Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
4
,
No
. 5, Oct
o
ber
2
0
1
4
,
pp
. 67
9~
69
0
I
S
SN
: 208
8-8
7
0
8
6
79
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
A
π
-CLCL Type Immittance Con
v
er
te
r for
Co
nstant Curr
ent
and Dynamic Load Applications
M Abd
u
r Raz
z
a
k
*
, Sum
aiya B Afz
a
l
**
and
Mee
y
a
d
M S
h
ab
ab
***
*
Department of Electrical
&
Electronic Eng
i
neer
ing, Ind
e
pend
ent University
, B
a
n
g
ladesh
**
Department of
Electrical and
Electron
i
c Engin
e
ering,
Univ
er
sity
of Melbourne, A
u
stralia
***
S
outhtech
(B
D) Lim
ited
,
Dha
k
a, B
a
ngl
ades
h
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Mar 11, 2014
Rev
i
sed
Jun
11,
201
4
Accepte
d J
u
l
6, 2014
Im
pedance-
adm
ittan
ce conver
t
er
is shor
tl
y
term
ed as im
m
ittance convert
er
.
In this
converter
, th
e outpu
t
curr
ent
is
proportion
a
l
to th
e
input v
o
ltag
e
an
d
the output voltage is proportion
a
l to th
e input current.
The outp
u
t current
is
thus
independen
t
of the load
. Th
is
res
earch ev
alu
a
tes
the
chara
c
t
e
ris
tics
of a
proposed
π
-CL
C
L im
m
ittan
c
e conver
t
er
, whi
c
h is
a com
b
in
ation o
f
th
e
ty
pi
ca
l
π
-
and T-ty
p
e
conf
igurations, for c
o
n
s
t
a
nt
c
u
r
r
e
nt
a
n
d dy
n
a
mi
c
l
o
ad
applications. Th
e input-ou
t
put
characteristics an
d e
fficien
cy
ch
aracteristics
are an
al
yz
ed an
d s
i
m
u
lated.
Th
e char
act
er
is
t
i
cs
are com
p
ared
t
o
that of th
e
ty
pi
ca
l
π
- and
T-ty
pe conv
er
ters. Th
e i
nput-output char
acteristics and
effic
i
enc
y
char
a
c
ter
i
s
tics
ar
e th
en exam
ined
ex
perim
e
nta
l
l
y
.
It
is
obs
erved
that
the
experi
m
e
ntal res
u
l
t
s
a
g
ree w
ith
those of the simulation ones, an
d
confirm
tha
t
th
e
π
-CLCL
config
uration
is m
o
re
effic
i
ent
than
th
e t
y
pi
ca
l
π
-
and T-t
y
pe im
m
ittan
ce conver
t
er
s while m
a
intain
ing a nearl
y
con
s
tant output
current
and
thus
appli
cabl
e
for
d
ynam
i
c lo
ads
.
Keyword:
C
onst
a
nt
cu
rre
nt
Dynam
i
c load
Efficiency c
h
a
r
acteristics
Immitance converter
Power electronics
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
M Abdur Razz
ak,
Depa
rt
m
e
nt
of
El
ect
ri
cal
& El
ectronic E
ngi
neering,
Ind
e
p
e
nd
en
t Un
iv
ersity, Banglad
esh,
Plo
t
-1
6, Blo
c
k-
B, Bash
und
h
a
r
a
,
Dh
ak
a-
1230
, Bang
lad
e
sh
E-m
a
il: razzak@iub.e
du.bd
1.
INTRODUCTION
Im
pedance-adm
i
ttance converter is shortly ter
m
ed as
im
m
ittance conve
rter,
whe
r
e the ter
m
‘immi
ttan
ce’ is a co
m
b
in
atio
n
of th
e
words
‘im
p
edance’ a
nd
‘a
dm
ittance’
. T
h
e term
‘im
m
i
ttance’ wa
s first
i
nve
nt
ed by
H
e
nd
ri
k
Wade B
ode [
1
]
.
A
n
i
m
m
i
tt
ance con
v
e
r
t
e
r i
s
a fou
r-t
e
r
m
i
nal
net
w
or
k i
n
w
h
i
c
h t
h
e
i
n
p
u
t
i
m
p
e
d
a
n
ce is co
nv
erted
in
t
o
th
e ad
m
ittan
ce o
f
t
h
e lo
ad
at th
e ou
tpu
t
termin
als [2,
3
]
. The
m
a
in
ch
aract
eristic
of t
h
i
s
c
o
nve
rt
er i
s
t
h
at
at
resona
nce
fre
que
ncy
,
t
h
e
out
p
u
t
cu
rren
t is prop
ortion
a
l to
the in
pu
t vo
ltag
e
an
d
t
h
e
out
put
v
o
l
t
a
ge
i
s
pro
p
o
rt
i
o
nal
t
o
t
h
e i
nput
cu
rre
nt
, w
h
i
c
h en
sures t
h
at
t
h
e o
u
t
p
ut
cur
r
ent
i
s
i
ndepe
n
d
ent
o
f
t
h
e
load. T
h
is fea
t
ure of immittance conve
rte
r
m
a
kes it
su
itable in
m
a
ny powe
r
electronics applications
especially whe
r
e c
onsta
nt currents a
r
e
nee
d
e
d
[6-13].
