ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 26, NO. 3, 2020
1Abs ac —A no el solu ion o a econnec ion-less
econ igu able il e is being p esen ed. The il e wo ks in he
cu en mode, ol age mode, and mixed mode ( ol age
ocu en ) o e ing six een ans e unc ions in o al. The
s uc u e u ilizes a ol age di e encing ansconduc ance
ampli ie , cu en ollowe and ol age, and cu en ampli ie s.
The designed s uc u e o e s he con ol o he pole equency
and quali y ac o and he adjus men o he band-s op/band-
pass a ea o a ailable unc ions. The p oposed design is
suppo ed by he PSpice simula ions using a ailable simula ion
models.
Index Te ms—Cu en mode; Elec onic con ol; Elec onic
econ igu a ion; F equency il e ; Mixed mode; Vol age mode.
I. INTRODUCTION
The e sa ili y o equency il e s, as one o he mos
undamen al and commonly used unc ional blocks in he
indus y, is o en a desi ed p ope y. A common a emp
in case o he design o equency il e s is ha he il e
p o ides mul iple ans e unc ions o e en be e all
s anda d ans e unc ions (all pass (AP), band s op (BS),
high pass (HP), band pass (BP), and low pass (LP) ) i
possible. These s uc u es a e usually based on he ac ha
hey include ei he mul iple inpu nodes, mul iple ou pu
nodes o bo h.
A ce ain amoun o p oposed solu ions [1]–[10] o e s
ans e unc ions in mul iple ope a ional modes in o de
o inc ease he e sa ili y o a gi en il e . The pape s s a e
ha he il e s in [1]–[5] p o ide unc ions in he cu en
mode (CM), as well as in he ol age mode (VM). The il e
in [6] o e s unc ions o he cu en and ansimpedance
( ol age o cu en ) mode, while pape [7] p esen s a il e
ope a ing in ol age and ansimpedance mode. Some o he
s uc u es [1]–[7] can also o e some unc ions o di e en
modes, bu his possibili y was no in oduced wi hin he
pape . Remaining e e ences [8]–[10] in oduce il e s
wo king wi h all possible combina ions - cu en , ol age,
ansimpedance, and ans esis ance (cu en o ol age)
mode. Se e al solu ions [4], [5], [10], a some poin , include
loa ing capaci o s in o de o p o ide ce ain unc ions. I is
a well-known ac ha loa ing capaci o s a e unsui able o
Manusc ip ecei ed 11 Feb ua y, 2020; accep ed 16 May, 2020.
Fo he esea ch, in as uc u e o he SIX Cen e was used.
he in eg a ion. As men ioned ea lie , hese s uc u es ha e
ei he mul iple inpu nodes, mul iple ou pu nodes o bo h.
This as well is a disad an ageous p ope y since i is
necessa y o swi ch be ween he inpu and ou pu nodes
o gi en s uc u e o he pu pose o changing he desi ed
unc ion. In such case, a swi ching logic needs o be
designed and added on he chip. Also, i he swi ching
be ween unc ions is con olled s ic ly digi ally, we a e
limi ed in he ma e o ine uning o ou pu esponses.
Mo eo e , he solu ion in [4] equi es a s uc u e
modi ica ion o be able o ope a e in a di e en mode.
Reconnec ion-less econ igu able il e s [11]–[17] b ing
a possible solu ion o he abo e-men ioned p oblem as he
esul ing ou pu esponse is se h ough he elec onically
con ollable elemen s, which a e usually con olled by DC
cu en o DC ol age, which can be ex e nally applied o he
chip. To he bes o au ho ’s knowledge, he e has been no
epo o a econnec ion-less econ igu able il e o e ing i s
unc ions in mul iple ope a ional modes. Table I p o ides a
b ie compa ison o he design in oduced in his pape wi h
ele an p e iously p oposed solu ions.
II. DESIGN DESCRIPTION
The il e ’s co e is based a ound a ol age di e encing
ansconduc ance ampli ie (VDTA) [18]. A cu en ollowe
(CF) [19], a iable gain ampli ie s (VGAs) [20], and
adjus able cu en ampli ie s (ACAs) [21] a e hen sui ably
added o he ci cui . The CF has been added so he HP
esponse can be aken om he high-impedance node ins ead
o being aken h ough C1 (in case o he CM) when he
capaci o could no be g ounded. The CF p o ides a copy o
a cu en om he inpu node a ailable om a high-
impedance ou pu a he han h ough he capaci o . VGAs
and ACAs hen p o ide he econnec ion-less
econ igu a ion o he esul ing ans e . The VDTA can be
desc ibe by he ma ix (1).
The in e -s uc u e o he VDTA is c ea ed by wo
ope a ional ansconduc ance ampli ie s (OTAs) [20]
as shown in Fig. 1, oge he wi h he schema ic symbol o
he VDTA. The OTAs ha e been implemen ed by uni e sal
cu en con eyo s (UCCs) [22] ( e minal Y1 and Y2 a e
used as di e en ial ol age inpu s, e minal X is g ounded
h ough a esis o R = 1/gm) in his pa icula case.
Dual-Mode Mul i unc ional Reconnec ion-Less
Recon igu able Fil e
Lukas Langhamme 1, *, Roman So ne 1, Jan D o ak1, Tomas Dos al2
1Facul y o Elec ical Enginee ing and Communica ion, B no Uni e si y o Technology,
Technicka 12, 61600 B no, Czech Republic
2Depa men o Technical S udies, College o Poly echnics,
Tols eho 16, 58601 Jihla a, Czech Republic
[email p o ec ed]
h ps://doi.o g/10.5755/j01.eie.26.3.25856
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ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 26, NO. 3, 2020
TABLE I. RECENTLY INTRODUCED RECONNECTION-LESS RECONFIGURABLE FILTERS COMPARED TO THE PROPOSED DESIGN.
Re . No.
[11]
[12]
[13]
[14]
[15]
[16]
[17]
Fig. 4
Yea
2015
2019
2015
2019
2016
2018
2019
-
No. o ac i e/passi e elemen s
4/2(3)1
5/4
4/2
5/2
2/3
4/4
4/2
8/2
All capaci o s g ounded
No
Yes
No
Yes2
Yes
Yes
No
Yes3
Ope a ional mode
VM
CM
VM
CM
CM
VM
VM
CM, VM,
(V→I)
No. o a ailable unc ions
7
6
7
9
5
7
6
7+7+2
No e: 1 – con ains mul iple solu ions, 2 – one o he capaci o s is i ually g ounded h ough he cu en inpu , 3 – one o he capaci o s is i ually
g ounded h ough ol age ou pu s o VGA elemen s.
11
11
2
2
0 0 0 0
0 0 0 0
00 .
00
0 0 0
0 0 0
p
np
mm
Zn
mm
ZZ
m
XZ
m
X
I
IV
gg
IV
gg
IV
g
IV
g
I







