Download High-Input and Low-Output Impedance Voltage

High-Input and Low-Output Impedance
Voltage-Mode Universal Biquadratic Filter
Using FDCCIIs
Hua-Pin Chen1*, and Yi-Zhen Liao2
1
Department of Electronic Engineering, De Lin Institute of Technology, Taipei, Taiwan, R.O.C.
Graduate Institute of Computer and Communication Engineering, National Taipei University of Technology,
Taipei, Taiwan, R.O.C.
*Email: [email protected]
2
Abstract—A novel high-input and low-output impedance
voltage-mode universal filter with three inputs and single
output employing two fully differential current conveyors, two
resistors, and two capacitors is proposed. The proposed
configuration can realize all the five standard biquadratic
filter functions. It maintains the following advantages: (i)
employment of only two current conveyors, (ii) employment of
only grounded capacitors, (iii) employment of only grounded
resistors, (iv) high-input and low-output impedance, (v) no
need to employ inverting type input signals, (vi) no need to
impose component choice conditions to realize specific
filtering functions, and (vii) low active and passive sensitivity
performances.
Index Terms—active filters, current conveyors, analog
electronics
I. Introduction
Current-mode active elements offer the main advantages
like greater linearity, low power consumption and wider
bandwidth over their voltage-mode counterparts [1-3]. Also,
the design of filter circuits employing current-mode active
elements may be used in phase-locked loop frequency
modulation (FM) stereo demodulators, touch-tone
telephone tone decoder and cross over networks used in a
three-way high fidelity loudspeaker [4]. As a current-mode
active device, the fully differential second-generation
current conveyor [5] was proposed to improve the dynamic
range processing is required. This element is a versatile
building block whose applications appear in the literature
978-1-4244-2186-2/08/$25.00 ©2008 IEEE
[6-10].
Active filters with high-input impedance are of great
interest because it can be easily cascaded to synthesize
high-order filters [11-14]. Besides, the difficulty of
realizing the operations of addition and subtraction of a
voltage-mode signal renders two special active elements,
namely, differential difference current conveyor (DDCC)
and fully differential current conveyor (FDCCII), both of
which have the ability to perform the operations of addition
and subtraction, to become very important for the design of
voltage-mode analog filter design [15]. Recently, a new
high-input and low-output impedance voltage-mode
universal biquadratic filter using three DDCCs has been
proposed by Chiu and Horng [16]. This proposed circuit
offers the following features: realization of all the standard
filter functions in the same configuration, no requirements
for component matching conditions, the use of only
grounded capacitors and resistors, high-input and
low-output impedance, and low active and passive
sensitivities.
In this paper, a new configuration for realizing
universal voltage-mode FDCCIIs filter is proposed.
The proposed circuit employs one fewer active to realize the
same voltage-mode universal biquadratic filter. It still
maintains the following advantages: (i) the employment all
grounded capacitors and resistors, (ii) high-input and
low-output impedance, (iii) no need to employ
inverting-type input signals, (iv) no need to impose
component choice, and (v) low active and passive
sensitivity performances.
Fig. 1. Block diagram of the FDCCII.
from the point of view of integrated circuit fabrications.
Because the Y input terminal of the FDCCII enjoy very
high input impedance, the proposed biquad filter can
straight cascade with another block circuit at its input ports
[15, 16]. Derived by each nodal equation of the proposed
circuit, the input-output relationship matrix form of Fig. 2
can be expressed as
G1Vi 2
⎤
⎡ sC1 G1 − G1 ⎤ ⎡V1 ⎤ ⎡
⎥
⎢
⎥
⎢
⎥
⎢− G sC
V
0
G
V
G
V
(2)
=
−
+
2
2 i3 ⎥ ,
⎥ ⎢ 2 ⎥ ⎢ 2 i1
⎢ 2
⎥⎦
⎢⎣ 1
0
1 ⎥⎦ ⎢⎣Vo ⎥⎦ ⎢⎣
Vi1
where G1 =
1
1
and G2 =
.
R1
R2
From the above matrix form, the output voltage Vo can be
derived as
Vo =
Fig. 2. Proposed high-input and low-output impedance
universal voltage-mode filter.