The immittance conve
r
sion
topology ha
s becom
e
attractive in
recent y
ears as a
nove
l
m
eans of
powe
r convers
i
on
because of its prope
r
ties that it conver
t
s
a constant voltage s
o
ur
ce to a consta
nt current
sou
r
ce a
nd
vi
c
e
versa
[2
, 3]
.
Hence
,
the immittance conve
rter m
a
y be utili
zed to conve
rt a voltage s
o
urce int
o
a current s
o
urc
e
and
vice versa whe
n
it is inserte
d
in
t
o
t
h
e hi
g
h
-
fre
que
n
c
y
l
i
nk part
o
f
a po
wer el
ect
ro
ni
c
s
syste
m
[3]. In the comm
unication fi
eld, an immittance conv
e
r
ter is also known as
a gyrator [4]. Som
e
r
e
son
a
n
t
conver
t
er
s
h
a
v
e
b
e
en
sho
w
n
t
o
ex
h
i
b
it immi
tt
an
ce con
v
e
r
s
i
o
n pro
p
e
r
ties
[
5
].
Th
e immi
ttan
c
e
con
v
e
r
t
e
r al
so
has m
a
ny
cons
t
a
nt
cur
r
ent
a
n
d dy
nam
i
c l
o
ad ap
pl
i
cat
i
ons
i
n
p
o
we
r el
ect
r
oni
cs a
nd m
a
ny
ot
her
field
s
su
ch
as p
h
o
t
ovo
ltaic in
v
e
rters [6
],
d
c
-d
c con
v
e
rter
s [7
], lo
w-p
a
ss filters [7
], ind
u
c
t
i
o
n
h
eating
,
p
l
asm
a
gene
rat
i
o
n [
8
]
,
HI
D l
a
m
p
bal
l
a
st
s [9]
,
capa
c
i
t
o
r cha
r
gi
ng
appl
i
cat
i
o
ns [
1
0]
, n
onc
o
n
t
act
ener
gy
t
r
ansm
i
ssi
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
679
–
6
90
68
0
sy
st
em
s [11]
,
hi
g
h
-
v
ol
t
a
ge d
c
t
r
ansm
i
ssi
on
l
i
nk [
1
2]
, an
d co
r
ona
-di
s
c
h
arge a
p
pl
i
cat
i
ons
ope
rat
i
n
g i
n
t
h
e
m
e
ga-he
r
tz ra
n
g
e
[1
3]
.
A lum
p
ed-c
onstant reactor L and ca
pacitor C can be
use
d
for the im
ple
m
entation
of a
n
i
mmittance
co
nv
erter i
n
a
co
m
p
act d
e
sign
.
So
m
e
lu
m
p
ed
-con
stan
t configu
r
ation
s
o
f
t
h
e immittan
ce co
nv
erter
h
a
v
e
b
e
en
st
udi
e
d
pre
v
i
o
usl
y
[
1
-
1
3]
. T
h
ere
are
f
o
u
r
t
y
pi
cal
co
nfi
gurations
of t
h
e i
mmittance
co
nv
erter th
at consist o
f
three l
u
m
p
ed reactive elem
en
ts nam
e
ly T-LCL type,
π
-CLC typ
e
, T-CLC typ
e
an
d
π
-
L
C
L
t
y
pe.
C
o
nve
rt
er
s
with
m
o
re th
an
fou
r
reactiv
e ele
m
en
ts are
b
i
gg
er,
h
eav
ier and
co
stlier an
d th
eir an
alysis and
d
e
sign
i
s
m
o
re
com
p
licated [14]. He
nce c
onverters ha
ving
m
o
re than four reactive elemen
t
s
ha
ve
n
o
t
been
st
u
d
i
e
d.
The T
-
LC
L t
o
p
o
l
o
gy
and i
t
s
a
ppl
i
c
at
i
ons
have
be
en st
u
d
i
e
d t
h
e
m
o
st
[1
5-
1
7
]
.
In t
h
i
s
art
i
c
l
e
, we
pr
o
pose
a new
co
nfigu
r
ation
o
f
th
e imm
i
tta
n
ce con
v
e
rter,
th
e
π
-CLCL co
nfigu
r
ation
,
wh
ich
is a com
b
in
atio
n
of t
h
e
π
-CLC
and
T-LC
L t
y
pe co
nve
rt
er
s. The
i
n
put
/
out
put
vol
t
a
ge
and curre
nt
characte
r
istics and the e
f
ficiency
characte
r
istics of the
propose
d
π
-CLCL i
mmittan
ce co
nv
erter are an
alyzed
both
th
eo
retically an
d
expe
rim
e
ntally. The c
h
aracte
r
istics are simulated and th
e si
m
u
latio
n
resu
lts are co
m
p
ared
to
th
at
o
f
the
expe
ri
m
e
nt
al
ones. T
h
e cha
r
a
c
t
e
ri
st
i
c
s of t
h
e
π
-CLCL configuration are
also com
p
ared to that of the
typical
π
-C
LC
t
y
pe a
n
d T
-
LC
L c
o
nfi
g
u
r
at
i
o
ns.