 

 

 


 


 

 

 




(1)
VDTA
VDTA
+
_gm1
+
_gm2
In
Ip
Vn
Vp
IX-
IX+
VX-
VX+
X+
X-
X+
X-
Z+
Z-
p
n
IZ+
IZ- VZ- VZ+
Ip
Vn
Vp
IX+
VX-
VX+
IZ+
IZ- VZ- VZ+
InIX-
Z+
Z-
p
n
OTA1OTA2
a)
b)
Fig. 1. Vol age di e encing ansconduc ance ampli ie (VDTA): a)
Schema ic symbol; b) Implan a ion o i s in e nal opology by wo OTAs.
The CF is desc ibed by ela ion Iou ± = ±Iin and i s
schema ic symbol, and implemen a ion by he UCC can be
seen in Fig. 2. The VGAs we e implemen ed by
comme cially a ailable de ices VCA822 [23] wi h hei
ol age gain A con olled by he DC con ol ol age VSET_A.
Thei unc ion can be exp essed as Vou ± = ±AVin. The las
used elemen ACA is c ea ed by comme cially a ailable
de ices EL2082 [24]. The beha io o he ACA ollows a
ela ion Iou ± = ±BIin, whe e he cu en gain B is con olled
by he DC con ol ol age VSET_B. The schema ic symbols o
he VGA and ACA a e depic ed in Fig. 3.
CF IOUT+
IOUT-
Y1
Y2
Y3
X
Z1+
Z1-
Z2+
Z2-
UCC
b)
IOUT+
IOUT-
IIN
IIN
a)
Fig. 2. Cu en ollowe : a) Schema ic symbol; b) I s implemen a ion by
he UCC.
B
ACA VSET_B IOUT
IIN
a) b)
+
_
VSET_A
VGA
AVOUT
VIN-
VIN+
Fig. 3. Schema ic symbols: a) Adjus able cu en ampli ie (ACA); b)
Va iable gain ampli ie (VGA).
The p oposed il e is p esen ed in Fig 4. The s uc u e
was designed in such way ha he inpu ol age is
dis ibu ed in o di e en nodes o he il e since he ol age
can be easily aken om one node and i does no equi e
an addi ional ac i e elemen o dis ibu e he inpu ol age
in compa ison o he ol age summa ion. In case o he CM,
on he o he hand, he cu en s o indi idual esponses a e
summed up in one node as he cu en summa ion can be
made wi hou a necessi y o an ex a ac i e elemen
in compa ison o he cu en dis ibu ion. The i s OTA
in he VDTA s uc u e has been implemen ed by mul iple
ou pu elemen , so i can o e one addi ional Z ou pu (Z - in
his case). The nega i e inpu o he second OTA is no
g ounded, bu used as an inpu (labeled as in Fig. 4). The
capaci o C1 and nega i e inpu s o he i s and second
OTAs in he VDTA s uc u e a e i ually g ounded h ough
he ou pu s o VGA elemen s aking in o conside a ion he
ac ha he ol age ou pu has ze o impedance in he ideal
case.
CF
B1
ACA1VSET_B1
IIN
+
_
VSET_A1
VGA1
A1
C1
VOUT
IOUT
B2
VSET_B2
B3
VSET_B3
ACA2
ACA3
+
_
VSET_A2
VGA2
A2+
_
VSET_A3
VGA3
A3
VIN
VDTA X+
X-
Z+
Z-
p
n
Z-
C2
Fig. 4. P oposed dual-mode mul i unc ional econnec ion-less
econ igu able il e .
The denomina o common o bo h he CM and VM is
gi en as
211221
2
)( mmm gggCCCD  sss
. (2)
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ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 26, NO. 3, 2020
The nume a o in case o he VM is
21 2 1 2 2 3 2 1 2
1 2 2
( ) ( )
,
mm
mm
N CC A C g A C g A
g g A
    

