Circuits and Systems, 2010, 1, 5-11
doi:10.4236/cs.2010.11002 Published Online July 2010 (http://www.SciRP.org/journal/cs)
Copyright © 2010 SciRes. CS
Voltage Mode Cascadable All-Pass Sections Using Single
Active Element and Grounded Passive Components
Jitendra Mohan1*, Sudhanshu Maheshwari2, Durg S. Chauhan3
1Department of Electronics and Communications, Jaypee University of Information Technology,
Solan, India
2Department of Electronics Engineering, Z. H. College of Engineering and Technology,
Aligarh Muslim University, Aligarh, India
3Department of Electrical Engineering, Institute of Technology, Banaras Hindu University,
Varanasi, India
E-mail: jitendramv2000@rediffmail.com
Received April 23, 2010; revised May 27, 2010; accepted June 2, 2010
Abstract
In this paper, four new first order voltage mode cascadable all-pass sections are proposed using single active
element and three grounded passive components, ideal for IC implementation. The active element used is a
fully differential current conveyor. All the proposed circuit possess high input and low output impedance
feature which is a desirable feature for voltage-mode circuits. Non-ideality aspects and parasitic effects are
also given. As an application, a multiphase oscillator is designed. The proposed circuits are verified through
PSPICE simulation results using TSMC 0.35 µm CMOS parameters.
Keywords: Analogue Signal Processing, All-Pass Filter, Current Conveyor, Voltage-Mode
1. Introduction
Voltage mode (VM) active filters with high-input and
low-output impedance are of great interest because seve-
ral cells of this kind can be directly connected in cascade
within voltage-mode systems without additional voltage
buffers. On the other hand, the use of grounded capacitor
is beneficial from the point of integrated circuit imple-
mentation and also having less parasitic compared to
floating counterparts [1].
First order all-pass filters are an important class of ana-
logue signal processing circuits which have been exten-
sively researched in the technical literature [2,3] due to
their utility in communication and instrumentation sys-
tems, for instance as a phase equalizer, phase shifter or
for realizing quadrature oscillators band pass filters etc.
Numerous first-order voltage-mode all-pass sections (VM-
APSs) employing different types of active element such
as current conveyors and its different variations have
been reported in the literature [4-24]. Among the cited
references, several VM-APSs employ a single standard
current conveyor [6-16,19-22]. Such circuits aim at reali-
zing the first order all-pass function using optimum num-
ber of passive components, rather using grounded compo-
nents or offering high input and low output impedance
feature together. The circuits reported in [17,18] enjoy
high input impedance but uses two active element and
three grounded passive components. Some of the circuits
described in [15,21-23] fall in the separate category of
tunable, resistorless realizations, the most recent of these
[22,23] enjoys high input and/or low output impedance.
A recent published all-pass filter circuit in [24] employ
two DVCCs and two passive components with the ad-
vantage of high input impedance and low output imped-
ance, which is ideal for cascading, but it still suffer from
floating resistor. But a careful survey reveals that none of
the reported works realizes a VM-APS using single ac-
tive element, grounded passive components, and also
providing high input impedance and low output imped-
ance features simultaneously.
This paper proposes four new first order VM cascad-
able all-pass sections, with high input and low output
impedance using single active element and three grounded
passive components, which are ideal for IC implementa-
tion. Each circuit employs two grounded resistors and
one grounded capacitor. The proposed circuits are based
on fully differential second generation current conveyor
(FDCCII), an active element to improve the dynamic
range in mixed mode application, where fully differential
signal processing is required [25]. As an application, the
J. MOHAN ET AL.
Copyright © 2010 SciRes. CS
6
proposed circuit realizes a multiphase oscillator. PSPICE
simulation results using TSMC 0.35 μm CMOS parameters
are given to validate the circuits.
The paper is organized as follows: in Section 2, the pro-
posed all-pass filters using FDCCII are presented. In
Section 3, parasitic and non-ideal analyses of the pro-
posed circuits are given. In Section 4, to verify the theo-
retical study the first order all-pass filters were con-
structed and simulated with PSPICE program. In Section
5, a multi- phase oscillator is implemented to show the
usefulness of the proposed circuits as an illustrating ex-
ample and finally the conclusion in Section 6.
2. Proposed Circuit
The FDCCII is an eight terminal analog building block
with a describing matrix equation of the form [25]
11
22
33
44
+
-
00 000000
00 000000
00 000000
00 000000
1 1100000
1 1010000
00 001000
00 000100
 