2.
LC LUMPE
D
IMMITTANCE CONVE
R
TER
The immittance converte
r ca
n be
represe
n
ted by th
e
bl
oc
k di
a
g
ram
as sho
w
n i
n
Fi
g
u
r
e 1. T
h
ere a
r
e
fou
r
typ
i
cal con
f
i
g
uratio
ns
o
f
th
e immittan
c
e circu
it
n
a
m
e
ly T-LCL typ
e
,
π
-CLC type
,
T-CLC type a
n
d
π
-
LCL type.
Figure
2 shows t
h
e circuit
diagra
m
of the a
b
o
v
e
-
m
e
nt
i
oned f
o
u
r
t
y
pes o
f
immittance converte
r.
Fi
gure
1. F
our
-
t
er
m
i
nal
imm
i
tt
ance convert
er
Fi
gure
2. Ty
pi
cal
confi
g
u
r
at
i
ons of
im
m
i
tt
ance convert
er
Th
e fou
r
-termi
n
a
l
m
a
trix
o
f
th
e i
mmittance converter, show
n i
n
Fi
g
u
res 1
& 2, can
be re
p
r
esent
e
d by
,
V
1
I
A
B
C
D
V
2
I
(1)
HereV
1
, I
1
, V
2
and I
2
are th
e
vo
ltag
e
s an
d
cu
rren
ts at th
e in
pu
t an
d ou
tp
u
t
po
rts resp
ectiv
ely; A is th
e
v
o
ltag
e
g
a
in
, B
is th
e tran
sfer im
p
e
d
a
n
ce, C is
th
e
transfer a
d
mittance and D is
the reverse c
u
rre
nt gain.
At
resona
nce f
r
eque
ncy
and
un
der i
d
eal
condi
t
i
ons (Q
1
, Q
2
>>1, whe
r
e
Qs are the qua
lity factors of
th
e circu
its), th
e i
mmittance converter can
be descri
bed as,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A
π
-CLCL Type Immittan
ce C
o
n
v
erter fo
r Co
n
s
t
a
n
t
Cu
rre
nt a
n
d
Dyn
a
mic
Loa
d
Ap
p
lica
t
i
o
n
s
(MA Ra
zzak)
68
1
V
1
I
0
jZ
0
j
1
Z
0
0
V
2
I
(2)
where, Z
0
(
LC
⁄
) i
s
t
h
e charact
eri
s
t
i
c im
pedance of
t
h
e im
m
i
t
t
a
nce conve
rsi
on ci
rcui
t
.
Eq
u
a
tio
n
(2
) can
b
e
rewritten
as,
V
j
Z
I
I
j
1
Z
V
(3)
From
(3), o
u
t
p
ut
curre
nt
and
vol
t
a
ge exp
r
essi
ons are,
I
∓
j
1
Z
V
V
∓
j
Z
I
(4)
From
(4), i
t
can be see
n
t
h
a
t
t
h
e out
p
u
t
curre
nt
i
s
pr
op
ort
i
onal
t
o
t
h
e
i
nput
vol
t
a
ge
whi
l
e
o
u
t
put
vol
t
a
ge i
s
pr
op
ort
i
onal
t
o
t
h
e
i
nput
cu
rrent
.
Thi
s
m
eans t
h
at
i
f
t
h
e i
nput
vol
t
a
ge i
s
cons
t
a
nt
t
h
en a co
n
s
t
a
nt
out
p
u
t
current
pro
p
o
r
t
i
onal
t
o
t
h
e i
nput
vol
t
a
ge i
s
achi
e
ved and i
f
t
h
e i
nput
curre
nt
i
s
const
a
nt
, a const
a
nt
out
p
u
t
vol
t
a
ge
pr
op
ort
i
onal
t
o
t
h
e i
n
p
u
t
cu
rrent
i
s
achi
e
v
e
d. There
f
ore
,
t
h
e out
p
u
t
cu
rrent
an
d v
o
l
t
a
ge are
i
ndepen
d
ent
o
f
t
h
e l
o
ad [
14,
1
8
]
.
a.
π
-CL
C
Immi
ttance
Conver
ter
B
y
analy
z
i
ng t
h
e respect
i
v
e imm
i
t
t
a
nce conversi
on ci
rcui
t
usi
ng Ki
rch
h
o
f
f’s l
a
ws i
t
i
s
fo
un
d t
h
at
t
h
e
load current and the
efficiency of the
π
-CLC imm
i
ttance converter can
be written as,
I
2
≅
V
1
Z
0
1
1
Q
Z
Z
(5)
η
≅
1
1
1
Q
Z
Z
1
Q
Z
Z
(6)
where, t
h
e l
o
a
d
im
pedance i
s
defi
ned as
Z
V
2
I
2
an
d Q, th
e
q
u
a
lity
facto
r
o
f
th
e circu
it, is d
e
fin
e
d
as
Q
ω
.
