IEEE Power Electronics Magazine - September 2017 - 46

We have determined this transfer function without writing a line of algebra, just by splitting the circuit into several
simple sketches, such as those of Figures 8-10, individually solved. Furthermore, as expected, (19) is already in a
canonical form, and you can easily see the presence of a
quasi-static gain, two zeros and a second-order denominator that you could further rearrange with a resonant term
~ 0 and a quality factor Q. There is no way that we could
have obtained this result this quickly considering the parallel combination of Z 1, Z 2, and R load .
Deriving transfer functions by inspection is a possibility
offered by FACTs in particular with passive networks. As the
circuit complicates and includes voltage- or current-controlled sources, inspection becomes less obvious, and you
need to resort to classical mesh and node analysis. However,

FACTs offers several advantages: as you split the circuit into
small individual sketches used to determine the coefficients
of the final polynomial form, you can always come back to a
particular drawing and individually correct it in case you have
found a mistake in the final expression. Also, as you determine the terms associated with the a i and b i of the transfer function, you naturally end up with a polynomial form
without investing further energy to collect and rearrange
the terms. Finally, as shown in [4], SPICE can be of great help
to verify your individual poles and zeros calculations in the
presence of complicated passive and active circuits.

A DCM-Operated SEPIC with Coupled Inductors
The SEPIC is a popular structure used in applications
where the output voltage must be smaller or larger than

X2
XFMR
25.0 V

25.0 V
2

1

Vout

C1
10 u

15.0 V
3
C2
10 uF

R2
1u 15.0 V

9

PWM
Switch VM

+

210 mV 8
+ Vdc
210 m
ac = 1

4

R3
1G

+

p

c

a

+
V1
10
15.0 V 5

d

X3
PWMVM
L = 100 u
Fs = 100 k

X1
PSW1

V3
Unknown

L2
100 u

Average Model
(a)

L2
100 u
V1
10

10
D1

+

2
+ 1 +
V2

C1
10 u

C2
10 uF

+ 8

X3
PSW1
5

+

V3
Unknown

X2
XFMR
Ratio = 1

Vout

4

Cycle-By-Cycle Simulation

X1
PSW1
(b)
FIG 11 Two examples of the SEPIC: (a) the average model and (b) the cycle-by-cycle approach. XFMR and PSW1 are subcircuit names.

46

IEEE POWER ELECTRONICS MAGAZINE

z	September 2017



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