26.1
Le transformateur idéal
Dans les transformateurs monophasés à deux enroulements, deux bobinages sont enroulés autour d'un noyau magnétique caractérisé par une section transve…
Dans les transformateurs monophasés à deux enroulements, deux enroulements sont enroulés autour d’un noyau magnétique ayant une section transversale A et une perméabilité magnétique μ. Le courant de phaseur i1 entre dans l’enroulement gauche et i2 quitte l’enroulement droit.
La loi d'Ampère stipule que la composante tangentielle de l'intensité du champ magnétique intégrée le long d'un chemin fermé est égale au courant net fermé. La longueur moyenne du circuit magnétique est choisie comme le chemin fermé, où le phaseur d’intensité de champ est constant.
En substituant la densité de flux magnétique et le flux du noyau, on obtient la loi d'Ohm pour les circuits magnétiques, où la force magnétomotrice nette est égale au produit de la réluctance du noyau et du flux du noyau.
Pour les transformateurs idéaux, la perméabilité du noyau est infinie, ce qui signifie une réticence nulle du noyau. Ainsi, les courants de phase sont en phase.
La loi de Faraday définit la tension induite par un flux variant dans le temps. En supposant un flux sinusoïdal à l’état stationnaire à fréquence constante, entièrement confiné au noyau, les tensions induites aux travers les enroulements et leur relation sont déterminées.
La substitution du rapport de rotation dans les relations primaires permet de calculer la puissance complexe entrant et sortant des enroulements, qui sont égales, ce qui implique qu’il n’y a pas de perte de puissance.
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Q1: How does Ampere's Law apply to transformer magnetic circuits?
Ampere's Law states that the magnetic field intensity's tangential component integrated along a closed path equals the net enclosed current. In transformers, the mean length of the magnetic circuit serves as this closed path, where the magnetic field intensity remains constant. This principle relates the magnetomotive force from primary and secondary windings to the core flux through the magnetic circuit's reluctance.
Q2: What does infinite core permeability mean for an ideal transformer?
Infinite core permeability implies zero core reluctance, meaning the magnetic core offers no resistance to magnetic flux. This ideal condition ensures that phase currents in both windings are in phase and that the magnetomotive force relationship simplifies significantly. Real transformers approach but never achieve this ideal condition, making equivalent circuits for practical transformers necessary for accurate analysis.
Q3: How does Faraday's Law determine voltage in transformer windings?
Faraday's Law defines the voltage induced by time-varying magnetic flux. Under sinusoidal steady-state conditions at constant frequency, the induced voltage in each winding is proportional to the number of turns and the rate of flux change. The turn ratio directly relates primary and secondary voltages, enabling voltage transformation between windings.
Q4: What is the relationship between turn ratio and transformer voltage transformation?
The turn ratio, defined as the primary turns divided by secondary turns, determines the voltage relationship between windings. By substituting this ratio into Faraday's Law equations, the secondary voltage can be calculated from the primary voltage. This relationship enables transformers with off nominal turns ratios to step voltage up or down as needed in power systems.
Q5: Why is power conserved in an ideal transformer?
Complex power entering the primary winding equals complex power leaving the secondary winding in an ideal transformer. This equality, expressed as S1=S2, indicates zero power loss within the transformer core and windings. Power conservation is fundamental to ideal transformer operation, ensuring that all input power transfers to the output without dissipation.
Q6: How do magnetic flux density and core flux relate in transformer analysis?
Magnetic flux density (B) and core flux (Φ) are related through the core's cross-sectional area. Substituting this relationship into Ampere's Law yields Ohm's law for magnetic circuits, where magnetomotive force equals reluctance times flux. This magnetic circuit analogy parallels electrical circuits, simplifying transformer analysis and design calculations.
Q7: What role does the magnetic core's cross-sectional area play in transformer operation?
The magnetic core's cross-sectional area A directly influences the relationship between magnetic flux density and core flux. A larger cross-sectional area accommodates greater flux for the same flux density, affecting the transformer's capacity to transfer power. Core geometry, including area and mean length, determines the magnetic reluctance and overall transformer performance characteristics.