# Comment on “Voltage-Mode All-Pass Filters Including Minimum Component Count Circuits”

Authors: Abhirup Lahiri
Journal: Active and Passive Electronic Components
 (2009)

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## Abstract

This comment is related to the recently published article
“Active and Passive Electronic Components” by S. Maheshwari
(2007), which presents single current differencing buffered
amplifier (CDBA) and current-controlled current differencing
buffered amplifier- (CC-CDBA-) based first-order voltage-mode
(VM) all-pass filtering (APF) sections. The paper is reviewed,
and additional first-order APF realizations have been proposed.


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## Body

## 1. Introduction

First-order
all-pass filters (APFs) are very important circuits for many analog signal
processing applications and are generally used in phase equalization and for
introducing a frequency-dependent delay while keeping the amplitude of the
input signal constant over the desired frequency range. The design of both
voltage-mode (VM) and current-mode (CM) APFs using active building blocks
(ABBs) has been researched extensively and numerous
circuits have been reported in the literature [1–15].One such recently proposed work in creating
voltage-mode (VM) APFs has been reviewed here. The work [16] presents APFs
based on a recently proposed ABB, namely, the current differencing buffered
amplifier (CDBA). The author had argued that the paper then was a first attempt
at creating VM APFs using CDBA or variant. Although a total of four circuits
had been exemplified in the paper [16], these examples do not exhaust the other
possible realizations of VM APFs using a single CDBA and reduced number of
passive components. This letter presents additional possibilities of such
realizations.


## 2. Discussion

A total of four
VM APFs had been proposed in [16], but all of them made use of floating
capacitors. Grounded capacitor realizations are fit for monolithic integration,
since grounded capacitor circuits can compensate for the stray capacitances at
their nodes [17, 18]. Hence, a possible drawback for all the circuits in [16]
is that they may not be suitable for monolithic integration. Another drawback
of the single CDBA-based APFs (in general) is the critical requirement of
resistor matching, for an example, the requirement of R′=R/2 for the first
circuit [16, Figure 2(a)] and R′=R for the second
circuit [16, Figure 2(b)]. Any mismatch would deteriorate the circuit operation
as APF. Even for the equivalent CC-CDBA-based circuits in [16], the parasitic
resistances at terminals p and n have to be
tuned by means of the bias current to meet the matching condition. Any desired
change in the pole frequency of CC-CDBA-based APFs by means of the bias current
could not be achieved independently, since the matching condition was needed to
be satisfied simultaneously for the APF operation. In this case, the CC-CDBA
circuits reduced the number of passive components, but the feature of current
tunability was not noninteractive. An advantage worth mentioning is the low
output impedance exhibited by the circuits, which made the circuits suitable to
be cascaded to produce higher-order filters. In the subsequent section,
additional realizations of single CDBA-based APFs have been proposed.


## 3. Additional Realizations

Without going
into the construction/schematic details of CDBA (which could be found in
[16, 19]), the circuits are directly reported.


### 3.1. CDBA-Based VM-APF—Figure1(a)

The CDBA-based
VM-APF is shown in Figure1(a) and it requires the use of matched resistors.
Since Vn=0, the capacitor is grounded (in the ideal case), a
feature which is absent in all the circuits in [16]. In the ideal case, CDBA is
characterized by(1)Vp=Vn=0,Iz=Ip−In,Vw=Vz.Using (1) and doing routine
circuit analysis, the voltage transfer function of circuit in Figure 1(a) is
given as(2)VoVin=R′(1−sCR)2R(1+sCR).
This circuit was initially proposed in [20] and it serves to counter the statement by Maheshwari in [16] that ”The CDBA has so far not been attempted for realizing voltage mode
first-order all-pass filters in open literature”. But in [20],the authors chose R′=2R for a unity gain, which is not required in cases where a suitable signal amplitude gain is desired.The proposed CDBA-based APFs: (a) VM APF (b) TI APF.
(a)(b)


### 3.2. CDBA-Based Transimpedance (TI) APF—Figure1(b)

A mixed-mode
filter having current-input and voltage output is useful as an interface
circuit connecting a CM circuit to the VM circuit. Since, the outputs of the
many digital/analog converters (DACs) are available as current signals, the
trans-impedance (TI) mode filters could be used for both filtering and
conversion operations [21, 22]. One such TI APF using a single ABB is proposed here
and is shown in Figure 1(b). The transfer function of the circuit is given as(3)VoIin=R′(1−sCR)1+sCR.The circuit not only uses a
grounded capacitor, but also does not require any component matching condition.