2.2 T-LCL
Immi
ttance
Conver
ter
Si
milar to
th
e
π
-C
LC
confi
gurat
i
on,
t
h
e l
o
ad c
u
rre
nt
eq
uat
i
on an
d t
h
e
effi
ci
ency
of
t
h
e T-LC
L
i
mmi
tt
an
ce co
nv
erter can
b
e
written
as,
I
2
≅
V
1
Z
0
1
1
Q
Z
Z
(7)
η
≅
1
1
1
Q
Z
Z
1
Q
Z
Z
(8)
2.
3
π
-LCL Immi
ttance
Conver
ter
The load c
u
rre
nt and the e
fficiency of the
π
-LCL im
m
ittance conve
rter can sim
ilarly be written as,
I
V
Z
1
Q
Q
1
Z
Z
(9)
η
≅
1
1
Q
Q
1
Z
Z
Q
Q
1
Z
Z
(10
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
679
–
6
90
68
2
2.4
T-CLC
Immittance Conver
ter
Usi
ng ci
rc
ui
t
anal
y
s
i
s
t
echni
ques i
n
a si
m
i
l
a
r m
a
nner,
the load c
u
rre
nt equati
on and the
efficiency of
t
h
e T-C
L
C
im
m
i
t
t
a
nce convert
er i
s
fou
nd t
o
be,
I
V
Z
1
Q
Q
1
Z
Z
(11
)
η
V
I
V
I
1
1
Q
Q
1
Z
Z
Q
Q
1
Z
Z
(12
)
For the special case where Q
1
=Q
2
=Q and Z
0
=Z
2
, for high values of Q, the efficiency char
acteris
tic of
al
l
four co
nfi
g
u
r
at
i
ons i
s
t
h
e sam
e
and appr
ox
im
at
ed as,
η
≅
1
1
2
Q
≅1
2
Q
(13
)
3.
PROP
OSE
D
π
-CLCL IMMITTANCE
CONVE
RTER
The pro
pose
d
π
-C
LC
L imm
itt
ance convert
er
i
s
shown i
n
Fi
gure 3
,
where
m
i
s
an arbi
t
r
ar
y
coeffi
ci
ent
i
n
t
h
e range
of
0 t
o
1
.
The i
n
duct
o
rs a
r
e assum
e
d t
o
have seri
es i
n
t
e
rnal
resi
st
ances r
1
and r
2
respectively; and
the capacitors
are assu
m
e
d to be ideal. This
π
-C
LC
L conve
rt
er i
s
a co
m
b
inat
i
on of t
h
e t
y
pi
cal
π
-C
LC
and
T-
LC
L confi
gura
t
i
ons. The pro
p
o
sed im
m
i
t
t
a
nce convert
er cor
r
espo
nds t
o
t
h
e T-LC
L ty
pe con
v
ert
e
r at
m
=
0, and
to
th
e
π
-C
LC
ty
pe at
m
=
1 as
show
n i
n
Fi
gur
e 2(a) a
nd Fi
g
u
r
e 2(
b),
respect
i
v
el
y
.
Fi
gure 3.
π
-CL
C
L type immittance converter
3.
1 Resonant
Fre
quenc
y
Ch
aracteristics
By analyz
ing t
h
e propose
d
π
-
C
LCL im
m
i
ttance co
nverter
c
i
rcuit using
Kir
c
hho
ff’s
laws,
the
A
,
B
,
C
,
D
param
e
t
e
rs are fo
un
d t
o
be,
A
j
ω
C
r
j
ω
L
1
B
j
ω
C
r
j
ω
L
r
j
ω
L
1m
r
j
ω
L
r
j
ω
L
1m
C
j
ω
mC
r
j
ω
L
j
ω
mC
j
ω
C
D
j
ω
mC
r
j
ω
L
r
j
ω
L
1m
j
ω
mC
r
j
ω
L
j
ω
mC
r
j
ω
L
1
m
j
ω
C
r
j
ω
1
m
L
1
(14
)
At
res
o
nant
fre
que
ncy
(t
aki
n
g
res
ona
nt
fre
qu
ency
ω
ω
),
ω
;
Z
;
Q
ω
;
Q
ω
R
e
pl
aci
ng t
h
e above
param
e
ters i
n
Eq
. (
1
4
)
,
and
i
g
n
o
ri
ng
t
h
e real
part
s si
nce Q
1
, Q
2
>> 1, the
A
,
B
,
C
,
D
param
e
t
e
rs at
resonant
f
r
e
que
ncy
can be ap
p
r
oxi
m
a
t
e
d as,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A
π
-CLCL Type Immittan
ce C
o
n
v
erter fo
r Co
n
s
t
a
n
t
Cu
rre
nt a
n
d
Dyn
a
mic
Loa
d
Ap
p
lica
t
i
o
n
s
(MA Ra
zzak)
68
3
A
j
1
Q
B
j
Z
1
1m
Q
Q
j
m
Q
C
j
1
Z
1
j
m
Q
D
j
1
Q
j
m
m
Q
1
Q
m
1m
Q
Q
(1
5)
Therefore, the
four-t
ermin
a
l matr
ix
o
f
th
e
netwo
r
k
b
eco
m
e
s:
V
1
I
j
1
Q
1
jZ
0
j
1
Z
0
j
1
Q
2
+jm
(
m
Q
1
-
1
Q
2
)
V
2
I
(16
)
If Q
1
a
nd
Q
2
ar
e hi
gh
(>1
00)
t
h
en
A=D=0 a
n
d
BC1
at an
y v
a
lu
e of m
wh
ich
is th
e p
r
operties o
f
an
i
d
eal
imm
i
t
t
a
n
ce convert
er as
sho
w
n i
n
Eq.
