Realization of Filter/Inverse Filter Topologies using single FTFNTA

In this manuscript, two different topologies are presented for the realization of a conventional filter/inverse filter using the Four Terminal Floating Nullor Transconductance Amplifier (FTFNTA). The first topology can synthesize the inverse low-pass (ILP), inverse high-pass (IHP), and inverse band-pass (IBP) filter with applicable impedance choices. Subsequently, another topology that can synthesize conventional low-pass (LP), and band-pass (BP) active filter, as well as inverse high-pass (IHP), and inverse band-pass (IBP) filter from the same circuit topology with a viable solution of impedances as resistor/capacitor. To verify the workability of both topologies, SPICE simulation is performed using 180nm CMOS TSMC technology.


Introduction
Inverse filter is a key element in some applications like communication [1], audio signal processing [2,3], and instrumentation [4].Sometimes in these applications signals get distorted during processing and transmission.To overcome these distortions and to reconstruct the desired signal inverse filters are used.However, the device transfer function characteristic that causes the distortion should be known in advance and the inverse of this transfer characteristic will give an idea of the required inverse filter transfer function.
In the literature, different active building blocks (ABBs) and their variants are used to design the active inverse filter functions .The comprehensive literature analysis is performed and illustrated on the basis of, the number of active and passive components used, mode of operation, the requirement of change in topology, capability to realize the conventional active filter using the same topology and tunability.
Literature review of these active inverse filters shows that the only [8,17] are the universal inverse filter.Among these two, the [8] is a current mode (CM) universal inverse filter designed using a single Four Terminal Floating Nullor (FTFN).But a separate topology was used for designing of each filter function.While [17] is a voltage mode (VM) universal inverse filter which requires two Current Differenced Buffered Amplifier (CDBA) ABBs.References [10,11] can realize single order inverse all-pass filter (IAPF) using single ABBs i.e.CCII (Current Conveyor II) and CDTA (Current-Differencing Transconductance Amplifier) respectively.Also [5][6][7]20] were limited to implement a single inverse filter function.For this [20] required three (CDTA) while [5][6][7] required only one (FTFN).In [26] two (CDBAs) and in [27] two Operational Trans-Resistance Amplifier (OTRAs) were used to design inverse band-reject filter (IBRF) and IAPF but the passive components count is large for both topologies.Even some of the existing topologies require more than two ABBs [9,[12][13][14][15][16] to construct the inverse filter functions.As more ABBs have been used, the larger chip area would be required for fabrication.Inverse low-pass (ILPF), inverse high-pass (IHPF), and inverse band-pass (IBPF) filter function were implemented by [13,15,16] while topologies of [9,12,14] provide an additional filter function of IBRF.
In [21], a CM & VM resistor less inverse filter topologies that realizes ILPF, IHPF, and IBP filter using OTAs.The number of OTAs used in this is very large which is not suitable for the fabrication process.There is another resistor less inverse filter is present in the literature [25].It required two to four Voltage Differencing Transconductance Amplifier (VDTA) and two capacitors for the realization of ILPF, IHPF, IBPF, & IBRF filter functions.Also, there are some topologies present in literature [18,19,[22][23][24][25] to implement an inverse filter using two ABBs.Inverse filter functions of ILPF, IHPF, and IBPF were implemented by [18,[22][23][24], while topologies of [19,25] provide an additional filter function of IBRF.The topologies present in [9,14,16,21,24,25] possess electronic tunability.For better-integrated circuit design, the circuit must have a fixed topology [5-7, 10-12, 16-18, 20, 22, 24-28] to implement the different inverse filter functions.In [28], the authors gave a fascinating idea of designing of the inverse filter along with the active filter realization using the same topology.In this, two CDBA ABBs along with three resistors and two capacitors are used to design active filter low-pass filter (LPF), high-pass (HPF), band-pass filter (BPF) responses and inverse active ILPF, IHPF, and IBPF filter responses.A detailed analysis of literature reveals the following: • Some topologies are resistor-less [21,25] • The filter parameters are electronically tunable [9,14,16,21,24,25] • [5-7, 10, 11, 14, 20] provides single response at a time while [8, 9, 13-15, 19, 21, 23] provide multiple responses by altering the topology • [17,25] provides universal inverse filter without altering the topology So it is concluded from the literature survey, as detailed above, that no universal inverse filters have been proposed using the FTFNTA as an active element and there is only one topology was proposed for designing of both filter and inverse filter using the same circuit so far.Therefore, the main objective of the manuscript is to propose a set of topologies which can produce a universal inverse filter i.e.ILPF, IHPF, and IBPF filters from the same configuration and an extension of this work is to produce both second-order active filter and inverse filter using the same configuration which produces LPF, BPF, IHPF, and IBPF responses.To achieve this proposed design require only one active building block and all grounded passive components.However it is not able to realize all the filtering transfer functions but it provides both active filter and inverse filter responses without altering the topology.Therefore, the proposed topology would give a compact realization.

