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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