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G AG AN
ELT-41736 Analysis of Electromagnetic Systems Small Exam 1 11.11.2013
Answer to all three guestions.
Jari Kangas

1. (a) Explain how E-field is defined and which factors affect on its value. Could there be cases

when E-field is egual to zero in a (sub)domain? If so, describe such cases briefly (aim to
highlight what is special about them).

==. * (b) Let us consider two charges, O; at (1,-1,-3) [m] and O» at (3,-3,2) [m]. O; experiences
force F = 8i — 8j + 4k [N] and charge of O1 is known to be 300/1C. Determine charge of
02. To simplify your calculations assume that €, F/m

2 (a) In the circuit below assume that 1, == (2— j4)A. Find the real and reactive powers given =
by the source. Assume that R=19, C = 54F, L = 1mH, and w = 1000 rad/s.

 

 

 

 

 

 

 

 

[Z
4 1 R
E(| 1). cC-
= =
(b) Consider a graph whose loop matrix is
1090117
= | 0 1 190 1/4
Draw a corresponding graph, if edges IV and V belong to cotree, and the loops are clock-
wise.
(c) Consider following statement: s
*In case of capacitors, say parallel plate capacitors, no charge is carried through the insu-
lating material between the plates by direct current (DC), but alternating current (AC)
can carry charge through the material.”
Do you agree or disagree with this statement. To get points, support your answer by an
— —argument or an example.
A. 3. (a) Below is an eguivalent circuit for a common emitter amplifier. The amplifier is used in

= a multistage amplifier as shown in picture (a) in the figure on the opposite side. In the
edguivalent circuit Rg = Rj||R2, output is taken over R;.

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LOAD
B C E
%
+
Vin i) Rg Tr Bin 4 Ro

 

i. Determine open-circuit voltage amplification A.
ii. Determine the input resistance R; = Vin/iin, approximate its value by assuming that
Rg > r; (use this approximation the guestion 3. (b) i., see opposite side).
iii. Determine the output resistance R, which is defined as

 

when output terminals open
n =
000 when output terminals shorted'
Vout

 
(b) i. The amplifier is used

in a multistage amplifier as shown below. The multistage amplifier

has four stages, each of them are similar. Determine the overall gain using simplified
amplifier model as shown in picture (b) below. Use the eguivalent circuit shown in the
picture (b) and the expressions that you derived in item 3.(a).

ii. Derive numerical es

B = 100. Yoc

timate for the overall gain in case Ro = R, = r, = Rs and

 

 

 

 

 

 

 

 

 

 

 

 

v V3

, 0) D 0)

Ao Same as Same as Same as
s R %

 

 

 

 

 

 

 

 

 

 

 

(1) (2) (3) (4)

(b)

Constants in free space and some formulas:

e dielectric constant e x 8.854 x 10"2F/m

speed of light c = 2.997925 «

ee*=1+oif|z| small

permeability jo & 4n x 10 7H/m

108m/s

intrinsic impedance 779 = 4 [5 = 1207 9

er=iz+jy+kz,r'=ir'+jy+kz
e curl(E) =o, Ja = p, and D= E

 

e Glr) = as =

== — Umaxz Iinaz — x
& Pave = 5Umaa maa = 285 nat = Urmslims

e fscurl(F) - nda = fs F-dl
e f, div(F) dv = f, F - nda
e fograd(f)- dL= F(b) — f(a)
e grad(f) = i +557 +kX

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