Circuits and Systems, 2013, 4, 29-33
http://dx.doi.org/10.4236/cs.2013.41006 Published Online January 2013 (http://www.scirp.org/journal/cs)
Universal Current-Mode Biquad Filter Using a VDTA
Dinesh Prasad1*, Data Ram Bhaskar1, Mayank Srivastava2
1Department of Electronics and Communication Engineering, Faculty of Engineering and Technology,
Jamia Millia Islamia, New Delhi, India
2D/O Electronics and Communication Engineering, Amity School of Engineering and Technology,
Amity University, Noida, India
Received October 9, 2012; revised November 9, 2012; accepted November 16, 2012
ABSTRACT
This paper presents a new current-mode single input multi output (SIMO) type biquad employing one voltage differ-
encing transconductance amplifier (VDTA), two grounded capacitors and a single grounded resistor. The configuration
realizes all basic filter functions (i.e. Low Pass (LP), High Pass (HP), Band Pass (BP), Notch (BR) and All Pass (AP)).
The natural frequency (ω0) and bandwidth (BW) are independently tunable. The workability of proposed configuration
has been verified using SPICE simulation with TSMC CMOS 0.18 μm process parameters.
Keywords: Current Mode Filter; Voltage Differencing Transconductance Amplifier
1. Introduction
Active filters are important basic building blocks, which
are frequently employed in electrical engineering appli-
cations. The current-mode approach [1] in designing ac-
tive filters has become more popular due to its advanta-
geous features such as larger dynamic range and wider
bandwidth as compared to voltage-mode counterparts
(particularly for the high frequency operations), simpler
filtering configurations and lower power consumption.
During the past few years, active filters using different
current-mode/voltage-mode building blocks have been
employed in which VDTA, recently introduced in [2],
appears to be a useful active building block for an easy
CMOS implementation of current-mode signal process-
ing/signal generation [3-5].
Various SIMO-type active filters using different active
elements are available in the literature see [6-13] and the
references cited therein. In references [6-9], SIMO-type
filter configurations employing 2/4 resistors and 2/3 ca-
pacitors have been presented. These proposed filter struc-
tures do not realize all the five filter responses. The con-
figurations presented in [10] and [11] although use one
resistor and two capacitors but fail to realize all the basic
filter functions. Although the biquads proposed in [12]
and [13] realize all the five filter functions but they use
two capacitors along with 2/3 resistors. Therefore, the
purpose of this communication is to propose a new
SIMO-type current-mode universal biquad filter em-
ploying one VDTA, two grounded capacitors and a sin-
gle grounded resistor, which realizes all the basic filter
functions i.e. LP, HP, BP, BR and AP. The natural fre-
quency ω0 and BW are independently tunable. The pro-
posed circuit also offers low active and passive sensitivi-
ties. The workability of proposed configuration has been
verified using SPICE simulation with TSMC CMOS 0.18
μm process parameters.
2. The Proposed New Configurations
The symbolic notation of the VDTA is shown in Figure
1, where VP and VN are input terminals and Z, X+ and X−
are output terminals. All terminals of VDTA exhibit high
impedance values [2]. The VDTA can be described by
the following set of equations:
11
2
2
0
00
00
P
N
mm V
Z
mV
X
mZ
X
gg V
I
IgV
gV I

















 



(1)
The proposed circuit configuration is shown in Figure
2.
A routine circuit analysis of Figure 2 yields the fol-
lowing filter transfer functions:

12
1
1
mm
o
LP
in
g
g
I
Ts (2)
I
Ds

 
1
1
2
2
m
o
BP
in
g
sC
I
Ts
I
Ds



 (3)
*Corresponding author.
C
opyright © 2013 SciRes. CS

D. PRASAD ET AL.
30
V
PVD
V
NX
Z
X
TA
IZ
V
P
V
V
N
V
+
-
IX+
IX-
V
Z
Figure 1. The symbolic notation of VDTA.
R1
C1
VX
Z
X
P
VDTA
VN+
-
I01
Iin
C2
I02
I03
Figure 2. The proposed configuration.
 
2
3o
in
I
3HP
s
Ts
I
Ds
 (4)



12
2
12
mm
gg
sCC
IDs



 31
4
oo
NOTCH
in
II
Ts   (5)



112
11 2
mmm
ggg
CCC
s




 