II. Circuit Description
The block diagram of the FDCCII is shown in Fig. 1 and
its terminal relations are given by
⎡I X + ⎤
⎢ ⎥
⎡V X + ⎤ ⎡0 0 1 − 1 1 0⎤ ⎢ I X − ⎥
⎢V ⎥ ⎢
⎥⎢ ⎥
⎢ X − ⎥ = ⎢0 0 − 1 1 0 1⎥ ⎢ VY 1 ⎥ .
(1)
⎢ I Z + ⎥ ⎢1 0 0
0 0 0⎥ ⎢VY 2 ⎥
⎢
⎥ ⎢
⎥
0 0 0⎦ ⎢VY 3 ⎥
⎣ I Z − ⎦ ⎣0 1 0
⎢ ⎥
⎣⎢VY 4 ⎦⎥
It is shown that the ideal of FDCCII all the four Y
terminals exhibit an infinite input resistance. The two ports
X exhibit zero output resistance and the two ports Z exhibit
an infinite input resistance. The proposed biquad filter,
based on two FDCCIIs, is shown in Fig. 2. Only two current
conveyors, two grounded capacitors, and two grounded
resistors are employed in Fig. 2. The employment of
grounded resistors and grounded capacitors are beneficial
s 2C1C2Vi1 − sC2G1Vi 2 + G1G2Vi 3
.
s 2C1C2 + sC2G1 + G1G2
(3)
Depending on the voltage status of Vi1, Vi2, and Vi3 in the
numerator of Eq. (3), one of the following five filter
functions is realized:
(i) low-pass: Vi1=Vi2=0, and Vi3=Vin;
(ii) band-pass: Vi1=Vi3= 0, and Vi2=Vin;
(iii) high-pass: Vi2=Vi3=0, and Vi1=Vin;
(iv) notch: Vi2=0, and Vi1=Vi3=Vin;
(v) all-pass: Vi1=Vi2=Vi3=Vin.
Note that there are not any component matching
conditions and inverting-type input signals needed in
realizing filtering functions.
The resonance angular frequency ωo and the quality
factor Q are given by
ωo =
Q=
G1G 2
.
C1 C 2
(4)
C1G2
.
C2G1
(5)
III. Effect of Non-Idealities
Taking into account the non-idealities of a FDCCII,
namely,
VX + = α aVY 1 − α bVY 2 + α cVY 3
,
VX − = −α dVY 1 + α eVY 2 + α f VY 4
,
IZ + = βa I X +
and
I Z − = β b I X − , where β i = 1 − ε i and ε i ( ε i << 1 ) denotes
the current tracking error and αV = 1 − ε V and ε v ( ε v << 1 )
denotes the differential voltage tracking error [10].
Reanalysis of the proposed circuit in Fig 2 that the
denominator of the transfer functions becomes
D( s ) = s 2 C1C2 + α a1α d 2 β a1 sC 2 G1 + α a 2α b1 β a1 β a 2 G1G2 . (6)
The resonance angular frequency ωo and the quality
factor Q are given by
ωo =
Q=
α a 2α b1β a1β a 2G1G2
C1C2
1
α a1α d 2
.
α a 2α b1β a 2C1G2
.
β a1C2 G1
(7)
(8)
Using the classical definition of sensitivity co-efficient
x ∂F
S xF =
.
(9)
F ∂x
where F represents one of ωo, Q and x represents any of
the passive elements (G1–G2, C1–C2) or the active
parameters ( α i , β i ). Using the above definition the active
and passive sensitivities of the proposed circuit shown in
Fig. 2 are given as
ωo
ωo
ωo
ωo
ωo
o
Sαωao2 = Sαωbo1 = S ω
β a1 = S β a 2 = S G1 = S G2 = − S C1 = − S C2 =
1
; SαQa 2 = SαQb1 = S βQa 2 = S CQ1 = S GQ2 = − S βQa1 = − S CQ2 =
2
1
;
SαQa1 = SαQd 2 = −1
.
− S GQ1 =
2
(10)
all of which are low and not larger than unity in absolute
value.
be seen, there is a close agreement between theory and
simulation. The noise behavior of the filter was simulated
using the INOISE and ONOISE statements of frequency
responses of the bandpass response with Vi2=Vin, and
Vi1=Vi3=0. Fig. 6 shows the simulated amplitude-frequency
responses for the BP filter with INOISE and ONOISE
designed R1=R2=15.9kΩ, and C1=C2=10pF. The total
equivalent input and output noise voltages are 24mV and
0.22mV, respectively.
