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konstan Kh. ry60/(& ht.
SMG-8146 RF-electronics preparatory II
Small Exam I 14.11.2011
Answer to three of the four guestions.

Jari Kangas

+ 1. (a) Consider the circuit below. Form a graph, a tree, and cotree associated with the circuit. Us-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ing them describe how many loops would be needed to state the KVL. How many eguations

would be needed to state the KCL? (3 p.) Jln in ERI
n-! arot -

+ + > C3

9— j3 10 — j9 Jin
+ 10 V
3v(|) 1+53 5+ j10
+ Zo
50 10 (|) 4+53
*-

 

 

 

 

 

 

(b) i. Consider electric networks, explain what are active, apparent, and reactive power and
how to interpret them. P= f4f4 >= (J

= ii. Find the complex power that the voltage source delivers. Let E = 10/90? V, R = 290,
L=2H,C=04F,w=2rad/s.

 

 

 

 

 

 

 

 

 

(3 p.)

 

2. (a) Explain how the electric susceptibility is defined. Explain also briefly (physical) origin of
it. (3p.)

+ (b) In the circuit below find % as a function of v (—00 < v < 00), assume ideal diodes. (3 p.)

F D i s

D; 12 V D>

 

 

 

 

 

 

40 10:V ==="

 

 

 

 

 

 

 

 

 

 
 

3. (a) Correct or incorrect? To get points, support your answer by an argument or an example.

- i Let F : R R3,h:R > R3, g:R?>R- The composition F(h(g(2))) is of type
R? > R? (1p)

«ji, Given a conducting body (such as a ball whose outer surface is covered with metal),
if a positive charged body (rod, for instance) is taken close to the conducting body,
charge distribution in the conducting body is altered. (1P)

"iii. When using a bipolar junction transistor in the active region it holds that Ig > 0 and
Ip = Bla: (Lp) Jez Je 7n

iv. Capacitor (parallel plate capacitor, for example) is such a device that it allows alter-
nating current (AC) to carry charge (i.e. current) through the insulating material that
is between the two conductors: (1P)

| (b) Consider two-ports and explain how useful parameters for two-ports can be defined (focus
on principles how to define them, picture may help in giving your answer). (2 p.)

4. (a) Explain how the Newton-Raphson algorithm (see the 3rd page for additional information)

works. Use of pictures may be beneficial as is your knowledge on the principles of the small
signal approximation. (3 p)

(b) Consider the expression below. Explain origin of the terms (picture may help in giving

your answer). (3 p.)

ö r-r'
] 4 %——. -nda.

g 4meo [r— Fl

Constants in free space and some formulas:
« dielectric constant eo & 8.854* 10 2F/m
e permeahility 0 % 4n x 10 7H/m

e speed of light c % 2.997925 x 108m/s

 

o intrinsic impedance 10 = ja = 120m O

e cnl1+4nif || small

e r=ir+jy+kzr= ig/ + jy + k?

e eul(E) = 0, div (D) = f: and D = E

> Bus = Pino — 4 1 Drrolina
e fy cwl(F)-nda = JosF: U

e fy div(F)dv = Joy F:nda

+ [orad(f) -d1 = (0) — Ho)

e arad(f) = 15£ +150 + K