(
2
).
3.
2 Inpu
t-O
utput
Ch
arac
teristic
s
When the loa
d
im
pedance
Z
is
connected to t
h
e ou
tp
u
t
termin
als,
V
1
and
I
1
can be
obtained from
Eq.(
16)
as,
V
1
j
I
1
1
Q
1
Z
2
Z
0
(17
)
I
j
1
Z
V
2
1
1
Q
m
m
Q
1
Q
Z
0
Z
2
(18
)
From
Eqs. (1
7)
& (1
8),
t
h
e o
u
t
put
cur
r
ent
an
d
vol
t
a
ge are f
o
un
d t
o
be,
I
≅
V
1
Z
0
1
1
Q
Z
Z
(19
)
V
≅
I
1
Z
0
1
1
Q
m
m
Q
1
Q
Z
Z
(20
)
Th
e first term
o
f
th
e ou
tp
u
t
cu
rren
t
an
d ou
tp
u
t
vo
ltag
e
is th
e id
eal ter
m
wh
ile th
e secon
d
term
is th
e
l
o
ss t
e
r
m
resul
t
i
ng from
t
h
e i
n
t
e
rnal
resi
stance of t
h
e i
nduc
t
a
nces. When t
h
e i
n
t
e
rnal
resi
stance i
s
negl
i
g
ibl
e
or
zero
,
th
e
q
u
a
lity facto
r
b
eco
m
e
s h
i
g
h
o
r
in
fi
n
ity. Un
d
e
r th
is co
nd
itio
n
,
the seco
n
d
term
b
eco
m
e
s n
e
g
l
i
g
ib
le o
r
zero giving the
ideal immittance
condi
t
i
on as
sho
w
n i
n
Eq.
(
4
).
3.3 Efficiency
Charac
teristic
Usi
ng E
q
.
(1
9)
~
(
20)
an
d i
g
n
o
r
i
ng
hi
gher
o
r
d
e
r t
e
r
m
s of Q
(si
n
ce Q
1
, Q
2
>>1), the e
fficiency of the
pro
pose
d
π
-CLCL i
mmi
t
t
an
ce
co
nv
erter can
b
e
written
as,
η
V
I
V
I
≅
1
1
1
Q
Z
Z
1
Q
m
m
Q
1
Q
Z
Z
(21
)
Differen
tiatin
g
Eq
.
(21
)
with
resp
ect to
Z
2
an
d
tak
i
ng
th
e d
e
riv
a
tiv
e equal to
0
,
it is fou
n
d
th
at th
e
maxim
u
m effic
i
ency
occurs when,
Z
Z
m
m
Q
Q
Q
Q
(22
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
679
–
6
90
68
4
Therefore, from Eqs. (21)
&
(22), m
a
xim
u
m efficiency,
η
, i
s
fou
nd t
o
be,
η
m
Q
Q
m
Q
Q
m
Q
Q
m
Q
Q
2
1
Q
m
1
Q
m
1
Q
(23
)
For a special c
a
se, where Q
1
=Q
2
=Q, Z
0
=Z
2
and m=0.5, the efficiency
characteristic of the
π
-CLCL
conve
rter can be written using
the binom
ial th
eorem
as,
η
≅
1
1
1.75
Q
≅1
1.75
Q
(24
)
For obt
ai
ni
ng h
i
ghest
effi
ci
ency
at
the characteristic
im
pedance Z
0
, it is fo
u
n
d
th
at,
m
m
Q
Q
Q
Q
1
(25
)
Sol
v
i
ng (2
5) w
i
t
h
m
=
0.5
gi
ve
s
Q
1
.
5
Q
(26
)
Th
e ab
ov
e cond
itio
n
will g
i
v
e
m
a
x
i
m
u
m ef
ficien
cy a
t
reso
n
a
n
ce.Th
e efficien
cy ch
arac
t
e
ristic o
f
th
e
π
-C
LC
L conve
rt
er i
n
t
h
i
s
case at
Z
0
=Z
2
can
b
e
written
u
s
in
g
th
e b
i
n
o
m
ia
l th
eo
rem
as,
η
≅1
1
.
333
Q
(27
)
Co
m
p
arin
g
Eq.(27
) with (13
)
,
it is clear th
at t
h
e m
a
x
i
m
u
m
efficien
cy
o
f
th
e propo
sed immittan
ce
conve
r
ter is
greater the e
ffici
ency of t
h
e f
o
u
r
basi
c t
o
pol
og
i
e
s desc
ri
be
d i
n
sect
i
o
n
2.