### 3.3. Nonideal Case

In the nonideal
case, consideringαp and αn as the current
transfer gains from p and n terminals to z terminal,
respectively, and β is the voltage
transfer gain from z to w terminal, the
characterizing equation of the CDBA is given as:(4)Vp=Vn=0,Iz=αpIp−αnIn,Vw=βVz.Using (4), the transfer function
of Figures 1(a) and 1(b) gets modified to(5)VoVin=βR′(αp+(αp−2αn)sCR)2R(1+sCR),(6)VoIin=βR′(αp−αnsCR)1+sCR,respectively. These effects
could be alleviated with a better design of CDBA, such that the values of
voltage/current transfer gains are close to unity.A nonideal effect, previously not considered in [16],
is the parasitic resistance Rz and parasitic
capacitance Cz appearing at
high-impedance z terminal.
Considering the effect of these nonidealities, (5) and (6) get modified to(7)VoVin=β(R′∥Rz)[αp+(αp−2αn)sCR]2R(1+sCR)[1+sCz(R′∥Rz)],(8)VoIin=β(R′∥Rz)(αp−αnsCR)(1+sCR)[1+sCz(R′∥Rz)],respectively.It is evident from (7) and (8), that there is a
first-order low-pass roll-off with a cut-off frequency of 1/(R′∥Rz)Cz and the pole
limits the high-frequency performance/potential of the circuit. Since Rz value is in the
order of MΩ and hence when
a resistor of value R′≪Rz is connected at
this terminal, Rz∥R′≈R′. Therefore, the working frequency range for the APF
operation is restricted to ω<1/R′Cz.


### 3.4. Equivalent APFs with Canonic Component Count

An evident
drawback is that unlike the circuits of [16], the proposed circuits here are
not directly compatible with CC-CDBA, that is, equivalent CC-CDBA circuits
cannot be directly realized from the CDBA counterparts. However, it could be
accomplished by using a modified CC-CDBA with dual bias currents, namely, the
dual-current-controlled CDBA (DCC-CDBA). A simple construction of this novel
ABB using two second-generation current-controlled conveyors (CCCII) [23] and
one unity gain voltage follower (buffer) is shown in Figure 2. The parasitic
resistances at the terminals p and n could be
expressed as Rp=VT/2IB1 and Rn=VT/2IB2, respectively.Figure 2
Implementation of
DCC-CDBA using CCCII.The DCC-CDBA equivalents derived from the CDBA-based
circuits of Figure1 have been shown in Figure 3. The circuits use minimum
number of active and passive components and hence present a low-cost solution.
For the DCC-CDBA-based VM-APF shown in Figure 3(a), the matching condition
required for the APF operation could be achieved by making Rp=2Rn, that is, adjusting the bias currents such that IB2=2IB1. For DCC-CDBA-based TI APF shown in Figure 3(b), the
required adjustment of the bias currents for the APF operation should be such
that IB2≫IB1. The angular pole frequency for the VM APF shown in
Figure 3(a) is ω0=1/RnC and is tunable
by means of the bias current IB2, but IB1 has to be
simultaneously adjusted to meet the required matching condition for the APF
operation—a drawback which is also present in the CC-CDBA APFs of [16].
Similarly, the pole frequency of TI APF shown in Figure 3(b) could be tuned by
bias current IB1.The proposed DCC-CDBA APFs: (a) VM APF (b) TI APF.
(a)(b)


## 3.1. CDBA-Based VM-APF—Figure1(a)

The CDBA-based
VM-APF is shown in Figure1(a) and it requires the use of matched resistors.
Since Vn=0, the capacitor is grounded (in the ideal case), a
feature which is absent in all the circuits in [16]. In the ideal case, CDBA is
characterized by(1)Vp=Vn=0,Iz=Ip−In,Vw=Vz.Using (1) and doing routine
circuit analysis, the voltage transfer function of circuit in Figure 1(a) is
given as(2)VoVin=R′(1−sCR)2R(1+sCR).
This circuit was initially proposed in [20] and it serves to counter the statement by Maheshwari in [16] that ”The CDBA has so far not been attempted for realizing voltage mode
first-order all-pass filters in open literature”. But in [20],the authors chose R′=2R for a unity gain, which is not required in cases where a suitable signal amplitude gain is desired.The proposed CDBA-based APFs: (a) VM APF (b) TI APF.
(a)(b)


## 3.2. CDBA-Based Transimpedance (TI) APF—Figure1(b)

A mixed-mode
filter having current-input and voltage output is useful as an interface
circuit connecting a CM circuit to the VM circuit. Since, the outputs of the
many digital/analog converters (DACs) are available as current signals, the
trans-impedance (TI) mode filters could be used for both filtering and
conversion operations [21, 22]. One such TI APF using a single ABB is proposed here
and is shown in Figure 1(b). The transfer function of the circuit is given as(3)VoIin=R′(1−sCR)1+sCR.The circuit not only uses a
grounded capacitor, but also does not require any component matching condition.


