26.1
理想的な変圧器
単相 2 巻線変圧器では、断面積 A と透磁率 μ で特徴付けられる磁気コアの周りに 2 つの巻線が巻かれています。フェーザ電流 i_1 が左巻線に入り、i_2 が右巻線から出ることで、電磁気原理による変圧器の基本的な動作が確立されます。
アンペールの法則は、変圧器内の磁場を理解するための基礎となり…
単相2巻線トランスでは、断面積Aと透磁率μを持つ磁気コアに2本の巻線を巻き付けます。フェーザ電流 i1 は左巻線に入り、i2 は右巻線を離れます。
アンペアの法則では、閉じた経路に沿って積分された磁場強度の接線成分は、正味の閉じた電流に等しいとされています。磁気回路の平均長は、電界強度フェーザが一定である閉経路として選択されます。
磁束密度とコア磁束を代入すると、磁気回路のオームの法則が得られ、正味の起磁力はコアのリラクタンスとコア磁束の積に等しくなります。
理想的なトランスフォーマーの場合、コアの透磁率は無限大であり、コアのリラクタンスがゼロであることを意味します。したがって、相電流は同相です。
ファラデーの法則は、時間変動する磁束によって誘導される電圧を定義します。固定周波数の正弦波定常磁束を仮定し、完全にコアに限定されると、巻線間の誘導電圧とその関係が決定されます。
一次関係の巻数比を代入すると、巻線に出入りする複雑な電力を計算するのに役立ちます。これは等しく、電力損失がないことを意味します。
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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.