Finally, to test the input dynamic range of the filter, the
simulation has been repeated for a sinusoidal input signal at
fo=1MHZ. Fig. 7 shows that the input dynamic range of the
BP response with Vi2=Vin, Vi1=Vi3=0, R1=R2=15.9kΩ, and
C1=C2=10pF, which extends up to amplitude of 0.8V (peak
to peak) without signification distortion.
V DD
M14
IB
M15
Z+
M16
M18
M19
M27
Vbp
Vbp
X+
M20
M17
M9
M22
M3 M4
Y3 Y1
M1 M2
Y2 Y4
M29
M33
M30
M34
X-
M5 M6
Z-
Vbn
M10
M25
M24
M11
M12
M21
Vbn
M31
M35
M32
M26
M23
M36
M28
I SB
VSS
Fig. 3. CMOS realization of the FDCCII.
10
high-pass
IV. Simulation Results
0
magnitude(dB)
To verify the theoretical prediction of the proposed
biquad filter, a simulation using H-Spice simulation with
TSMC 0.35μm process was performed and the CMOS
implementation of an FDCCII is shown in Fig. 3 [8] with
the NMOS and PMOS transistor aspect ratios (W/L=5μ/1μ)
and (W/L=10μ/1μ), respectively. The supply voltages are
VDD=-VSS=1.65V, the biasing voltages are Vbp=-Vbn=0V,
and the biasing currents are IB=ISB=100μA. The component
values of Fig. 2 were given by R1=10kΩ, R2=2kΩ,
C1=79.5pF and C2=15.9pF, leading to a center frequency of
fo=1MHZ and quality factor of Q=5. Fig. 4 shows the
simulated and theoretical response of low-pass, band-pass
and high-pass of Fig. 2. Fig. 5 shows the simulated and
theoretical response of notch and all-pass of Fig. 2. As can
M8
M7
M13
-10
-20
low-pass
band-pass
-30
fo=1MHz
Q=5
-:theoretical
-40
-50
5
10
o:simulation
*:simulation
x:simulation
6
10
frequency(Hz)
7
10
Fig. 4. Simulated frequency responses of low-pass, band-pass and
high-pass of Fig.1 at fo=1MHz and Q=5.
Table 1.Performance parameters of recently reported voltage-mode filter.
10
Criteria
Circuits
0
magnitude(dB)
all-pass
The new
circuit
-10
-20
-30
fo=1MHz
Q=5
-:theoretical
o:simulation
-40
*:simulation
-50
5
10
Ref. [8] in
2005
notch
6
10
frequency(Hz)
7
Ref. [16] in
2007
Ref. [14] in
2004
10
Fig. 5. Simulated frequency responses of notch and all-pass of Fig.1 at
fo=1MHz and Q=5.
Ref. [13] in
2003
Ref. [12] in
2001
(i)
one
DDCC
one
FDCCI
I
one
FDCCI
I
three
DDCCs
three
CCIIs
Two
OTAs
one
CCII
three
CCIIs
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
yes
yes
yes
yes
yes
yes
no
no
no
no
yes
no
yes
yes
yes
yes
yes
yes
no
no
no
no
no
no
no
no
no
no
yes
no
no
no
no
no
yes
no
V. Conclusions
Fig. 6. The equivalent input and output noises against frequency.
In 2007, Chiu and Horng proposed a good high-input and
low-output impedance voltage-mode universal biquadratic
filter using three DDCCs, two grounded capacitors and
resistors. In this paper, although the use of FDCCII can be
divided into two separate DDCC’s, the proposed circuit
still maintains the following advantages: (i)
employment of two current conveyors, (ii) employment of
only grounded capacitors, (iii) employment of only
grounded resistors, (iv) high-input and low-output
impedance, (v) no need to employ inverting type input
signals, (vi) no need to impose component choice
conditions to realize specific filtering functions, and (vii)
low active and passive sensitivity performances. The main
features of the proposed circuit are compared with those of
previous works in Table 1.
