# hw5sol.pdf - 1 ℎ 1 2 ℎ ℎ 1 = 2 = −50 × ℎ = 1...

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Unformatted text preview: 1. ℎ 1 & 2 ℎ ℎ , , { 1 = 2 = −50 × ℎ , = 1 × (5 + 5) − = 2 × { 1 Vo 10 1 1 + 50 −50 , = × (5 + 5 + ) 1 1 + 50 −50 = { ⇒ = 5 5 5 + 5 + 1 1 + 50 −50 =− 6 13 + = 0.0056674∠132.87° 1565 3130 2 1 , 2 , 3 ℎ ℎ , , = 120 { 1 3 = , 1 − 2 3 − 2 2 + = 20 100 400 2 − 3 1 1 = 3 ( + ) 100 −50 { 100 , = − 6960 5520 − = 64.841∠ − 141.58° 137 137 3 ℎ , 1. 200 cos(1000 − 30°) 200∠ − 30° -j500 50 200 ,1 , ,1 = × 50 200 50 × 200 = × 200 = 3.5777∠33.435° (√3 − ) × 50 + 200 − 500 2 50 + 200 − 500 → ,1 () = 3.5777 cos(1000 + 33.435°) 2. 10 cos(2000) 10∠0° -j250 50 200 ,2 , ,2 = −10 × 1 50 − 250 × × 200 = 5.6569∠ − 135° 50 − 250 50 − 250 + 200 → ,2 () = 5.6569 cos(2000 − 135°) 3. , () = 3.5777 cos(1000 + 33.435°) + 5.6569 cos(2000 − 135°) 4. 1. , , { = −2 = −2 , { 1 = 1 1 + 2 2 = 1 + 2 2 ℎ , 1 = −50 × 1 ℎ , = 2 2 2 = = + 2 = 391.08∠74.291° Ω 2 1 + 50 2. − , , , = −2 { , = −2 = 0 , = 1 1 { 1 2 = 1 ℎ , 1 √3 = 50 × 1 + 1 = 0.5∠ − 120° = 0.5(− − ) 2 2 ℎ , , = −2 = − × 1 √3 0.5 (− 2 − 2 ) = 0.72761∠74.036° 50 + 1 ( ) 3. ℎ − , , { , = −2 = 0 , = 2 , { 1 = 1 1 + 2 2 = 1 + 2 2 = 0 ℎ , 1 √3 = 50 × 1 + 1 = 0.5∠90° = 0.5(− − ) 2 2 ℎ , , = 2 = − × 2 1 √3 0.5 (− 2 − 2 ) 2 50 + (1 − ) 2 = 1.8605∠ − 0.25512° 4. ℎ , (), 0.72761∠74.036° 391.08∠74.291° Ω , (), 1.8605∠ − 0.25512° 391.08∠74.291° Ω 5 , 1 = 2 = 16 { = √1 2 = √1 2 = 4 , { 1 = 1 1 + √1 2 2 2 = √1 2 1 + 2 2 → 1 √1 1 = = 2 √2 4 , { = 1 = 2 = −1 + 2 1 = −1 + 2 { = 5 × (1 + 2 ) + 2 = 2∠ − 90° = −2 1 × ℎ , 1 = × (3 × 1 + 12 × 2 ) { 5 × (1 + 2 ) + × (4 × 1 + 16 × 2 ) = −2 1 × ) × 1 + 12 × × 2 = 0 →{ (4 × + 5) × 1 + (16 × + 5) × 2 = −2 (3 × + (3 × + ) 1 1 × 1 = − ( + ) × 1 12 × 4 12 2 → 1 1 )] × 1 = −2 [(4 × + 5) − (16 × + 5) × ( + { 4 12 2 2 = − 2 1 = − 1 1 (4 × + 5) − (16 × + 5) × ( + ) 4 12 2 → (3 × + ) 1 1 =− × 1 = − ( + ) × 1 { 2 12 × 4 12 2 ℎ , & →{ 1 = 0.14451∠ − 15.543° 2 = 0.037333∠164.46° & { 1 = 0.48172∠ − 105.54° 2 = 1.9269∠ − 105.54° . () = 2 () = 1.9269 cos(104 − 105.64°) . () = 2 () − 1 () = 1.4451 cos(104 − 105.64°) . = 1 = 0.14451∠ − 15.543° = 20 → ′ = 0.14446∠ − 15.626° → 6. ℎ ℎ ℎ ℎ ′ . & , ℎ ℎ , 1 1 + 2 2 = 0 ℎ . 1: 9 , 18 ℎ ℎ → −9 × 18 ℎ 4: 1 , 9 × 18 ℎ ℎ →− 9 × 18 4 ℎ, = 2 =− Ω 9 × 18 81 − 4 ...
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