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Tampere University of Technology —DEF-34106 Converter Dynamics and EMC 31.10. 2017

Electrical Energy Engineering

Teuvo Suntio Programmable calculator allowed 5 guestions/ä 6 pts

Fig. 1 shows an electrical eguivalent circuit representing the dynamics of DDR-controlled
second-order switched-mode converters operating in CCM. Define symbolically based on

Fig. 1 a) Z,, (i.e., %,/i), b) Z,, (i.e., %, /i,), and €) G, (i.e., V, /%, ). Each correct

answer gives 2 pts.

Ouestion 1.

 

Fig. 1

 

Fig. 2 shows the measured input impedances of a DDR-controlled buck converter eguipped

Ouestion 2.
with an LC input filter (Z,).

a) Isthe converter stable? (Justify your answer)
b) What is the approximate crossover freguency of the output-voltage feedback loop?
€) The open-loop input impedance (Z, ,), and the LC-filter output impedance (Z,)

overlaps as visible in the figure. What effect this overlap has in the converter?

Each correct answer gives 2 pts.

 

 

 

 

 

 

  

 

 

5

S

v

S

2

=

D

S

= 1 2 3 4
10 10 10 10

Freguency (Hz)

90

8

2 of

g insse

a

E

a
10" 10? 105 10f

Freguency (Hz)

Fig. 2

13)
Tampere University of Technology —DFF-34106 Converter Dynamics and EMC 31.10. 2017
Electrical Energy Engineering

Teuvo Suntio

Ouestion 3.

Ouestion 4.

Programmable calculator allowed 5 guestions/ ä 6 pts

A typical complementary sensitive function (T(s)) of a closed-loop system can be given by
according to Eg. (1).

2

T(s$="3 (1)

s +820, + 07
a) Explain the meaning of £ and &,.

b) Derive the expression for the loop gain Z(s) based on Eg. (1).
e) 1£ 260, <O0 then how many RHP poles will exist in the system?

Each correct answer will give 2 pts.

If we know that the set of transfer functions (i.e., G parameters) of the converter in Fig. 3a

can be given by
in | [0 78 GS]
ja] n 0 Cal; (2)
”, Ga -Z5 Gall -
d

then compute the corresponding set of transfer functions (i.e., Y parameters) representing the
dynamics of the converter in Fig. 3b according to

[äi] [W mo a].
[]-[X -Yl i] : 9)

NEN

=

The power stage of the converter is the same all the time.

 

 

L Output LA

Fig. 3 — VF-converter (a) voltage-output mode, and (b) current-output mode.

 

 

Each correct transfer function will give 1 pt.

23)
Tampere University of Technology —DEE-34106 Converter Dynamics and EMC 31.10.2017
Electrical Energy Engineering
Teuvo Suntio Programmable calculator allowed 5 guestions/ & 6 pts

Ouestion 5. — Fig. 4 shows the Bode plot of the open-loop output impedance of a buck converter. Its
analytic form is given in Eg. (4).

a) Estimate the values of L, C, x; , and 7. based on Fig. 4 (Each correct value gives 1 pt)
b) What is the characteristic impedance of this circuit and what is its value? (2 pts)

2. I. (n + sL)1+ sr;C) (4)
LC pyshittj 1

s +s =
L LC

20 " " T r E "

 

Magnitude (dB)

 

 

 

 

 

 

90 F r ; : / r n
> 45+t 4
S
g
E 45t J

-90 £ i N ; A | J
101 407 405 010 405105 10107
Freguency (Hz)
Fig. 4

33)