 

 

 

 

 

 

 

 

 

 

 


 
YY
YY
YY
YY
XX+
XX-
Z
+Z+
Z
-Z-
IV
IV
IV
IV
VI
VI
IV
IV
(1)
The symbol and CMOS implementation of FDCCII
are shown in Figure 1 [25]. The Y1, Y2, Y3, and Y4 termi-
nals are high-impedance terminals, while X+ and X– ter-
minals are low-impedance ones. The Z+ and Z– terminals
are high impedance nodes suitable for current outputs.
FDCCII is a useful and versatile active element for ana-
log signal processing. The applications of FDCCIIs in
filters and oscillators design using only grounded passive
components were demonstrated in [26,27].
The voltage transfer function of an all-pass filter can
be given as
1
=1
OUT
IN
Vsτ-
K
Vsτ- (2)
where K is the gain constant and its sign determines whe-
ther phase shifting is from 0° to –180° or from 180° to 0°,
and τ is the time constant. The four proposed first order
VM cascadable all-pass sections using a single FDCCII
and three grounded passive components are shown in
Figures 2(a)-2(d). The four circuits in Figures 2 (a)-2(d)
are characterized by the voltage transfer function as
12 1
11
(1/)[(1/) (1/)]
=+(1/ )




OUT
IN
VsCR R
K
VsRC
(3)
For R2 = R1/2 Equation (3) becomes
11
11
-1
=+1
OUT
IN
VsR C
K
VsRC
(4)
where the value of K = +1 for Circuit-I and Circuit-II
(Figures 2(a) and 2(b)) and the value of K = –1 for Cir-
cuit-III and Circuit-IV (Figures 2 (c) and 2(d)).
I
Y
1
I
Y2
I
Y3
I
Y
4
I
X+
I
X-
Y
1
Y
2
Y
3
Y
4
I
Z+
I
Z-
X
+X-
Z
-
Z
+
FDC CІІ
(a)
V
DD
V
SS
M25
M26
M24
I
SB
M13
I
B
M14
M15
M16
M17
I
Z+
Z
+
I
X+
M18
M19
M20
M21
M22
M23
+
V
bp
V
bn
M3 M4
M10 M11
M1 M2Y
3
Y
1
M5 M6
Y
2
Y
4
M12
M7 M8 M9
a b
M28
M27
M29
M30
M31
M32
V
bp
V
bn
I
Z-
-
Z
-
I
X-
M33
M34
M35
M36
(b)
Figure 1. Fully differential second generation current conveyor (a) symbol (b) CMOS implementation [25].
J. MOHAN ET AL. 7
Copyright © 2010 SciRes. CS
V
IN
Y
1
Y
2
Y
3
Y
4
X
+
X-
Z
-
Z
+
FDC CІІ
V
OUT
R
1
R
2
C
1
V
IN
Y
1
Y
2
Y
3
Y
4
X
+
X-
Z
-
Z
+
FDC CІІ
V
OUT
R
1
R
2
C
1
(a) (b)
V
IN
Y
1
Y
2
Y
3
Y
4
X
+X-
Z
-
Z
+
FDC CІІ
V
OUT
R
1
R
2
C
1
V
IN
Y
1
Y
2
Y
3
Y
4
X
+
X-
Z
-
Z
+
FDC CІІ
V
OUT
R
1
R
2
C
1
(c) (d)
Figure 2. Proposed first order cascadable all-pass filters (a) circuit-I; (b) circuit-II; (c) circuit-III and (d) circuit-IV.
The salient features of the four proposed circuits are
high input and low output impedance, single active ele-
ment and use of grounded passive components; the three
features are not exhibited together in any of the available
works, including the most recent circuits [4-24]. It may
be noted that the new circuits are based on a topology
with input at Y and output at one of the X terminals, the
other X-terminal being terminated by a resistor. The four
proposed circuits with similar properties being derivable
from a topology are a result of the versatility of FDCCII.
It is also worth mentioning that four additional new
circuits can further be obtained from the proposed cir-
cuits by replacing the resistor (R2) with a capacitor (C2).
However these circuits would employ a capacitor at X
terminal, thus degrading high frequency operation. This
aspect will not be further elaborated for brevity reasons.
3. Parasitic and Non-Ideal Analysis
3.1. Parasitic Effects
A study is next carried out on the effects of various para-
sitic of the FDCCII used in the proposed circuits. These
are port Z parasitic in form of RZ//CZ, port Y parasitic in
form of RY//CY and port X parasitic in form of series re-
sistance RX [13]. The proposed circuits are reanalyzed
taking into account the above parasitic effects. The volt-
age transfer function (assuming R << RY or RZ and RX <<
R), for the circuits of Figures 2(a)-2(d), is given as
11
11
(1/ ())[(1/')(1/)]
=+(1/ ())

