Exam text content

 

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SMG-8046 RF-electronics preparatory 1
Small Exam 2, 10.10.11 at 9.15
Answer to three of the four guestions. Each guestion gives maximum of 5 points.

* 1. (a) Explain how the transfer function is defined. Explain also what kind of informa-
tion can be obtained from the transfer function.

(b) Consider the following circuit. Assume ideal operational amplifier and analyze VW
as function of Vi and V». Based on your result, how would you characterize the

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

connection.
R
R L
Vo ir
m Ya

vi
Find value for the transfer function when w = 0 and w = 090. How would you

reason the results.

+ 2 (a) Find the transfer function € for the following case. Let C = 1F, L = 1H, R =10.

 

U2

 

 

 

 

 

 

-—
(b) Find the Taylor polynomia! of degree 4 for f(x) = sin(z).

3. (a) The switch in the circuit below is closed at t = 0, the capacitor has at that
moment charge (o = 5004C (whose polarity is as in the picture). Obtain i and
charge g in the capacitor for % > 0, also sketch the graph of g.

i Em
1k0

50 vi) 20, P

 

 

 

 

 

— 0
5

 

 

 

(b) Describe how the directional derivative is defined, reason also why and where such
a construction could be needed.

TURN OVER

 
 

384 (a) In the Gram-Schmidt process we encounter terms like AEP fy where fj;, g are

- p <fx:fr>
scalar functions and

b
<s:g>= | 19äx
a
defines an inner product for functions in the interval [a,b]. Ex
pret this kind of terms.

4 (b) Consider the plot below, it is obtained using Matlab and the
scribe it briefly. Suppose that you would need to get rid of t

 

lain how to inter-

Fourier tools. De-
e first two peaks.

Form a (as simple as possible) circuit, include also possible values for components

of the circuit.

600

500

400

g
5

Amplitude

200

 

 

o l sil]

 

0 50 100 150 200 260 300 350

Freguency [Hz]