## 3.3. Nonideal Case

In the nonideal
case, consideringαp and αn as the current
transfer gains from p and n terminals to z terminal,
respectively, and β is the voltage
transfer gain from z to w terminal, the
characterizing equation of the CDBA is given as:(4)Vp=Vn=0,Iz=αpIp−αnIn,Vw=βVz.Using (4), the transfer function
of Figures 1(a) and 1(b) gets modified to(5)VoVin=βR′(αp+(αp−2αn)sCR)2R(1+sCR),(6)VoIin=βR′(αp−αnsCR)1+sCR,respectively. These effects
could be alleviated with a better design of CDBA, such that the values of
voltage/current transfer gains are close to unity.A nonideal effect, previously not considered in [16],
is the parasitic resistance Rz and parasitic
capacitance Cz appearing at
high-impedance z terminal.
Considering the effect of these nonidealities, (5) and (6) get modified to(7)VoVin=β(R′∥Rz)[αp+(αp−2αn)sCR]2R(1+sCR)[1+sCz(R′∥Rz)],(8)VoIin=β(R′∥Rz)(αp−αnsCR)(1+sCR)[1+sCz(R′∥Rz)],respectively.It is evident from (7) and (8), that there is a
first-order low-pass roll-off with a cut-off frequency of 1/(R′∥Rz)Cz and the pole
limits the high-frequency performance/potential of the circuit. Since Rz value is in the
order of MΩ and hence when
a resistor of value R′≪Rz is connected at
this terminal, Rz∥R′≈R′. Therefore, the working frequency range for the APF
operation is restricted to ω<1/R′Cz.


## 3.4. Equivalent APFs with Canonic Component Count

An evident
drawback is that unlike the circuits of [16], the proposed circuits here are
not directly compatible with CC-CDBA, that is, equivalent CC-CDBA circuits
cannot be directly realized from the CDBA counterparts. However, it could be
accomplished by using a modified CC-CDBA with dual bias currents, namely, the
dual-current-controlled CDBA (DCC-CDBA). A simple construction of this novel
ABB using two second-generation current-controlled conveyors (CCCII) [23] and
one unity gain voltage follower (buffer) is shown in Figure 2. The parasitic
resistances at the terminals p and n could be
expressed as Rp=VT/2IB1 and Rn=VT/2IB2, respectively.Figure 2
Implementation of
DCC-CDBA using CCCII.The DCC-CDBA equivalents derived from the CDBA-based
circuits of Figure1 have been shown in Figure 3. The circuits use minimum
number of active and passive components and hence present a low-cost solution.
For the DCC-CDBA-based VM-APF shown in Figure 3(a), the matching condition
required for the APF operation could be achieved by making Rp=2Rn, that is, adjusting the bias currents such that IB2=2IB1. For DCC-CDBA-based TI APF shown in Figure 3(b), the
required adjustment of the bias currents for the APF operation should be such
that IB2≫IB1. The angular pole frequency for the VM APF shown in
Figure 3(a) is ω0=1/RnC and is tunable
by means of the bias current IB2, but IB1 has to be
simultaneously adjusted to meet the required matching condition for the APF
operation—a drawback which is also present in the CC-CDBA APFs of [16].
Similarly, the pole frequency of TI APF shown in Figure 3(b) could be tuned by
bias current IB1.The proposed DCC-CDBA APFs: (a) VM APF (b) TI APF.
(a)(b)


## 4. Concluding Remarks

The recently
proposed CDBA-based first-order voltage-mode all-pass filters (APFs) have been
reviewed, and additional realizations of APFs with the same component count
have been reported. Novel transimpedance APFs have also been proposed. It is
expected that this paper, in conjunction with the previous work [16], will
prove to be beneficial for analog circuit designers, and the researchers in
this field and that CDBA circuits with more advantageous features would be
reported in the near future.



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*Source: 595324-2009-05-04.xml*