 


OUT P
IN P
VsCCR R
K
VsRCC
(5)
where, R = R2 + RX, (for Figures 2(a)-2(d)), K = +1, (for
Figures 2(a) and 2(b)), K = –1, (for Figures 2(c) and
2(d)), and CP = CZ+ + CY4 (for Figures 2(a) and 2(c)),
and CP = CZ- + CY3 (for Figures 2(b) and 2(d)).
From (5), it is seen that the gain is unity and the
pole-frequency is
11
1
)
(+
o
P
ωRCC (6)
From (5), the parasitic resistance/capacitances merge
with the external value. Such a merger does cause slight
deviation in circuit’s parameters, which can be elimi-
nated by pre-distorting the element values to be used
in the circuit. It is seen that the pole-frequency would
be slightly deviated (in deficit) due to these parasitics.
The deviation is expected to be small for an integrated
FDCCII; the actual value would be given in the ‘simula-
tion results’.
3.2. Non-Ideal Analysis
Taking the non-idealities of the FDCCII into account, the
relationship of the terminal voltages and currents can be
rewritten as
11
22
33
44
123
45 6
1
2
00000000
00000000
00000000
00000000
00000
00000
0000 000
0000000
 
 
 
 
 
 
 
 
 
 
 
 
 
YY
YY
YY
YY
X+ X+
X- X-
Z
+Z+
Z
-Z-
IV
IV
IV
IV
VI
VI
IV
IV

 
(7)
where αi (i = 1, 2) accounts for current transfer gains and
βi (i = 1, 2, 3, 4, 5, 6) accounts for voltage transfer gains
of the FDCCII. These transfer gains differ from unity by
the voltage and current tracking errors of the FDCCII.
More specifically, αi = 1 δi, (|δi| << 1) δ1 is the current
tracking error from X+ to Z+ and δ2 is the current track-
ing error from X– to Z–. Similarly, βi = 1 – εi, (|εi| << 1)
where, voltage tracking errors are ε1 (from Y1 to X+), ε2
(from Y2 to X+), ε3 (from Y3 to X+), ε4 (from Y1 to X–), ε5
(from Y2 to X–), and ε6 (from Y4 to X–). The circuits of
Figures 2(a)-2(d) are reanalyzed using (7) and the
non-ideal voltage transfer functions are found as
Circuit-I:
1261 525112
5
11
[() /]
(1 /)




OUT
IN
Vs RRCRR
VsCR
 
(8)
Circuit-II:
J. MOHAN ET AL.
Copyright © 2010 SciRes. CS
8
2341121112
1
11
[() /]
(1 /)




OUT
IN
Vs RRCRR
VsCR
 
(9)
Circuit-III:
11614 24112
4
11
[() /]
(1 /)


 

OUT
IN
VsRRCRR
VsCR
 
(10)
Circuit-IV:
2351 222112
2
11
[() /]
(1 /)


 

