26.1
El transformador ideal
En los transformadores monofásicos de dos devanados, dos devanados se enrollan alrededor de un núcleo magnético caracterizado por un área de sección t…
En los transformadores monofásicos de dos devanados, dos devanados se envuelven alrededor de un núcleo magnético que tiene un área de sección transversal A y una permeabilidad magnética μ. La corriente de fasor i1 entra en el devanado izquierdo y i2 sale del devanado derecho.
La ley de Ampere establece que el componente tangencial de la intensidad del campo magnético integrado a lo largo de un camino cerrado es igual a la corriente neta encerrada. La longitud media del circuito magnético se selecciona como el camino cerrado, donde el fasor de intensidad de campo es constante.
Sustituyendo la densidad de flujo magnético y el flujo del núcleo se obtiene la ley de Ohm para circuitos magnéticos, donde la fuerza magnetomotriz neta es igual al producto de la reluctancia del núcleo y el flujo del núcleo.
Para los transformadores ideales, la permeabilidad del núcleo es infinita, lo que implica cero reluctancia del núcleo. Por lo tanto, las corrientes de fase están en fase.
La ley de Faraday define el voltaje inducido por un flujo variable en el tiempo. Suponiendo un flujo sinusoidal de estado estacionario con frecuencia constante, confinado completamente al núcleo, se determinan los voltajes inducidos a través de los devanados y su relación.
La sustitución de la relación de giro en las relaciones primarias ayuda a calcular la potencia compleja que entra y sale de los devanados, que son iguales, lo que implica que no hay pérdida de potencia.
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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.