Acknowledgment
The authors would like to thank the National Science
Council and Chip Implementation Center of Taiwan, ROC.
The National Science Council, Republic of China supported
this work under grant number NSC 96-2221-E-237-009.
References
[1]
Fig. 7. The input and output waveforms of the BP response for a 1
MHz sinusoidal input voltage of 0.8V (peak to peak).
[2]
B. Wilson, ‘‘Recent developments in current conveyor and
current-mode circuits,’’ Proceedings of IEE, vol. 137, pp.63–77,
1990.
G. W. Roberts and A. S. Sedra, ‘‘All current-mode frequency
selective circuits,’’ Electron. Lett., vol. 25, pp. 759–761, 1989.
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
C. M. Chang, ‘‘Current mode allpass/notch and bandpass filter using
single CCII,’’ Electron. Lett., vol. 27, pp. 1812–1813, 1991.
M. A. Ibrahim, S. Minsri, and H. Kuntman, ‘‘A 22.5MHz
current-mode KHN-biquad using differential voltage current
conveyor and grounded passive elements,’’ Int. J. Electron. Commun.
(AEÜ), vol. 59, pp. 311–318, 2005.
A. A. El-Adwy, A. M. Soliman, and H. O. Elwan, ‘‘A novel fully
differential current conveyor and applications for analog VLSI,’’
IEEE Trans. Circuits Syst.—II: Analog Digital Signal Process, vol.
47, pp. 306–313, 2000.
C. M. Chang, B. M. Al-Hashimi, H. P. Chen, S. H. Tu and J. A. Wan,
‘‘Current mode single resistance controlled oscillators using only
grounded passive components,’’ Electron. Lett., vol. 38,
pp.1071–1072, 2002.
C. M. Chang, B. M. Al-Hashimi, C. L. Wang and C. W. Hung,
‘‘Single fully differential current conveyor biquad filters,’’ IEE Proc.
Circuits, Devices Syst., vol. 150, pp. 394-398, 2003.
C. M. Chang and H. P. Chen, ‘‘Single FDCCII-based tunable
universal voltage-mode filter,’’ Circuit, Systems, and Signal Proc.,
vol. 24, pp. 221-227, 2005.
S. Maheshwari, I. A. Khan and J. Mohan, ‘‘Grounded capacitor
first-order filters including canonical forms,’’ Journal of Circuits,
Systems, and Computers, vol. 15, pp. 289-300, 2006.
J. W. Horng, C. L. Hou, C. M. Chang, H. P. Chou, C. T. Lin, and Y. H.
Wen, ‘‘Quadrature oscillators with grounded capacitors and resistors
using FDCCIIs,’’ ETRI Journal, vol. 28, pp. 486-494, 2006,.
J. W. Horng, J. R. Lay, C. W. Chang and M. H. Lee, ‘‘High input
impedance voltage-mode multifunction filters using plus-type
CCIIs,’’ Electron Letts, vol. 33, pp. 472-473, 1997.
J. W. Horng, ‘‘High-input impedance voltage-mode universal
biquadratic filter using three plus-type CCIIs,’’ IEEE Trans Circ
Syst—II: Analog Digital Signal Process, vol. 48, pp. 996-997, 2001.
J. W. Horng, ‘‘High-input impedance voltage-mode universal
biquadratic filter using two OTAs and one CCII,’’ Int J Electron, vol.
90, pp. 185-191, 2003.
J. W. Horng, ‘‘High input impedance voltage-mode universal
biquadratic filters with three inputs using three plus-type CCIIs,’’ Int
J Electron, vol. 91, no. 8, pp. 465-475, 2004.
C. M. Chang, A. M. Soliman, and M. N. S. Swamy, ‘‘Analytical
synthesis of low sensitivity high-order voltage-mode DDCC and
FDCCII-grounded R and C all-pass filter structures,’’ IEEE Trans
Circ Syst—I: Fundamental Theory Applications, vol. 54, pp.
1430-1443, 2007.
W. Y. Chiu and J. W. Horng, ‘‘High-input and low-output impedance
voltage-mode universal biquadratic filter using DDCCs,’’ IEEE
Trans Circ Syst—II: Analog Digital Signal Process, vol. 54, pp.
649-652, 2007.