OUT
IN
VsRRCRR
VsCR
 
(11)
From (8)-(11), it is seen that the pole-frequency is un-
altered by FDCCII non-idealities for all the transfer func-
tions of the respective circuit, but the filters gain are
slightly modified due to the FDCCII non-idealities. Thus
the pole-frequency sensitivity to the FDCCII nonideali-
ties is zero, and the filters gain sensitivity to these non-
idealities is found within unity in magnitude. This sug-
gests a good sensitivity performance for the proposed
circuits.
4. Simulation Results
To verify theoretical result the proposed filter circuits
were simulated by the PSPICE simulation program. The
FDCCII was realized based on the CMOS implementa-
tion as shown in Figure 1 [25] and simulated using
TSMC 0.35 μm, level 3 MOSFET parameters as listed in
Table 1. The aspect ratio of the MOS transistors are listed
in Table 2, with the following DC biasing levels Vdd =
Vss = 3.3 V, Vbp = Vbn = 0 V, and IB = ISB = 1.7 mA. The
circuit-I (Figure 2(a)) was designed with C1 = 50 pF,
Table 1. 0.35 μm level 3 MOSFET parameters.
NMOS:
LEVEL = 3 TOX = 7.9E – 9 NSUB = 1E17
GAMMA = 0.5827871 PHI = 0.7 VTO = 0.5445549 DELTA = 0
UO = 436.256147 ETA = 0 THETA = 0.1749684
KP = 2.055786E – 4 VMAX = 8.309444E4 KAPPA=0.2574081
RSH = 0.0559398 NFS = 1E12 TPG = 1 XJ = 3E – 7
LD = 3.162278E – 11 WD = 7.04672E – 8 CGDO = 2.82E – 10
CGSO = 2.82E – 10 CGBO = 1E – 10 CJ = 1E – 3 PB = 0.9758533
MJ = 0.3448504 CJSW = 3.777852E – 10 MJSW = 0.3508721
PMOS:
LEVEL = 3 TOX = 7.9E – 9 NSUB = 1E17
GAMMA = 0.4083894 PHI = 0.7 VTO = –0.7140674
DELTA = 0 UO = 212.2319801 ETA = 9.999762E – 4
THETA = 0.2020774 KP = 6.733755E – 5 VMAX = 1.181551E5
KAPPA = 1.5 RSH = 30.0712458 NFS = 1E12 TPG = –1
XJ = 2E – 7 LD = 5.000001E – 13 WD = 1.249872E – 7
CGDO = 3.09E – 10 CGSO = 3.09E – 10 CGBO = 1E – 10
CJ = 1.419508E – 3 PB = 0.8152753 MJ = 0.5
CJSW = 4.813504E – 10 MJSW = 0.5
R1 = 2 k and R2 = 1 k. The theoretical designed pole
frequency was 1.59 MHz. The phase and gain plots are
shown in Figure 3. The phase is found to vary with fre-
quency from 180° to 0° with a value of 90° at the pole fre-
quency, and the pole frequency was found to be 1.54 MHz,
which is close to the theoretical value. The circuit was
next used as a phase shifter introducing 90° shift to a
sinusoidal voltage input of 1 Volt peak at 1.59 MHz. The
input and output waveforms are given in Figure 4 which
verify the circuit as a phase shifter. The THD variation at
the output for varying signal amplitude at 1.59 MHz was
also studied and the results shown in Figure 5. The THD
for a wide signal amplitude (few mV-1V) variation is
found within 4.27% at 1.59 MHz. The Fourier spectrum
of the output signal, showing a high selectivity for the
applied signal frequency (1.59 MHz) is also shown in
Figure 6. Both theoretical and simulated pole frequen-
cies are found to closely match; the discrepancy (deficit)
in simulated frequency being the result of various para-
sitic discussed in Section 3.
Table 2. Transistor aspect ratios for the circuit shown in
Figure 1.
Transistors W(µm)L(µm)
M1-M6 60 4.8
M7-M9, M13 480 4.8
M10-M12, M24 120 4.8
M14,M15,M18,M19,M25,M29,M30,M33,M34 240 2.4
M16,M17,M20,M21,M26,M31,M32,M35,M36 60 2.4
M22,M23,M27,M28 4.8 4.8
1
Phase (degree)
150d
100d
50d
0d
Frequency
10KHz 100KHz 1.0MHz 10MHz 100MHz
Gain (dB)
2
40
20
0
-20
-40
SEL>>
Figure 3. Gain and phase responses for the circuit-I.
Time
0s 0.5us 1.0us 1.5us 2.0us 2.5us
Amplitude
Output
2.0v
0v
-2.0v
SEL >>
Input
Figure 4. Input/output waveshapes for Circuit-I at 1.59 MHz.
J. MOHAN ET AL.
Copyright © 2010 SciRes. CS
9
VIN (mV)
0.1 1 10 100
1000
THD (%)
6
4
2
0
Figure 5. THD variation at output with signal amplitude at
1.59 MHz.
Frequency
0Hz 4MHz 8MHz 12MHz
1.0
v
0
v
0.5v
SEL>>
V
(
1
)
V
(
4
)
Figure 6. Fourier spectrum of Input-output signal at 1.59 MHz.
Similarly, the circuit-III (Figure 2(c)) was designed
with the same values and frequency as above. The phase
and gain plots are shown in Figure 7. The phase is found
to vary with frequency from 0 to –180° with a value of
–90° at the pole frequency, and the pole frequency was
found to be 1.54 MHz, which is close to the theoretical
value. The circuit was next used as a phase shifter intro-
ducing –90° shift to a sinusoidal voltage input of 1 Volt
peak at 1.59 MHz. The input and output waveforms
are given in Figure 8 which verify the circuit as a phase
shifter.
5. Application Example
To further illustrate the utility of the proposed circuits a
sinusoidal oscillator producing a number of quadrature
signals was realized using the Circuit-I (Figure 2(a)). By
connecting Y2 terminal, the input node to the Z-terminal
of FDCCII, connecting resistor (R) and capacitor (C) at
X– and Z– terminals of FDCCII. The resulting circuit is
shown in Figure 9. The circuit analysis yields the fol-
lowing characteristic equation
1
Phase (degree)
0d
-50d
-100d
-180d
Frequency
10KHz 100KHz 1.0MHz 10MHz 100MHz
Gain (dB)
2
40
20
0
-20
-40
SEL>>
Figure 7. Gain and phase responses for the circuit-III.
Time
0.5us
1.0us
1.5us
2.0us 2.5us
3.0us
Amplitude
Output
2.0v
0
v
-2.0v
SE L>>
Input
Figure 8. Input/output waveshapes for Circuit-III at 1.59 MHz.
V
OUT1
R
1
R
2
C
1
V
OUT2
R
V
OUT3
C
Y
1
Y
2
Y
3
Y
4
Z
+
Z
-
X
+
X
-
FDC C ІІ
Figure 9. Multiphase oscillator using Circuit-I of Figure 2(a).
212
111 12
11 0
''' '