2
321
5
ooo
AP
in
ss
III
Ts ID


(6)
where

12
11 12
mm
21
g
g
CC




Dsss RC  (7)
The natural frequency ω0, BW and quality factor Q0
are given by:
12
0
12
mm
g
g
CC
  (8)
11
1
BW RC  (9)
12
2
11
2
mm
0
g
gCR
C
Q (10)
3. SPICE Simulation Results
To verify the theoretical analysis, the proposed configu-
ration was simulated using CMOS VDTA from [2].
Power supply voltages were taken as VDD = −VSS = 1 V
and IB1 = IB2 = 150 μA, IB3 = IB4 = 42.38 μA biasing cur-
rents are used. The passive elements of the configuration
were selected as C1 = C2 = 0.01 nF and R1 = 1.58 KΩ.
The transconductances of VDTA were controlled by bias
currents. Figure 3 shows the simulated filter responses of
LP, BP, HP, BR and AP. These results, thus, confirm the
validity of the proposed configuration. A comparison
with other SIMO-type current-mode biquads using a sin-
gle active device is presented in Table 1.
4. Conclusion
A new current-mode SIMO-type biquad filter has been
presented which uses only one VDTA and three ground-
ed passive elements. The proposed filter can realize the
second-order LP, BP, HP, BR and AP responses. The
circuit employs all grounded passive components (which
is desirable for IC implementation) and offers low active
and passive sensitivities. The natural frequency (ω0) and
bandwidth (BW) are independently tunable. SPICE
simulations have established the workability of the pro-
posed formulation.
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
HP
Freque ncy (Hz)
Current Gain
AP BP
LP
BR
Figure 3. Frequency response.
Table 1. Comparison with other SIMO-type current-mode
biquads using a single active devic e.
Reference No. of active
component
No. of
resistors
No. of
capacitors
All five filter
function
realized
[6] 1 4 2 NO
[7] 1 3/4 3 NO
[8] 1 2 2 NO
[9] 1 2 2 NO
[10] 1 1 2 NO
[11] 1 1 2 NO
[12] 1 3 2 YES
[13] 1 2 2 YES
Proposed1 1 2 YES

D. PRASAD ET AL.
31
4. Acknowledgements
This work was performed at the Advanced Analog Signal
Processing Laboratory of the Department of Electronics
and Communication Engineering, F/o Engineering and
Technology, Jamia Millia Islamia, Jamia Nagar, New
Delhi-110025, India.
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[1] C. Toumazau, F. J. Lidgey and D. G. Haigh, “Analogue IC
Design: The Current-Mode Approach,” Peter Peregrinus
Limited, London, 1990.
[2] D. Biolek, R. Senani, V. Biolkova and Z. Kolka, “Active
Elements for Analog Signal Processing, Classification,
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No. 4, 2008, pp. 15-32.
[3] A. Yesil, F. Kacar and H. Kuntman, “New Simple CMOS
Realization of Voltage Differencing Transconductance
Amplifier and Its RF Filter Application,” Radioengineer-
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[4] D. Prasad and D. R. Bhaskar, “Electronically-Controllable
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[5] J. Satansup, T. Pukkalanun and W. Tangsrirat, “Electroni-
cally Tunable Single-Input Five-Output Voltage-Mode
Universal Filter Using VDTAs and Grounded Passive
Elements,” Circuits, Systems, and Signal Processing,
2012 (online). doi:10.1007/s00034-012-9492-0
[6] A. Fabre and J. L. Houle, “Voltage-Mode and Current-
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Conveyors,” IEEE Proceedings-G: Circuits, Devices and
Systems, Vol.139, No.7, 1992, pp. 491-497.
[7] C. M. Chang, C. C. Chien and H. Y. Wang, “Universal
Active Current Filters Using Single Second Generation
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1993, pp. 1159-1160. doi:10.1049/el:19930775
[8] E. Yuce, B. Metin and O. Cicekoglu, “Current-Mode Bi-
quadratic Filters Using Single CCIII and Minimum Num-
ber of Passive Elements,” Frequenz: Journal of RF-En-
gineering and Telecommunications, Vol. 58, No. 9-10,
2004, pp. 225-227.
[9] B. Chaturvedi and S. Maheshwari, “Current Mode Biquad
Filter with Minimum Component Count,” Journal of Ac-
tive and Passive Electronic Components, Vol. 2011, 2011,
Article ID: 391642. doi:10.1155/2011/391642
[10] D. Biolek, V. Biolkova and Z. Kolka, “Current-Mode
Biquad Employing Single CDTA,” Indian Journla of
Pure and Applied Physics, Vol. 47, No. 7, 2009, pp. 535-
537.
[11] W. Tangsrirat, “Novel Current-Mode and Voltage-Mode
Universal Biquad Filters Using Single CFTA,” Indian
Journal of Engineering and Material Science, Vol. 17,
2010, pp. 99-104.
[12] C. N. Lee and C. M. Chang, “Single FDCCII-Based
Mixed-Mode Biquad Filter with Eight Outputs,” AEU:
International Journal of Electronics and Communications,
Vol. 63, No. 9, 2009, pp. 736-742.
doi:10.1016/j.aeue.2008.06.015
[13] D. Prasad, D. R. Bhaskar and A. K. Singh, “Universal
Current-Mode Biquad Filter Using Dual Output Current
Differencing Transconductance Amplifier,” AEU: Inter-
national Journal of Electronics and Communications, Vol.
63, No. 6, 2009, pp. 497-501.
doi:10.1016/j.aeue.2008.02.012

