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 [1] due to their several salient features such as inherently wider bandwidth, greater linearity, wider dynamic range, simple circuitry and low power consumptions. Consequently, several current-mode active elements such as second generation current conveyor (CCII), differential difference current conveyor (DDCCII), current differencing buffer amplifier (CDBA), operational transconductance amplifier (OTA), current controlled current conveyor (CCCII), current differencing transconductance amplifier (CDTA), current controlled current differencing transconductance amplifier (CCCDTA), cur- rent controlled current conveyor transconductance amplifier (CCCCTA), voltage differencing transconductance amplifier (VDTA) etc. and their applications in filters design are introduced in the literature [2] - [26] . Among them VDTA is latest one. It has the advantage of its electronic tuning ability through two transconductance parameters; hence it does not need a resistor in practical applications. Subsequently, the VDTA based circuits realizations occupy less chip area. This device can be operated in both current- and voltage-modes, providing flexibility to the circuit designers [25] .

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 [19] - [26] . But as far as the topic of this paper is concerned, the filter circuits operated in either voltage-mode or trans-admittance-mode-mode or in both modes simultaneously, using VDTAs, are of interest. The reported voltage- mode filter based on VDTA [22] - [24] uses only single VDTA and three (two capacitors and one resistors) [22] or two passive elements (only two capacitors) [23] [24] . Two of the circuits [22] [23] can realize all the standard filtering functions (LP, BP, HP, BR and AP) by the use of three inputs and single-output. However, both circuits are not able to provide orthogonal electronic tunability of pole frequency and quality factor. Moreover, the circuit [22] requires inverting type voltage input to realize AP filtering function. Third of the circuit [24] can realizes only three filtering functions (LP, BP and HP) by the use of two inputs and two outputs. The single-input five-output biquad filter reported in Ref. [25] employs two VDTAs, two grounded capacitors, two grounded resistors and realizes all the five standard filtering functions, simultaneously, in voltage-mode only with feature of orthogonal electronic tunabilty of pole frequency and quality factor. Another valuable filter circuit with single-input multi-output [26] consists of two VDTAs, two capacitors and realizes only two filtering functions (LP, BP) in voltage-mode and three filtering functions (BP, LP and BR) in trans-admittance-mode, simultaneously.

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 [24] [25] whose symbolic diagram is shown in Figure 1 where P, N are two high impedance input terminals and Z, Zc, X⁺, 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 of VDTA. Further voltage across auxiliary Z terminal is also transferred to a current at terminals X⁺ and

X⁻ (and) by other transconductance parameters of VDTA. The and are the transconductance parameters of first and second stage of VDTA respectively, whose value are controlled by biasing currents and of VDTA, respectively. The relationship of input output terminals of VDTA can be described by the following matrix equation.

The CMOS realization of VDTA is also shown in Figure 2 which consists of two Arbel-Goldminz transconductance [25] . For the CMOS implementation of VDTA as shown in Figure 2, and can be approximately expressed by the following equations [25] .

and

where is transconductance gain of i^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 Figure 3, which employs two VDTAs and two capacitors with one is permanently grounded. The analysis of the circuit of Figure 3 for three applied voltage inputs V₁, V₂ and V₃, will give the following expression for the voltage output at

where

Here, are transconductance gains of first and second stage of VDTA (1) respectively and, are transconductance gains of first and second stage of VDTA (2), respectively. It is evident from Equation (4) that various biquad filtering responses in voltage-mode can be obtained at V₀ through appropriate selection of input voltage signals (V₁, V₂, and V₃).

1) If V₁ = V_in and V₂ = V₃ = 0, the filter configuration provides LP response.

2) If V₂ = V_in and V₁ = V₃ = 0, the filter configuration provides BP response.

3) If V₃ = V_in and V₁ = V₂ = 0, the filter configuration provides HP response.

4) If V₁ = V₃ = V_in, V₂ = 0, the filter configuration provides BR response.

5) If V_in1 = V_in2 = V_in3 = V_in and, the filter configuration provides AP responses.

It can be concluded from above operational description that the proposed filter configuration in Figure 3 is capable of realizing all the five standard filtering responses in voltage-mode without requiring minus-type and/or double input voltage signal(s). However, AP realization requires matching condition.

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 V₂ (V_in) and remaining voltage inputs set to zero (V₁ = V₃ = 0). In this case transadmittance mode transfer function can be derived as

The filter characteristic parameters like pole-frequency (ω₀), quality-factor (Q₀), and band-width (ω₀/Q₀) for the proposed filter configuration can be expressed

If and, then Equation (11) becomes

,

and

It is clear from Equation (10) and Equation (11) that filter parameter Q₀ can be widely varied electronically by varying independent of ω₀. Similarly, ω₀ 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 and represents the voltage tracking errors for first and second stages of j^th VDTA respectively, where j = 1, 2. If we re-analysed the proposed circuit in Figure 3 using Equation (13), the filter parameters ω₀, Q₀, and BW are changed to

The active and passive relative sensitivities of and for the proposed filter are calculated as

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 Figure 3 was examined using PSPICE simulations. Simulation was performed based on CMOS structure of VDTA as shown in Figure 2, with transistor model of 0.18 µm MOSFET from TSMC [27] . Aspect ratio of each MOS transistors is given in Table 1. To design the proposed biquad filter for obtaining and Q₀ = 1, the active and passive components were selected as, , ,

. Figure 4 shows the voltage-mode gain and phase responses of LP, BP, HP, BR and AP. Figure 5 shows the transadmittance gain of LP, BP and HP filtering responses. The simulation result shows the simulated pole frequency as 7.49 MHz which is fairly closed to the designed value of 7.7 MHz. The total power dissipation for the circuit is 2.71 mW. Figure 6 shows the electronic tunability feature of Q₀ independent of ω₀ for the proposed filter by performing the simulation of various voltage-mode BP responses at

different values of by keeping other currents as constant of 50 µA. The corresponding quality factor at constant pole frequency of 7.49 were found as Q₀ = 3.14, 1.58, 0.909, 0.707 which prove the electronic tunability feature of Q₀ independent of ω₀ 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 Figure 7. It indicates that noise spectral density is quite small and it attains a maximum value equal to 14 nV/Hz^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 C₁ = C₂ = 10 pF. The simulation was done simultaneously for 100 runs. The corresponding result is shown in Figure 8. From this result, the standard deviation is measured as 292.42 kHz, which demonstrates that the circuit is reasonable sensitive towards capacitive passive components. For 5% Gaussian deviation, the sensitivity is 145.35 kHz. Lastly, the time domain behaviour of the proposed filter in Figure 3 was also investigated by applying a sinusoidal input voltage having peak to peak amplitude of 300 mV at a signal frequency of 200 KHz. Figure 9 shows the time domain sinusoidal voltage input (V₁ = V_in) and corresponding LP voltage output signal. From Figure 9, it was observed that 300 mV peak to peak sinusoidal input voltage signal of frequency 200 KHz is acceptable without significant distortions.

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) Q₀ control of independent of ω₀ 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.