 


RR
ss
CRC RCC RRR (12)
At the frequency of oscillation, with s = jω, the Equa-
tion (5) gives the frequency of oscillation (FO) and con-
dition of oscillation (CO) as
12
112
:''
O
RR
FO ωCCRR R; CO: CR C1R1 (13)
Assuming R = R1 = 2R2; C = C1
J. MOHAN ET AL.
Copyright © 2010 SciRes. CS
10
1
:2''
O
FO ωCR (14)
From Figure 9, at oscillating frequency the circuit pro-
vides three quadrature voltage outputs (VOUT1, VOUT2 and
VOUT3) whose phasor relationship is shown in Figure 10.
The circuit was designed with C1 = C = 50 pF, R1 = R
= 2 k, and R2 = 1 k, the theoretical frequency of os-
cillation was around fo = 1.59 MHz, whereas the simu-
lated values as found from the result was fo = 1.54 MHz.
The quadrature oscillations are shown in Figure 11.
6. Conclusions
This paper has presented four new first-order VM casca-
dable all-pass sections, each employing single FDCCII,
two resistors and one capacitor. The salient features of all
the proposed circuits are high input and low output im-
pedance, single active element and use of grounded pa-
ssive components. The proposed circuits with grounded
components in each case are suited for IC implementa-
tion in CMOS technology. Non-ideality aspects and par-
asitic effects are also studied. The circuits are verified th-
rough PSPICE simulations using TSMC 0.35 µm CMOS
parameters. Application example in the form of multi-
phase oscillator is also given and also verified with good
results. The proposed circuits are ideal for voltage-mode
applications as well as good for IC implementation, mak-
ing them a future prospect for integration.
VOUT1
VOUT2
VOUT3
Figure 10. Phasor diagram of multiphase oscillator.
Time
0s 0.5us 1.0us 1.5us 2.0us 2.5us
Amplitude
V
OUT1
1.0v
0v
SEL>>
V
OUT2
V
OUT3
-1.0v
Figure 11. Quadrature voltage outputs of multiphase oscil-
lator.
7. Acknowledgements
The authors would like to thank the anonymous review-
ers for their valuable comments.
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