D. PRASAD ET AL.
32
Appendix: Non-Ideal Analysis
Considering the non-ideal effect of various parameters of
VDTA i.e., the finite X-terminal parasitic impedance
consisting of a resistance X in parallel with capaci-
tance X, the parasitic impedance at the Z-terminal
consisting of a resistance
R
C
Z
R in parallel with capaci-
tance
Z
C, the parasitic impedance at the Vp-terminal
consisting of a resistance
p
R in parallel with capaci-
tance
p
C
R
C
and the parasitic impedance at the Vn-terminal
consisting of a resistance n in parallel with capaci-
tance n. The parasitic impedances belong to the circuit
shown in Figure 2 are indicated in Figure A1.
Considering the above parasitic impedances, the natu-
ral frequency ω0 and quality factor Q0 are found to be:

12
2
mm
1
0
12 12
1111
xn
z
z
xzx
RR RR
CC CC CCCC


 


 nnz
gg
CC CC 
R1
C1
VX
Z
X
P
VDTA
VN
(a)
+
-
I01
Iin
Rx
Cx
RnCn
C2
I02
I03
CzRz
Rp
Cp
Figure A1. Parasitic impedances of VDTA affecting the
circuit of Figure 2.

12 12 122
1222
11
11
mmzx zxnnz
z
xn zzz
zzz xxnn
1
0
11
xn
g
g CCCCCCCCCCCC
R
CC C CCCCCC
RRRRRRRRR



  
 







RR R
Q

 (b)
The sensitivity of ω0 and quality factor Q0 with respect to its active and passive elements are given as:
12
00 0
1
12
12 12
0 0
12 1
1
11
11
1
,
1111 1111
22
11
,
1111 1111
22
mm
x n
mm z
ggR
mm mm
xnz xnz
xz nz
RR
mm m
xnz xnz
gg RR
SS S
gg gg
RR RRRR RR
RR RR
SS
gg gg
RR RRRR RR
 

 

 

  
  

 

 

 

  
  

 






2
2
11 11
m
nnz
xn
RR RRCC C
CC C
C C







 




0 0
1
12
0 0
2
112
12 12
1
21 1
12 12212 1
, 2
1111
2
,
22
z
z
zx nz
RC
zxzx
mm
xnz
xn z
C C
zxzxnnzz
SS
CC CC CC CC C
gg
RR RR
CC CCCC
SS
CC CC CC CCCC CCCC CC

 
  



 






 
 





0 0
22
2 2
12 12212 122
,
22
x n
xzx nnz
xz nz
C C
zxzxnnzzxzxnnz
CC CC CCCC
CC CCC C
SS
CC CC CC CC CC CCCC CCCC CC CC CC
 


 
 
12
00 0
1
12
12
11
1
11 111
2
,
1111
2
mm
zx
n
mm
QQ Q
ggR
mm
xnz
D
RR RRR
gg
SS S
gg
RR RR

 


 



 
 





12
12
1
1
1111
mm
z
mm
xnz
gg
R
Dg
RR RR
2z
C C
g



















 
 




D. PRASAD ET AL. 33
 

 

12
0
12
12
0
12
2
1
1
2
1
1
11 1111
2,
1111
11 1111
2
1111
x
n
mm z
xz xnz
Q
R
mm
xnz
mm z
nz xnz
Q
R
mm
xnz
DggCC
RR RRRR
S
Dgg
RR RR
DggCC
RR RRRR
S
Dgg
RR RR






 

 





 
 









 

 



 


 



 
12
0
12
00
12
1
11
1
21
12
1
,
11111 1111
2
1111
11
11
2
2,
z
mm x
zxn xnz
Q
R
mm
xnz
xn
z
z QQ
CC
Dgg
RRRRRRRR
S
Dgg
RR RR
CCCCDE
CCCDE
R
SS
DE








 








 
 




 
 




,
11
n
xn
CCC
RR R








 






0 0
0
12
1
2
11
11
22
11
2,
z x
n
zxn xz
xn
Q Q
C C
nzp
z Q
C
DE
CCCCDE CCC
RR R
SS
DE DE
CCCCDE
R
SDE
,
11
,,
z
DE
R



 







  
 







 



(c)
where
 
1 222
12 12
11
xn zzz
zx zx
zzz xxnn
CC C CCCCCC
DECC CC CC CC C
RRRRRRRRR

 



2
,.
nnz
CC C (d)
From the above mentioned sensitivity values, it is easy
to figure out that all the active and passive sensitivities
are no more than half in magnitude.