InductanceandCapacitance电感与电容.ppt

Example 3.5 1. Before switch closes (t 0) Example 3.5 2. After switch closes (t = 0) (假設儲存於兩電容之總電荷數不變) C1, C2, 並聯 等效電容兩端電壓 Example 3.5 儲存於兩電容之總能量為switch closes 前之一半 儲存與兩電容之能量 Parasitic resistances or parasitic inductance (寄生電阻消耗或寄生電感儲存能量) 3.4 Inductance 電感  電感為線圈(coil)形式之導線圍繞磁性核心的電路元件。 電流流過線圈會產生磁場(magnetic field)或磁通量(magnetic flux)。 電流改變會產生磁場改變(Faraday’s law) ，而磁場改變會產生一個電壓(感應電動勢)在線圈兩端，而此電壓值正比於產生磁場的電流改變率。 V-I Relationship  理想電感兩端電壓與電流對時間微分成正比。 常數L為電感值(inductance)，單位為亨利(H, henries)，等於volt seconds/ampere (V ?Sec/A) 。 一般電感值在數個micro H(1uH= 10-6)到數十H之間。 通過電感的電流參考方向為電感兩端電壓降落的方向(由正極流入，負極流出)，具 passive configuration特性。 Current in Terms of Voltage Stored Energy (Assume i(t0)=0) Example 3.6 Voltage, Power, and Energy for an Inductance L=5 H, i(t) is given. Plot voltage, the power delivered and energy stored for t = 0~5 s. 1. Express i(t) as a function of time 2. Calculate v(t) Example 3.6 Voltage, Power, and Energy for a Inductance 3. p(t) 4. Energy Example 3.7 Inductor Current with Constant Applied Voltage Switch closes at t=0, connecting a 10-V source to a 2-H inductance. Find i(t). 剛導通時i(t)=0. 1. V(t) Example 3.7 Inductor Current with Constant Applied Voltage Switch closes at t=0, connecting a 10-V source to a 2-H inductance. Find i(t). 2. i(t) t0 If we open the circuit at t=1, since we got a large voltage. 開關含有電感的電路會產生大電壓。 3.5 Inductance in Series and Parallel  KVL Inductance in Parallel  KCL Inductance in Parallel  Exercise 3.10 The 2-H and 3-H are in series ? 5 H. The equivalent 5H is in parallel with the 5-H and 4-H ? 1/(1/5 + 1/4 + 1/5) = 1.538 H. The equivalent 1.538 H is in series with the 1-H and 6-H ? 1.538 + 1 + 6 = 8.538 H. 3.6 Practical Inductors 3.7 Mutual Inductance (互感) 若數個線圈圍繞相同的磁性核心，則不同線圈通過電流所引發的磁通量會彼此影響。 自感(self inductance) L1 L2表示自身的電感效應，互感(mutual inductance) M 表示彼此相互影響所產生的電感效應。 不同線圈電感效應產生的磁力線方向可能相同(增加)或相反(減弱)。 以兩端黑點為參考方向，兩線圈電流皆流入或流出黑點則電感效應增強。