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In this paper, a biquad filter configuration based on two voltage differencing transconductance amplifiers (VDTAs) as newly active elements and only two capacitors as passive elements is proposed which can realize voltage-mode low pass (LP), band pass (BP), high pass (HP), band reject (BR) and all pass (AP) filtering responses using three voltage inputs. Simultaneously, the same configuration can also be used to obtain LP, BP and HP filtering responses in transadmittance-mode. The proposed biquad is capable of providing electronic control of quality factor independent of pole frequency through single transconductance parameter (biasing current). It also offers the advantage of low active and passive sensitivity. To support the theoretical analysis, the PSPICE simulation of the proposed circuit is done using 0.18 μm CMOS technology from TSMC.

In the last few decades, current-mode active elements have been preferred over voltage-mode active elements in the designing of high performance continuous time analog filters [

Literature survey shows that quite a number of VDTA based biquad filter either as single-input multi-output (SIMO) and/or as multi-input single-output (MISO) types have been reported in the available literature till date [

Considering the above facts, a new biquad filter configuration is proposed in this paper. The proposed configuration can realize BP, HP, LP, RN, and AP responses in voltage-mode as three-input single-output structure and LP, BP, HP responses in trans-admittance-mode as single-input three-output structure. The configuration comprises of only two VDTAs, two capacitors as active and passive elements, respectively and does not require 1) external resistor(s), and 2) minus and/or double type voltage input signal(s) to realize any filtering response. Moreover, it has less active and passive sensitivity.

Voltage differencing transconductance amplifiers is relatively new active element [^{+}, X^{−} are the high impedance output terminals. The differential voltage across high impedance input terminals P and N(V_{P} − V_{N}) is transferred to a current at high impedance output terminals Z and Zc (I_{Z} and I_{Zc}) by transconductance parameters ^{+} and

X^{−} (

The CMOS realization of VDTA is also shown in

and

where ^{th} transistor (i = 1, 2, 3, 4, 5, 6, 7, 8). I_{Bi}, W_{i}, L_{i} are the

bias current, effective channel width and length of i^{th} MOS transistor, respectively. μ is the effective carrier mobility and C_{OX} is the gate oxide capacitance per unit area of the MOS transistors.

The proposed biquad filter configuration is shown in _{1}, V_{2} and V_{3}, will give the following expression for the voltage output at

where

Here_{0} through appropriate selection of input voltage signals (V_{1}, V_{2}, and V_{3}).

1) If V_{1} = V_{in} and V_{2} = V_{3} = 0, the filter configuration provides LP response.

2) If V_{2} = V_{in} and V_{1} = V_{3} = 0, the filter configuration provides BP response.

3) If V_{3} = V_{in} and V_{1} = V_{2} = 0, the filter configuration provides HP response.

4) If V_{1} = V_{3} = V_{in}, V_{2} = 0, the filter configuration provides BR response.

5) If V_{in1} = V_{in2} = V_{in3} = V_{in} and

It can be concluded from above operational description that the proposed filter configuration in

In addition to above voltage mode filtering responses, the same configuration can also be used to realize LP, BP, HP transadmittance mode responses across I_{LP}, I_{BP} and I_{HP}, respectively, by applying only one voltage input V_{2} (V_{in}) and remaining voltage inputs set to zero (V_{1} = V_{3} = 0). In this case transadmittance mode transfer function can be derived as

The filter characteristic parameters like pole-frequency (ω_{0}), quality-factor (Q_{0}), and band-width (ω_{0}/Q_{0}) for the proposed filter configuration can be expressed

If

and

It is clear from Equation (10) and Equation (11) that filter parameter Q_{0} can be widely varied electronically by varying _{0}. Similarly, ω_{0} and BW are electronically orthogonal tunable.

For non ideal characteristics of the VDTA, the port relations of currents and voltages in Equation (1) can be changed as follow.

where ^{th} VDTA respectively, where j = 1, 2. If we re-analysed the proposed circuit in _{0}, Q_{0}, and BW are changed to^{ }

The active and passive relative sensitivities of

and

From Equation (15)-(17), it is clear that the proposed circuit possess low active and passive sensitivities, less than or equal to unity in magnitude.

In this section the performance of the proposed biquad filter configuration of _{0} = 1, the active and passive components were selected as

_{0} independent of ω_{0} for the proposed filter by performing the simulation of various voltage-mode BP responses at

different values of _{0} = 3.14, 1.58, 0.909, 0.707 which prove the electronic tunability feature of Q_{0} independent of ω_{0} for the proposed filter. Now, the noise effect for the proposed filter is considered by showing the voltage-mode BP output noise spectral density in ^{1/2}. Further, Monte-Carlo analysis is also performed to perceive the effect of capacitive deviations on the performance of proposed circuit. The voltage-mode BP response has been simulated with 10% Gaussian deviation in C_{1} = C_{2} = 10 pF. The simulation was done simultaneously for 100 runs. The corresponding result is shown in _{1} = V_{in}) and corresponding LP voltage output signal. From

This paper has presented a biquad filter configuration based on VDTAs which employs two VDTAs and two capacitors and offers the following attractive features:

1) Capable of realizing LP, BP, HP, BR, and AP filtering responses in voltage-mode and LP, BP, and HP filtering responses in trans-admittance-mode from the same configuration.

2) No employment of resistor(s), hence suited for integration.

3) The circuit is canonical by the way of using only two capacitors.

4) No need of minus type and/or double type input voltage signal to realize any filtering response, hence make the circuit simpler.

5) Q_{0} control of independent of ω_{0} through single transconductance parameter (biasing current), hence suited for practical applications.

6) Low active and passive sensitivity performance.

7) Low power consumptions.

With above mentioned features and exhaustive simulation results, it is very suitable to implement the proposed filter circuit in monolithic chip for use in modern microelectronic system applications, such as controls, voice and data communications.