4.
RESULTS
A
N
D
DI
SC
US
S
I
ONS
The load current charact
eris
tics
and the efficiency cha
r
acter
istics of each configuration were
sim
u
la
ted using MATLAB.
The characteristic
im
pedance Z
0
was t
a
ken
as Z
0
=20.8
Ω
a
nd m
was t
a
ken t
o
be
m
=
0.5. Load w
a
s vari
ed from
0
Ω
to
6
0
Ω
an
d
i
nput
vol
t
a
ge was t
a
ken t
o
be V
1
=220
V rm
s. Prot
ot
y
p
es o
f
t
h
e
π
-
CLCL,
π
-CLC
an
d
T-LCL co
n
f
igu
r
atio
n
s
were bu
ilt u
s
in
g
in
du
cto
r
s and
cap
acito
rs availab
l
e
in
th
e mark
et.
The experim
e
n
t
al param
e
ters
for the
π
-C
LCL t
opol
ogy
are l
i
s
t
e
d
i
n
Tabl
e 1. An i
nduct
o
r of 19
5uF wa
s use
d
because it was
the maxim
u
m
valu
e found i
n
the market. Since
Q
ω
, a high L
res
u
lts in a higher Q. A
92.4
μ
F
i
nduct
o
r was s
e
l
ect
ed si
nce an i
nduct
o
r
hal
f
t
h
e val
u
e
of the l
a
rger one
was needed. C
a
paci
t
o
r val
u
es were
selected so as to k
eep the characteristic
im
pedance equal to 20.8
Ω
. Th
e q
u
a
lity fact
o
r
s were
fou
n
d
to
b
e
Q
1
=12.
6 an
d Q
2
=35.3.
Table 1. Circuit Param
e
ters fo
r Ex
perim
e
nts
Circuit para
m
e
te
rs
Values
m 0.
5
Resonant fr
equenc
y
f
r
[kHz] 17.
028
I
nductor
s
L
[
μ
H] L
1
=
195
(
1
-m
)L
2
=92.
4
Capacitors C [
μ
F]
m
C
1
=0.
193 C
2
=0.
448
Characteristic
I
m
p
e
dance Z
0
[
Ω
] 20.
8
4.1 Load
Current
Char
acteris
t
ics
The load c
u
rre
nt char
acteristics of the
π
-C
L
C
L t
y
pe imm
itt
ance convert
er
for
Q
1
=Q
2
=Q
are shown i
n
Fi
gure 4. As c
a
n be seen fro
m
t
h
e graphs t
h
e l
o
ad curre
nt
re
m
a
in
s fa
irly
co
n
s
tan
t
as lo
ad
is in
creased
u
p
to
t
h
ree t
i
m
e
s
t
h
e charact
eri
s
ti
c im
pedance. Ideal
ly
, t
h
e current
shoul
d rem
a
in const
a
nt
. Ho
wever, beca
use of t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A
π
-CLCL Type Immittan
ce C
o
n
v
erter fo
r Co
n
s
t
a
n
t
Cu
rre
nt a
n
d
Dyn
a
mic
Loa
d
Ap
p
lica
t
i
o
n
s
(MA Ra
zzak)
68
5
loss due to the
quality factor Q the current
decreases sli
ghtly with load. Al
so, it is
obvi
ous from
the figure that
th
e h
i
g
h
e
r th
e
Q v
a
lu
e, th
e less is th
e d
ecrease in
cu
rren
t wh
ich
m
ean
s th
e
less is th
e effect o
f
th
e lo
ss term
o
f
out
p
u
t
curre
nt
.
For
Q=1
50 t
h
e
l
o
ad cur
r
ent
gr
aph i
s
al
m
o
st
a
straight line. Therefore,
since
the curre
nt deviates
o
n
l
y slig
h
tly w
ith
lo
ad
, it can
b
e
said
th
at th
e co
nv
erter p
r
o
v
id
es o
u
t
pu
t cu
rren
t in
d
e
p
e
n
d
e
n
t
o
f
th
e lo
ad
.
Fi
gure 4.
Loa
d
current
, I
2
, characteris
tics curve of
π
-C
LC
L t
y
pe im
m
i
tt
ance
conve
rt
er
Fi
gure 5 i
s
a co
m
p
ar
i
s
on of t
h
e sim
u
l
a
ti
on resul
t
s
and exper
i
m
e
ntal
result
s
of t
h
e out
put
curre
nt
of t
h
e
π
-CLCL imm
ittance converter. Id
eally, accor
d
ing to the sim
u
lation, if quali
ty factor is extr
em
ely high, the load
cu
rren
t
sho
u
l
d
re
m
a
in
co
n
s
tan
t
at 4
0
.
7
m
A. Ho
wev
e
r, with
a q
u
a
lity fac
t
o
r
o
f
Q
1
=1
2.6 a
n
d Q
2
= 35.
