electromagnetic fields – hw5dqtuan/truong 2011-2012/hw5 new.pdf · 2011-11-23 · electromagnetic...

BMCS – Khoa Điện – ĐHBK Tp.HCM

Electromagnetic Fields – hw5

(Ans: 6.366 pF )

5.1:



5.2:



(Ans: (a) 4m (b) I(0) = 0 (c) Yes (n2 = 1) (d) 2m (e) V(l/2) = 0 (f) I(l/2) ≠ 0 (g) 1m (h) 4m (i) 100∠0o V )

5.2(cont.):



5.3:

(Ans: a) 2 cm b) 65 nH )

5.4:

(Ans: a) 20 cm b) 1 pF )


Electromagnetic Fields – hw5(5.5) An air-dielectric line of characteristic impedance Z0 = 75Ω is terminated by a load impedance (45 + j60)Ω. Find the input impedance of the line for each of the following pairs of values of the frequency f and the length L of the line: (a) f = 15MHz, L = 5m; (b) f = 50MHz, L = 3m; and (c) f = 37.5MHz, L = 5m ?

Ans : (a) (45-j60)Ω; (b) (45+j60)Ω; (c) (225+j0)Ω

(Ans: a) 97.56 – j21.95Ω b) 500 Ω )

5.6:



(5.7). For the system shown in Fig.5.6, find the input impedance of the line and the time-average power delivered to the load 100 Ω.

(Ans: 40 – j30 Ω ; 40 W )



(Ans: a) 35.3+j66.2Ω b)55.1mW c)19.45mW d)150Ω e) 40.8mW f)30.61mW )

5.8:


Electromagnetic Fields – hw55.9:



(Ans: 3.81; 2.17 W ; 0.361W and 0.903 W )

5.10: Given Ė = 34∠0oV; Zn = 100Ω, ZL1 = 40 – j30 Ω, ZL2 = 100 + j50 Ω, Z0 = 50 Ω, ℓ = λ/4, ℓ1 = λ/2, ℓ2 = 3λ/4 . Find:

(a) SWR on the ℓ line (b) P supplied by the source (c) P delivered to each load ?

ℓ+_ Ė

Zn

ZL1Z0 Z0

ℓ1

ℓ2Z0

ZL2



(Ans: a) 0.632∠-71.6o b) 4.44 c) 2cm d) 0.75cm )

5.11:

5.12:

(Ans: 2 ; 22.22 W ; 52.7∠2.68 V )



5.13:



(5.14) A line of characterictis impedance 60Ω is terminated by a load consisting of the series combination of R = 30Ω, L = 1µH, and C = 100pF. Find the values of SWR and dmin for each of the following radian frequencies of the source: (a) ω = 108; (b) ω = 2x108; and (c) ω = 0.8x108.

(5.15) Standing-wave measurements are performed on a line of characteristic impedance 60Ω terminated by a load ZR. For each of the following sets of the standing-wave data, find ZR: (a) SWR = 1.5, a voltage minimum right at the load; (b) SWR = 3.0, two successive voltage minima at 3cm and 9cm from the load; and (c) SWR = 2.0, two successive voltage minima at 3cm and 7cm from the load

Ans: (a) 2,0; (b) 14.94, 0.309λ; (c) 3.324, 0.115λ

Ans: (a) (40+j0)Ω; (b) (180+j0)Ω; (c) (48+j36)Ω



(5.16)

Ans: PL1 = 100 W; PL2 = 25 W )



(5.17)

Ans: (a) 0.75 W (b) 1.219 W )



(5.18)

Ans: (a) 0.125 W (b) – j5V; – 0.05 – j0.05 A )



(5.19)

Ans: (a) – jVin/Z0 (b) not possible (c) 4A )



(5.20)


Electromagnetic Fields – hw5(5.21)

Ans: 30Ω; 10Ω; 1050m; i(z,t) = 2/3δ(t – z/v)+ 1/3δ(t + z/v – 7µ) – 1/9δ(t – z/v – 7µ)A )



(5.22) The system shown in Fig.5.16 the switch S is closed at t=0. Assumse Vg(t) to be a direct voltage of 90V and draw the voltage and current bounce diagrams. From these bounce diagrams, sketch:(a) the line voltage and the line current versus t (up to t = 7.25µs) at z = 0, z = l, and z = l/2; and (b) the line voltage and line current versus z for t = 1.2µs and t = 3.5µs.



(5.23) The system shown in Fig.5.17 is in steady state. Find (a) the line voltage and current, (b) the (+) wave voltage and current, and (c) the (-) wave voltage and current.


Electromagnetic Fields – hw55.24:



(5.25) In the system shown in Fig.5.19(a), the switch S is closed at t = 0. The line voltage variations with time at z = 0 and z = l for the first 5µs are observed to be as shown in Fig.5.19(b) and (c). Find the values of V0, Rg, RL, and T ?



(5.26) In the system shown in Fig.5.20, assume that Vg is a constant voltage source of 100V and the switch S is closed at t = 0. Find and sketch: (a) the line voltage versus z for t = 0.2µs; (b) the line current versus z for t = 0.4µs; (c) the line voltage versus t for z = 30m; and (d) the line current versus t for z = – 40m ?

electromagnetic fields – hw5dqtuan/truong 2011-2012/hw5 new.pdf · 2011-11-23 · electromagnetic...

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