s s s
(3)
and he nume a o o he CM is
21 2 3 2 1 2 1 2 1
() m m m
N CC B C g B g g Bs s s
. (4)
As i can be seen, he esul ing ou pu esponse depends
on he se ing o ol age gains A o he VM and cu en
gains B o he CM all con olled elec onically by DC
ol ages. The il e p o ides all s anda d ans e unc ions
(AP, BS, HP, BP, and LP) in bo h modes. The se ing
o con ol ol ages in dependence on he esul ing ou pu
esponse is s a ed in Table II. The il e also o e s unc ions
BP and HP (bo h pola i ies) o he mixed mode ( ol age
o cu en ). The con ol ol ages can be unde s ood as
ollows: A = 0 o -1 V, A = 1 o 0 V, and A = 2 o 1 V
when e e ing o he VGA and B = 0 o 0 V and B = 1 o
1 V in case o he ACA. The pole equency and quali y
ac o o he il e in bo h cases a e exp essed as:
12
0
12
1,
2
mm
gg
CC


(5)
12
21
.
m
m
Cg
QCg

(6)
The e o e, 0 can be con olled wi hou a ec ing Q by he
change o gm1 and gm2 i a simple condi ion gm1 = gm2 is
ul illed. Simila ly, Q can be con olled wi hou a ec ing 0
by changing he a io be ween gm1 and gm2 as long as he
esul o he mul iplica ion o gm1 and gm2 emains
unchanged.
TABLE II. THE SETTING OF THE CONTROL VOLTAGES IN
RELATION TO PARTICULAR OUTPUT RESPONSE.
VM
HP
BP
LP
BS
AP
VSET_A1
0 V
-1 V
-1 V
0 V
0 V
VSET_A2
-1 V
-1 V
0 V
0 V
0 V
VSET_A3
-1 V
0 V
0 V
0 V
1 V
CM
HP
BP
LP
BS
AP
VSET_B1
0 V
0 V
1 V
1 V
1 V
VSET_B2
0 V
1 V
0 V
0 V
1 V
VSET_B3
1 V
0 V
0 V
1 V
1 V
III. VERIFICATION
The e i ica ion o he design has been made wi h he help
o PSpice simula ions in ol ing a ailable simula ion models
o he UCC and comme cially a ailable de ices VCA822
and EL2082 o implemen ac i e elemen s in he way
sugges ed in he p e ious sec ion. The alues
o ansconduc ances and he passi e pa s we e chosen o be
gm1 = gm2 = 1 mS and C1 = C2 = 1 nF. The e o e, he
heo e ical alues o he pole equency and quali y ac o
a e equal o 0 = 159.2 kHz and Q = 1.
The cu en mode ans e unc ions o BS, HP, BP, and
LP ob ained om he simula ions a e compa ed wi h he
heo e ical expec a ions in Fig. 5. Simila ly, he same
ans e unc ions, bu his ime o he ol age mode, a e
p esen ed in Fig. 6 again compa ed wi h he heo e ical
expec a ions. In bo h cases, we can see a good alignmen
o he simula ion esul s wi h he heo y. E en ual
di e ences a lowe and highe equencies a e due o
pa asi ic cha ac e is ics o used ac i e elemen s and hei
bandwid h limi a ions.
Low pass
High pass
Theo y
Band pass
Band s op
Fig. 5. T ans e unc ions o BS, HP, BP, and LP in case o he CM:
simula ion esul s (colo ed solid cha ac e is ics) and heo y (black dashed
cha ac e is ics).
Low pass
High pass
Theo y
Band pass Band s op
Fig. 6. T ans e unc ions o BS, HP, BP and LP in case o he VM:
simula ion esul s (colo ed solid cha ac e is ics) and heo y (black dashed
cha ac e is ics).
The band-s op unc ion o he ol age mode has been
selec ed o he p esen a ion o he con ollabili y o 0. This
abili y is demons a ed o i e di e en se ings o alues
o ansconduc ances gm1, gm2 (gm1 = gm2). The chosen alues
a e 560 µS, 750 µS, 1 mS, 1.33 mS, and 1.77 mS esul ing
in he heo e ical 0 o 89.1 kHz, 119.4 kHz, 159,2 kHz,
211.7 kHz, and 281.7 kHz. The ob ained simula ion esul s
a e depic ed in Fig. 7.
Theo y
gm1 = gm2 = 568 µS
0 = 87.9 kHz
gm1 = gm2 = 750 µS
0 = 115.9 kHz gm1 = gm2 = 1 mS