3, t
h
e l
o
ad
current decrea
ses slightly with load. As ca
n be seen
f
r
o
m
t
h
e fi
gure, t
h
e out
p
u
t
curr
ent
obt
ai
ned fr
om
t
h
e
ex
p
e
rim
e
n
t
s s
h
o
w
s litt
le d
e
v
i
atio
n
as lo
ad
is in
creased to
th
ree ti
m
e
s th
e reson
a
n
t
frequ
en
cy. Th
u
s
, th
e
ex
p
e
rim
e
n
t
a
l
d
a
ta is in
co
n
f
o
r
mi
ty wi
th
th
e si
m
u
la
tio
n
resu
lts.
Fi
gu
re
5.
O
u
t
p
ut
C
u
rre
nt
C
h
a
r
act
eri
s
t
i
c
s
4.2 Efficiency
Charac
teristics
Fig
u
r
e
6
illu
strates th
e g
r
ap
h
o
f
efficien
cy ag
ain
s
t th
e factor m
co
n
s
id
erin
g
Q
1
=Q
2
=Q. As can be
seen
fro
m
th
e fig
u
r
e th
at fo
r equ
a
l
q
u
a
lity facto
r
s, th
e
m
a
x
i
m
u
m
efficien
cy o
ccu
rs at
m
=
0
.
5
.
0
10
20
30
40
50
60
8
8.
5
9
9.
5
10
10.
5
11
L
oad
[
ohm
]
Loa
d C
u
rrent
[
A
]
C
u
rre
n
t @ Q
2
=
5
0
C
u
rre
n
t @ Q
2
=
1
0
0
C
u
rre
n
t @ Q
2
=
1
5
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
679
–
6
90
68
6
Figure 6.
Efficiency
ve
rs
us m
cur
v
e
of
π
-CL
C
L type immittance converte
r
Figures 7~9 com
p
are
the effic
i
ency character
istics of the
π
-
C
LC
L imm
itt
ance convert
er
wi
t
h
t
h
at
of
th
e typ
i
ca
l fo
ur co
nfig
uratio
ns fo
r d
i
fferen
t
Q v
a
lu
es. Th
e
blue curves re
present the
efficiency of the typical
fou
r
co
nfi
g
urat
i
ons;
t
h
e red c
u
rves
represe
n
t the efficiency
of the
π
-C
LC
L t
y
pe im
m
itt
an
ce convert
er
h
a
vi
n
g
Q
1
=Q
2
while the green curves repr
esent the efficiency of the
π
-C
LC
L ty
pe convert
er
havi
ng
Q
1
=1.5Q
2
as
deri
ved i
n
(
2
6
)
. As can be se
en from
t
h
e sim
u
l
a
ti
on resul
t
s
, t
h
e
π
-C
LC
L t
y
pe has hi
gher
efficiency than the
typ
i
ca
l fo
u
r
con
f
ig
uratio
n
s
for all th
ree v
a
lues o
f
Q.
T
h
e
hi
gher
t
h
e
val
u
e of
Q
t
h
e
better is the efficiency.
Also
, th
e co
nv
erter with
Q
1
=1.5Q
2
has
higher efficiency than that with Q
1
=Q
2
. For the case Q
1
=1.5Q
2
,
maxim
u
m effic
i
ency occurs when Z
2
=20.8
Ω
, which is the characteristic
im
pe
dance of the circuit whereas for
the case Q
1
=Q
2
m
a
xim
u
m efficiency does not occur when Z
2
=Z
0
but
at
Z
2
=18.
0
Ω
.
Fi
gure 7.
C
o
m
p
ari
s
on of
e
ffi
ciency character
istics of
π
-C
LC
L t
y
pe im
m
itt
ance
converter a
nd typical
confi
g
urat
i
ons for Q
= 50
The efficiency characteristics
of the
π
-CLCL converter
obtained experi
mentally is co
mpared to the
si
m
u
la
tio
n
result in
Fig
u
r
e
1
0
.
Th
e exp
e
rim
e
n
t
al d
a
ta d
e
m
o
n
s
trates th
e tren
d
of th
e si
m
u
la
tio
n
resu
lt. Figu
re
11
shows t
h
e co
m
p
ar
i
s
on of
t
h
e experim
e
nt
al values of the efficiency
of the
π
-CLCL,
π
-CLC and T-LCL
confi
g
urat
i
ons.
As can be seen from
t
h
e f
i
gure, t
h
e
π
-C
LCL confi
g
u
r
at
i
on has hi
gher ef
fi
ci
ency
t
h
an bot
h t
h
e
π
-C
LC
and T-
LC
L t
y
pe conv
erters as expected.
Figure 12 pres
ents the efficie
n
cy of the
π
-C
LC
L convert
er
at
resonant
fre
quency
and at
freq
u
enci
es
±5% of t
h
e res
onant
fre
quenc
y
.
Fi
gure 13 p
o
r
t
r
ay
s t
h
e effi
ci
ency
of t
h
e convert
er at
resonant
freq
u
ency
and at
0
0.
2
0.
4
0.
6
0.
8
1
98
98
.
0
5
98
.
1
98
.
1
5
98
.
2
98
.
2
5
98
.