Theoretical Analysis of Proposed Circuits
The schematic of an FTFNTA is illustrated in Fig. 1 and its characteristic equation is stated in Eq. (1).0 0 0 0 0 0 00 00 00 00 Where g m is the transconductance, α is the voltage transfer gain, β is the current transfer gain and γ is the transconductance transfer accuracy.Ideally, the value of α, β and γ is unity.These α, β and γ are accountable for the non-ideality of FTFNTA.

Proposed First Topology
The proposed topologies are shown in Fig. 2 and Fig. 3.Both topologies are explained in this section one by one.

Fig. 2 First topology of proposed inverse filter
Fig. 3 Second topology of proposed filter/inverse filter By considering the proposed topology of Fig. 2 for designing of ILPF, IHPF, and IBPF using single FTFNTA.By applying the nodal analysis in Fig. 2, the generalized transfer function (TF) is obtained as: With the appropriate selection of admittance parameters Y 1 -Y 5 in Eq. ( 2), different inverse filter functions can be received across the output node (V out ), as given in Table 1.

Sensitivity Analysis of First Topology
The active and passive sensitivities of ω 0 and Q 0 for the designed inverse filter, mentioned in Table 1, can also be derived as follow: For ILPF ( ) ( ) For IHPF 1, Table 1 The functionality of the proposed inverse filter of Fig. 2 Admittance parameters Type of filter Inverse filter transfer function, angular frequency and quality factor 13 13 11 , YY RR ; ; ; For IBRF (case-I) 1, It is clear from Eqs. ( 3) -( 8) that all the sensitivity values are lying in the specified range from -1 to 1.

Proposed Second Topology
Another circuit for designing of the inverse filter along with a normal active filter is shown in Fig. 3.This topology will produce the transfer function of inverse filter i.e.IHPF and IBPF as well as active filter function of LPF and BPF.A detailed analysis of these designed filters is given in Table 2.By applying the nodal analysis in Fig. 3, the generalized transfer function (TF) is obtained as:

Sensitivity Analysis of Second Topology
Sensitivity analysis of the proposed circuits as mentioned in Table 2 is also derived as follows: For active LPF 0000 For active BPF 0000 For IHPF 0000 For IBRF 0000 So the sensitivity values of designed topology are lying in the specified range from -1 to 1, as evaluated in Eqs. ( 10)- (17).
Table 2 The functionality of the proposed inverse filter of Fig. 3 Sr.no.Impedance parameters Type of filter Conventional filter/inverse filter transfer function, angular frequency and quality factor ZR sC

Smulation Results
To confirm the operability of the designed filter/ inverse filter configurations, SPICE simulations are performed by 0.18µm CMOS technology.CMOS structure of the FTFNTA and aspect ratio of transistors used in it are taken from [29,30] to build the FTFNTA device.The time domain analysis of the proposed IBPF filter for the sinusoidal input current of 2 mA peak-to-peak and 1.59 MHz frequency, leads to a 1.59 MHz sinusoidal output current with a phase shift of 90° and DC component 0.217 mA, as shown in Fig 8 .Further, some other important properties like the total harmonic distortion (THD) and input-output noise, for IBPF filter, is also evaluated.The change in THD with peak sinusoidal input current of 157.28 kHz frequency is illustrated in Fig. 9 where a load resistor of 1 kΩ is connected.The minimum value of THD is 3.073%.The dynamic range of IBPF lies between 0.1 mA to 16 mA (peak amplitude) without significant noise disturbance and non-linear distortion (for less than 4% THD value).Also, the input and related output noise is illustrated in Fig. 10.

Comparison
A correlation of the proposed topologies with known topologies is illustrated in Table 3.By observing the comparison table it is concluded that the proposed design is better than the existing topologies.The proposed design is able to generate both filter and inverse filter functions using a single active building block i.e.FTFNTA without altering the configuration of topology.Only 28 has such capability but it requires two CDBAs as an ABB and slightly more passive component comparatively.Also, some of the existing structures provide IBRF and/or IAPF functions which are not provided by the proposed design.But these topologies require either a more number of active and/or passive components or a change is required in structure to obtain these additional responses.Electronic tunability is the area in which the proposed topology is lacking.

Conclusion
In this manuscript two different topologies are presented for designing of the inverse filter in addition to conventional filters with the help of one FTFNTA and five passive components.Designed filter/ inverse filter functions have low sensitivities.PSPICE simulation validates the results of the proposed design.

Declarations
Funding: Not applicable Conflicts of interest/Competing interests: The authors have no conflicts of interest to declare that are relevant to the content of this article.

Fig. 4 Fig. 5 Fig. 6
Fig. 6 illustrates the frequency response of the IHPF and IBPF.The designed inverse filters using second topology have an operating frequency of 1.7 MHz and 1.85 MHz respectively.

Fig. 10
Fig. 10 Input and related output noise versus frequency

Table 3
Comparison with the existing topologies of inverse filter