0 = 155.6 kHz
gm1 = gm2 = 1.33 mS
0 = 205.1 kHz
gm1 = gm2 = 1.77 mS
0 = 272.9 kHz
Fig. 7. The con ollabili y o 0 demons a ed o i e di e en se ings o
ansconduc ances gm1 and gm2.
The alues o 0 acqui ed om he simula ion a e
compa ed wi h he heo e ical alues in Table III. The
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ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 26, NO. 3, 2020
ob ained simula ion esul s show sligh ly lowe alues han
he heo e ical p esump ions, ne e heless he esul s yield
only small di e ence, which can be easily compensa ed
assuming he elec onic con ol o he ansconduc ances. I
would be possible o p o ide an elec onic con ol o 0 and
Q by a di e en ype o implemen a ion o he OTA elemen
un o una ely, he comme cially a ailable elemen s wi h he
elec onic con ol o hei ansconduc ance usually o e
only one ou pu and i would ha e o be cons uc ed by
mul iple ac i e elemen s.
TABLE III. THE CONTROL OF THE POLE FREQUENCY.
gm1, gm2
560 µS
750 µS
1 mS
1.33 mS
1.77 mS
0 heo e ical
[kHz]
89.1
119.4
159.2
211.7
281.7
0 simula ed
[kHz]
87.9
115.9
155.6
205.1
272.9
The s op-band a ea (as much as he pass-band a ea)
o a ailable unc ions can be easily adjus ed i equi ed. This
can be seen in Fig. 8 demons a ed on he CM band-pass
unc ion. The band-s op a ea a lowe equencies can be
con olled by he adjus men o he alue o cu en gain B1,
while he band-s op a ea a highe equencies can be
adjus ed by B3. In simila manne , he band-s op/band-pass
a eas o he VM unc ions can be adjus ed by changing he
alue o A2 o lowe equency band and A1 o highe
equency band. This ea u e also allows he il e o o e
special unc ions o high-pass and low-pass wi h ans e
ze o (HPZ, LPZ). The se ing o he Fig. 8 is as ollows
VSET_B1 (o VSET_B3) = 0.1 V, 0.03 V, and 0.01 V. The
colo ed solid lines show he adjus men o he highe
equency band (con olled by B3) and he black dashed lines
s and o he adjus men o he lowe equency band
(con olled by B1).
VSET_B3 = 0.03 V
VSET_B3 = 0.01 V
VSET_B3 = 0.1 V
VSET_B1 = 0.1 V
VSET_B1 = 0.03 V
VSET_B1 = 0.01 V
Fig. 8. Demons a ion o he adjus abili y o he band-s op a eas o he CM
band-pass unc ion o a ious se ings.
The u he analysis o he p oposed il e ing s uc u e
includes a sensi i i y analysis. The ab ica ion misma ch
(ce ain inaccu acy o indi idual ou pu s o each ac i e
elemen and he ole ance o used passi e pa s) can
signi ican ly in luence he esul ing ans e cha ac e is ics.
Based on his ac , he il e ope a ing in he CM in ol es 12
pa ame e s (C1, C2, gm11, gm12, gm13, gm21, gm22, n1, n2, B1, B2,
and B3) and 9 pa ame e s (C1, C2, gm11, gm12, gm21, n1, A1, A2,
and A3) in he VM. Pa ame e s gm11, gm12, gm13, gm21, and
gm22 a e ansconduc ances o indi idual ou pu s o OTA
elemen s wi hin he VDTA, n1 and n2 a e ans e s
o indi idual ou pu s o he CF, pa ame e s B1, B2, and B3
a e cu en gains o indi idual ACA elemen s, and, inally,
A1, A2, and A3 s and o he ol age gains o VGAs.
The co esponding denomina o (common o bo h cu en
and ol age modes) conside ing hese pa ame e s akes a
o m o
21 2 2 11 1 12 21 1
( ) .
eal m m m
D CC C g n g g n  s s s
(7)
The eal nume a o s o he il e wo king in he CM and
VM a e gi en by he ollowing equa ions:
2
_ 1 2 2 3 2 13 1 2
12 22 1 1
()
,
eal CM m
mm
N C C n B C g n B
g g n B
  

