetic field that corresponds to that of a bar magnet with a clear north and south pole.

The magnetic field lines are self-contained and form a so-called vortex field. The course of the field lines is determined outside the magnet from north to south and closes in the magnet from south to north. If the right hand grips a coil in such a way that the technical current direction points in the direction of the fingertips, then the splayed thumb points to the north pole of the magnetic field.

If a periodically changing excitation current flows through a coil, then the magnetic flux Φ through this coil changes proportionally. If this magnetic excitation field passes through a second coil, known as a secondary or induction coil, it generates an induction voltage at its connections. There is normally no electrically conductive connection between the primary excitation or field coil and the secondary induction coil. Both coils are arranged on a closed ferromagnetic core and only coupled via the periodically changing magnetic field. This classic design with galvanically separated coils is called a single-phase transformer or transformer.

The principle of energy transfer

The primary coil converts the supplied electrical energy into magnetic energy. The closed ferromagnetic iron core concentrates the magnetic field lines. They penetrate the secondary coil and generate electrical energy in it again by induction. The efficiency of the energy transfer is very high with a fixed magnetic coupling between the two coils. Since the iron core, as a short-circuited conductor ring, also acts like a coil, eddy currents arise in it. They are converted into thermal energy and reduce the efficiency. In order to minimize the high eddy current losses in the solid core, the ferromagnetic core consists of laminated and mutually insulated, packed sheets with optimized cross-sections or made of ferrite materials.

In the case of a transformer, energy is transmitted by electromagnetic induction.
The magnetic core should be good magnetically but poorly electrically conductive.
A permanent energy transfer takes place only through alternating fields.
A transformer cannot transmit direct voltage or direct current.

Transformers are used in power engineering for voltage and current conversion. They galvanically separate circuits from each other and can transmit electrical energy with a high degree of efficiency. In communications engineering, they are mostly referred to as transformers and are used to adapt different input and output impedances of the circuits. With a mechanically or electrically variable coupling factor, they were and are sometimes part of special band filter circuits.

Lossless transformer

The basic properties should be explained using the ideal lossless transformer. The coils behave purely inductively, there are no effective resistances and no winding capacities. The core material has no magnetic resistance, the magnetic flux only runs in the ferromagnetic core and does not scatter to the outside. The magnetic coupling factor with 100% energy transfer has the value 1. A magnetizing or no-load current is not taken into account and the laminated ferromagnetic core is free of coupling capacities.

Two coils wound in the same direction are located on one leg of a ferromagnetic closed UI core. A sinusoidal excitation voltage is applied to the primary and field coil. During the positive half-wave, the coil current should flow from A to E in the technical direction. Determined by the rule of the right fist, your magnetic north pole is at the bottom and the magnetic field lines in the core point in this direction.

This magnetic field, which changes over time, flows through the secondary or induction coil in the same direction. An induction voltage is created at the coil ends. If the phase position of the secondary voltage in relation to the primary voltage is displayed with the oscilloscope, then there is phase equality. The arrow direction of the induction voltage also points from A to E in the direction of the primary applied excitation voltage. This apparently contradicts the law of induction, where, according to Lenz's rule, a minus sign would be expected.

The observation is in agreement with the representations on the induction side. In the picture above, the winding direction of the induction coil is clockwise. The field lines run in a positive direction coming from above and generate an electrical field rotating to the left in a closed conductor loop. For the coil as a conductor loop open on the left, this means that there is positive potential at the rear at A and negative potential at the front at E. If the secondary circuit is closed, the current flows from A to E into the induction coil in a technical direction and generates a magnetic field that is directed against the primary excitation field. Lenz's rule is thus fulfilled.

The standardized circuit symbol of a transformer with two magnetically coupled coils is based on two coils arranged one above the other with the same winding direction. They are located on the same core segment and the magnetic flux flows through them in the same direction. The coils are moved horizontally in one plane and the direction of the magnetic flux is shown as a vertical arrow between them. In this standardized representation, all reference arrows run in the same direction. The poles with the same phase position are marked with a point for clear identification.

In terms of energy, the transformer in the symbolic representation as a two-port acts with the primary winding as a consumer. The current arrow points in at the entrance gate at the top. The secondary winding acts as a generator. The current direction arrow at the top of the exit gate points outwards.

If the secondary coil is mentally shifted over the closed core to the parallel leg, then A and E of the coils are diagonally opposite one another, as in the left part of the picture. If the phase positions in the measuring direction A to E are carried out with the oscilloscope, then there is phase equality. The standardized representation of the transformer is based on staggered coils as in the picture on the right and the connections A and E of both coils are directly opposite one another. In the measuring direction A to E, an inverse phase position is determined. With the same coil connections now directly opposite, the magnetic flux in both coils is opposite in relation to the same connection.

The following video clip shows the functional principle of the ideal transformer as a continuous film and then in individual consecutive 90 ° period segments. Each section is run through twice before switching. The video can be controlled with the help of the fade-in control bar so that the text sections can be read comfortably.

Main transformer equation

On the secondary side, the no-load voltage U2 is proportional to the number of turns N2. For sinusoidal voltages, their peak value is directly proportional to the maximum value of the magnetic flux Φ and can be expressed by the magnetic flux density B and by the cross-sectional area A of the core. The peak value is still dependent on the angular frequency of the excitation current. With the connection of all relationships, the main transformer equation follows for sinusoidal excitation. The minus sign takes Lenz's rule into account, but is usually left out.

With the ideal transformer, the main transformer equation applies without restriction to both coil windings. The open circuit voltage is directly proportional to the number of turns. The magnetic flux is the same in both windings. The transmission ratio is derived as follows.

In the ideal transformer, the ratio of the no-load voltages corresponds to the ratio of the associated number of turns of the coils.

The transformer transmits electrical power. When the secondary side is loaded, current flows there, which leads to a proportional primary current. The ideal transformer works without any loss of power and the secondary power drawn is balanced by an equally large primary drawn power. With this approach, the current translation can be derived.

In the ideal transformer, the currents behave inversely to the number of turns of the windings.

If both transmission equations are multiplied with one another, the transformation ratio for the alternating current resistances or impedances through the ideal transformer follows after conversion.

The ideal transformer transmits impedances with the square of its winding ratios.

The transformer under load

When the circuit is closed on the secondary side, current flows through the load circuit and the secondary coil. It generates a magnetic flux in the transformer core, which is opposite to the primary-side magnetic flux Φ and weakens it. The primary coil reacts to the smaller magnetic flux by reducing its self-induction voltage. So much current flows from the excitation voltage source through the primary coil until the initial magnetic flux is restored in the core. The ideally working transformer strives to maintain the initial electromagnetic equilibrium.

For many applications and circuit descriptions it is sufficient to only consider the ideal characteristic properties of the components. A description without the specified restrictions can be found in the chapter for the real single-phase transformer.