Comment on “ Voltage-Mode All-Pass Filters IncludingMinimum Component Count Circuits ”

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.

One such recently proposed work in creating voltagemode (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.

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.

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

CDBA-Based VM-APF-Figure 1(a).
The CDBA-based VM-APF is shown in Figure 1(a) and it requires the use of matched resistors.Since V n = 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 Using ( 1) and doing routine circuit analysis, the voltage transfer function of circuit in Figure 1(a) is given as 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 which is not required in cases where a suitable signal amplitude gain is desired.

CDBA-Based Transimpedance (TI) APF-Figure 1(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 transimpedance (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 The circuit not only uses a grounded capacitor, but also does not require any component matching condition.

Nonideal Case.
In the nonideal case, considering α p and α n 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: Using ( 4), the transfer function of Figures 1(a) and 1(b) gets modified to 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 R z and parasitic capacitance C z appearing at high-impedance z terminal.Considering the effect of these nonidealities, ( 5) and ( 6) get modified to 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 R z )C z and the pole limits the high-frequency performance/potential of the circuit.Since R z value is in the order of MΩ and hence when a resistor of value R Rz is connected at this terminal, R z R ≈ R .Therefore, the working frequency range for the APF operation is restricted to ω < 1/R C z .

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 R p = V T /2I B1 and R n = V T /2I B2 , respectively.
The DCC-CDBA equivalents derived from the CDBAbased circuits of Figure 1 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 R p = 2R n , that is, adjusting the bias currents such that I B2 = 2I B1 .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 I B2 I B1 .The angular pole frequency for the VM APF shown in Figure 3(a) is ω 0 = 1/R n C and is tunable by means of the bias current I B2 , but I B1 has to be simultaneously adjusted to meet the required matching condition for the APF operationa 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 I B1 .

Concluding Remarks
The recently proposed CDBA-based first-order voltagemode 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.