3
m
E
ffi
c
i
e
n
c
y
0
10
20
30
40
50
60
90
91
92
93
94
95
96
97
98
99
10
0
Lo
ad
[
o
h
m
]
E
f
f
i
c
i
enc
y
Ef
f
i
ci
en
cy
o
f
pi
-
C
LCL
w
i
t
h
Q1
=
Q
2
=
50
Ef
f
i
ci
en
cy
of
4 con
f
i
g
s.
w
i
t
h
Q
1
=
Q
2=
50
E
f
f
i
c
i
en
c
y
o
f
pi
-
C
LCL
w
i
t
h
Q1
=
1
.
5
Q2
;
Q1
=
7
5
,
Q2
=
5
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A
π
-CLCL Type Immittan
ce C
o
n
v
erter fo
r Co
n
s
t
a
n
t
Cu
rre
nt a
n
d
Dyn
a
mic
Loa
d
Ap
p
lica
t
i
o
n
s
(MA Ra
zzak)
68
7
±10%
of t
h
e re
sonant
f
r
eque
n
c
y
.
There i
s
very
l
i
t
t
l
e
di
ffe
rence in the efficiency in al
l fiv
e
cases indicating that
the efficiency is not m
u
ch affect
ed by the changes in
frequency.
Fi
gure 8.
C
o
m
p
ari
s
on of
e
ffi
ciency character
istics of
π
-C
LC
L t
y
pe im
m
itt
ance
converter a
nd typical
confi
g
urat
i
ons for Q
= 10
0
Fi
gure 9.
C
o
m
p
ari
s
on of
e
ffi
ciency character
istics of
π
-C
LC
L t
y
pe im
m
itt
ance
converter a
nd typical
confi
g
urat
i
ons for Q
= 15
0
0
10
20
30
40
50
60
90
91
92
93
94
95
96
97
98
99
100
Loa
d
[
o
h
m
]
E
f
f
i
c
i
enc
y
E
f
f
i
c
i
en
c
y
of
pi
-
C
LC
L w
i
t
h
Q
1
=
Q
2=
100
E
f
f
i
c
i
en
c
y
of
4 c
o
n
f
i
g
s
.
w
i
t
h
Q
1
=
Q
2=
100
E
f
f
i
c
i
en
c
y
of
pi
-
C
LC
L w
i
t
h
Q
1
=
1
.
5
Q
2
;
Q
1
=
150,
Q
2
=
100
0
10
20
30
40
50
60
90
91
92
93
94
95
96
97
98
99
10
0
Lo
a
d
[
o
h
m
]
E
ffi
ci
ency
E
f
f
i
ci
en
cy
o
f
pi
-
C
LC
L w
i
t
h
Q
1
=
Q
2
=
15
0
E
f
f
i
ci
en
cy
o
f
pi
-
C
LC
L
w
i
t
h
Q
1
=
1
.
5
Q
2
;
Q
1
=
2
25,
Q
2
=
1
5
0
E
f
fi
ci
en
cy
o
f
4 c
o
n
f
i
g
s.
w
i
t
h
Q
1
=
Q
2=
1
5
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
679
–
6
90
68
8
Figure
10. E
ffi
ciency cha
r
acteristics of
π
-C
LCL immittance conve
rter
Fi
gu
re
1
1
. C
o
m
p
ari
s
on
of
ex
peri
m
e
nt
al
dat
a
o
f
ef
fi
ci
ency
of
π
-CLCL,
π
-CLC and T
-
LC
L confi
g
urations at
reso
na
nt
f
r
eq
u
e
ncy
Fi
gu
re
1
2
. C
o
m
p
ari
s
on
of
ex
peri
m
e
nt
al
dat
a
o
f
ef
fi
ci
ency
of
π
-CLCL at
f
r
and ±5%
of
f
r
0
10
20
30
40
50
60
0
10
20
30
40
50
60
70
80
90
100
Lo
ad
[o
h
m
]
E
f
f
i
cienc
y
E
x
per
i
m
en
t
a
l
D
a
t
a
S
i
m
u
la
t
i
o
n
R
e
s
u
lt
0
10
20
30
40
50
60
0
10
20
30
40
50
60
70
80
90
10
0
Lo
ad
[o
h
m
]
E
f
ficie
n
cy
E
ffi
c
i
e
n
c
y
of
p
i
-
C
L
C
L
E
ffi
c
i
e
n
c
y
of
p
i
-
C
L
C
E
ffi
c
i
e
n
c
y
of
T
-
L
C
L
0
10
20
30
40
50
60
0
10
20
30
40
50
60
70
80
90
100
Lo
ad [
o
h
m
]
E
f
fi
ci
e
n
cy
Ef
f
i
c
i
enc
y
@
+
5
% re
s
o
n
ant
f
r
e
que
nc
y
Ef
f
i
c
i
enc
y
@
-
5
% re
s
o
n
ant
f
r
e
que
nc
y
Ef
f
i
c
i
enc
y
@
r
e
s
o
n
a
n
t
f
r
e
que
nc
y
Evaluation Warning : The document was created with Spire.PDF for Python.