課程名稱︰電路學 課程性質︰必修 課程教師︰陳信樹 開課學院：電資學院 開課系所︰電機系 考試日期（年月日）︰2012/01/13 考試時限（分鐘）：10:10 ~12:00 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Circuits , Final Exam. 1.(10%)Some oscillator designs avoid the need for inductors by employing the phase-shift network in Fig.1 , where Z_a = R and Z_b = 1/jωC. Find V_x and V when I_4 = 1 A degree 0 , and use your results to determine ω_osc at which ∠(V_x/V)=degree(-180). Hint : work with X = -1/ωC for convenience. I → ─── ─── ─── ○───│ Z_a│─────│Z_a │─────│Z_a │────────○ + ─── │ ─── │ ─── │ ─── + ─── + ─── + I_1 ↓│Z_b │ V_1 I_3↓│Z_b │ V_3 I_4↓│Z_b │ V_x ─── - ─── - ─── - - │ │ │ ○─────────────────────────────────○ Fig.1 2.(10%)An inductive motor draws 24kW and 60 A form a 500-V,60 Hz source. The total current drops to 50A when a capacitor is connected in parallel with motor. Show from a power triangle that there are two possible values of capacitor and find those values. 3.(20%)Draw the asymptotic Bode plot of the gain and phase for -0.004s(s+100) H(s)＝────────. (s+10) 4.(15%) Consider the circuit in Fig.2.Given that i_s=5mA and R=4kΩ,use node analysis to calculate v_1 , v_2 , and i_l. i_1 15V ← + - ────────○─────── │ │ │ R 5kΩ │ ────■───────■─── │ + │ + │ ↑○ 2kΩ ■ │ i_s│ v_1 -│ V_2 ■ 10kΩ │ ○ i_2 │ │ - 27v +│ - → │ ──────────────── Fig.2 5.(10%)The two-port network in Fig.3 represents an amplifier.When i_x=3i_2, use the direct method to obtain z-parameter matric [z]. i_1 → 1 H 10Ω ←i_2 + ○───◆───────────■───○+ │ │ ■ ∕﹨ v_1 5Ω │ ↓ v_2 │ ﹨∕ i_x │ │ - ○───────────────────○- Fig.3 6.(15%)Use Table 13.1 and Table 13.2 to find he inverse Laplace transform f(t) of the s-domain function below 5s F(s) = ───────. (s^2 + 25)^2 7.(20%)Use s-domain analysis to find i_L(t) for t>=0 in the following circuit, if v_s = 10v for t<0 =-10v for t<= 0 → i_L ──◆────── + +│ 0.5H │ │ v_8(t) ○ ■ ─ v_C -│ 5Ω │ ─ │ │ │1/40 F ───────── _ Fig.4 Table 13.1 Laplace Transform Properties ─────────────────────────────────────── Operation Time Function Laplace Transform ─────────────────────────────────────── Linear combination Af(t) + Bg(t) AF(s)+BG(s) Multiplication by e^(-at) e^(-at)f(t) F(s+a) Multiplication by t tf(t) -dF(s)/ds Time delay f(t-t_0)u(t-t_0) e^(-st_0)F(s) Differentiation f'(t) sF(s) - F(0^-) f''(t) s^2F(s) - sf(0^-)-f'(0^-) Integration ∫ f(λ)dλ F(s)/s ─────────────────────────────────────── Table 13.2 Laplace Transform Pairs ─────────────────────────────────────── f(t) F(s) ─────────────────────────────────────── A A/s u(t)-u(t-D) (1-e^(-sD))/s t 1/s^2 t^r r!/s^(r+1) e^(-at) 1/(s+a) te^(-at) 1/(s+a)^2 t^r e^(-at) r!/(s+a)^(r+1) sinβt β/(s^2 + β^2) cos(βt+φ) (scosφ - βsinφ)/(s^2 + β^2) e^(-at)cos(βt+φ) ((s+a)cosφ-βsinφ)/(s+a)^2 +β^2 ─────────────────────────────────────── --

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