IEEE Power Electronics Magazine - September 2017 - 47

the input without sacrificing the polarity, as with a buckboost converter. The SEPIC can be operated with coupled
or uncoupled inductors in CCM or DCM. The benefits of
the coupled inductors are explored in [9] and will not be
discussed here. Our interest lies in determining the control-to-output transfer function of the coupled-inductor
SEPIC when operated in DCM. Figure 11 represents the
autotoggling, voltage-mode control PWM switch des cribed in [10] and connected in a SEPIC configuration.
The load is purposely reduced to force DCM. A transient

Average

16.0

(V)

12.0

Cycle by
Cycle

8.00
4.00
0

Vout (t )
7.00

21.0

35.0
(m)

49.0

63.0

step is applied after the start-up sequence is completed. A
cycle-by-cycle circuit is captured and simulated in similar
operating conditions.
A simulation is run to compare the output responses of
both circuits. As confirmed by Figure 12, the two responses
are extremely close to each other. The left side of the
curve describes the startup sequence, while the right-side
section shows how both models react to the load step.
Having identical responses at this stage is a first indication
that the large-signal model, on average, properly mimics
the SEPIC internals and we can proceed with the smallsignal version.
The large-signal model of the DCM PWM switch is
replaced by its small-signal version derived in [10], which
differs from that described in [5]. Both models lead to identical analyses; however, V. Vorpérian in [5] considered a
common-common configuration (terminal c is grounded),
while I kept the original common-passive configuration
for the sake of building an autotoggling DCM-CCM model.
The schematic updated with the small-signal model of the
DCM PWM switch appears in Figure 13. The right-side
parameters list computes all the k-coefficients needed for
the analysis.

Determining the Quasistatic Gain

FIG 12 The average model transient response exactly matches
that of the cycle-by-cycle model.

To determine the quasi-static gain, you short all the inductors and open all the capacitors as detailed in Figure 2.

X2
XFMR
C3
10 u

L1
100 u
1

Vout

3
C2
10 uF

a
a

R1
1k

{k1}∗V(d1) + {k2}∗V(a, c)
V1
{Vin}

R4
1u

+
p
5

+
12
{k3}∗V(d1) + {k4}∗V(a, p)+{k5}∗I(VIC)+{k6}∗V(a, c)

+
VIC
R2
1u
R3
1G

p

c
c

DCM Model
d1

Duty
Ratio

+ Vdc
210 m
ac = 1

Parameters
Fsw = 100 k
L = 100 u
Vin = 10
d1 = 210 m
Vac = Vin
Vap = 24.8492
Ic = 36.899 m
k1 = Vac∗d1/(Fsw∗L)
k2 = d12/(2∗Fsw∗L)
k3 = Vac∗Vap∗d1/(Fsw∗L∗Ic)
k4 = Vac∗d12/(2∗Fsw∗L∗Ic)
k5 = -Vac∗Vap∗d12/(2∗Fsw∗Ic2 ∗L)
k6 = Vap∗d12/(2∗Fsw∗Ic∗L)

FIG 13 This is the small-signal model of the SEPIC operated in DCM. Node d1 is the duty ratio bias and the injection point.
All small-signal coefficients are automated in the parameters window.

September 2017

z	IEEE POWER ELECTRONICS MAGAZINE

47
Table of Contents for the Digital Edition of IEEE Power Electronics Magazine - September 2017