s s s
(8)
2
_ 1 2 1 2 11 1 2
2 21 1 3 12 21 1 2
( ) (
).
eal VM m
m m m
N C C A C g n A
C g n A g g n A
  

s s s
. (9)
The ela i e sensi i i y o he il e o a change o
an indi idual pa ame e can be desc ibed as [25]
 
( ) ( )
__
Re ,
K j K j
R qi R qi
SS


(10)
whe e K = K(jω) is a complex ans e o he il e
K = IOUT/IIN and qi ep esen s i h pa ame e o he il e .
Maple ool was used o pe o m he ma hema ical exp ession
o he sensi i i ies.
Figu es 9 and 10 show he esul s o he sensi i i y
analysis ac oss whole equency ange om 100 Hz
o 100 MHz.
Fig. 9. Rela i e sensi i i y o he HP unc ion o he CM o indi idual
pa ame e s in dependence on he equency.
Figu e 9 shows he esul s o he HP unc ion in case
when he p oposed il e ope a es in he cu en mode
(sensi i i ies o pa ame e s gm12, gm22, B1, and B2 a e ze o as
hese pa ame e s a e no con ained in he ans e unc ion
o he HP unc ion) and Fig. 10 p esen s he esul s o he
LP unc ion in case o he VM (sensi i i y o A1 is ze o).
F om he g aphs, i can be seen ha all sensi i i ies a e
ela i ely low ( hey a e a ound one, which is he ypical
alue). The highes sensi i i y is a ound he pole equency
o he il e (159.2 kHz), which is well known ac .
The DC ans e unc ion o LP in case o bo h modes
we e ca ied ou (Figs. 11 and 12) in o de o show he
a ailable egion, whe e he ci cui ac s linea ly.
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ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 26, NO. 3, 2020
Fig. 10. Rela i e sensi i i y o he LP unc ion o he VM o indi idual
pa ame e s in dependence on he equency.
Fig. 11. Dynamic ange o he LP unc ion o he CM.
Fig. 12. Dynamic ange o he LP unc ion o he VM.
IV. CONCLUSIONS
The p oposed il e can p o ide 16 unc ions in o al
in h ee ope a ion modes (7 in he CM, 7 in he VM, and 2 in
case o ol age o cu en ans e ) in co espondence wi h
he se ing o elec onically con ollable pa ame e wi hou
any equi ed s uc u e modi ica ion. The in ended unc ion
has been e i ied by PSpice simula ion and shows good
ag eemen wi h he heo y. The il e also o e s a simple
con ol o i s pole equency (see Fig. 7) and adjus men
o he band-s op/band-pass a eas o a ailable unc ions (see
Fig. 8).
CONFLICTS OF INTEREST
The au ho s decla e ha hey ha e no con lic s o in e es .
REFERENCES
[1] C. Lee, “Independen ly unable mixed-mode uni e sal biquad il e
wi h e sa ile inpu /ou pu unc ions”, In e na ional Jou nal o
Elec onics and Communica ions (AEÜ), ol. 70, pp. 1006–1019,
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