Electronically tunable current mode biquad filter based on single VDTA and grounded passive elements

This paper presents a new filter structure based on only single voltage differencing transconductance amplifier (VDTA) and three grounded passive elements and has capability to low pass (LP), band pass (BP), high pass (HP), band reject (BR) and all pass (AP) biquad filtering functions at an explicit current output by the use of appropriate selection of three current input signals. Hence, it is fully integrable, canonical in nature and universal current-mode (CM) biquad. Besides it, the proposed filter also enjoys few more desirable features such as low active and passive sensitivities, low power consumption and orthogonal tunability of pole frequency and quality factor by electronic means. The presented filter is simulated using PSPICE in 0.18μm CMOS process. KeywordVDTA, Biquad, Tunable filter, Current-mode


TABLE I. COMPARISON OF DIFFERENT SINGLE ACTIVE ELEMENT BASED CM FILTERS WITH PROPOSED CM FILTER CIRCUIT
Keeping above points in the mind, this study proposes a new current-mode filter by the use of only single active element and has number of attractive features which are (i) realizes all five standard filtering functions in CM without needing inverted current input signal(s), (ii) use of only grounded passive elements which is ideally suited for IC fabrication, (iii) high output impedance for current filtering response(s), (iv) providing low active and passive sensitivities, (v) orthogonal current control of the pole frequency and quality factor.
II. VDTA DESCRIPTION The VDTA is relatively new element and has been popularized and frequently used in designing of analog filters [10,13,22,[26][27][28][29] in last few years. The symbolic diagram of VDTA is shown in Fig.1. The characteristic equation defining the relationship between various terminals voltage current of VDTA can be described as. 1 1 Here, g m1 and g m2 are trans-conductance parameters of VDTA which depending on the biasing current I B1 and I B2 of VDTA, respectively. The CMOS implemented model of VDTA as per Fig.1 is depicted in Fig.2. The expression of g m1 and g m2 in term of I B1 and I B2 , respectively, for CMOS implemented model of VDTA [27] shown in Fig.2 can be formulated as. 1 1

III. PROPOSED CURRENT MODE BIQUAD FILTER
The proposed CM biquad with three current input signals (I 1 , I 2 and I 3 ) and single current output signal (I out ) is shown in Fig.3 which consists of single VDTA, one grounded resistor (R) and two grounded capacitors (C 1 and C 2 ). On analysing the circuit in Fig.3, the current response at I out can be derived, mathematically as given in the following equation.
From the above equation, it can be found that the circuit of Fig. 3 is capable of realizing various CM filtering functions. But, each of the filtering functions can be synthesized by suitable selection of the current input signal(s) as discussed below.
i. If I 1 =I 2 =0 and I 3 =I in , a LP filter can be obtained. ii. If I 1 =I 3 =0 and I 2 =I in , a BP filter can be obtained. iii. If I 2 =I 3 =0 and I 1 =I in , a HP filter can be obtained. iv. If I 1 =I 3 = I in, I 2 =0, g m1 R= 1, a BR filter can be obtained. v. If I 1 =I 2 =I 3 = I in, and g m1 R= 1, an AP filter can be obtained. Above discussion conclude that the filter structure shown in Fig.3 can realizes all five standard CM filtering functions without needing inverted/scaled-input signal(s). Moreover, the expression of filter parameters can be determined as: Where ω 0 , and Q 0 are angular pole frequency and quality factor. It is clear from Eq. (5)-(6) that Q 0 can also be electronically tuned independent of ω 0 by simultaneous variation in both g m1 and g m2 . Similarly, ω 0 can also be electronically tuned independent of Q 0 by varying g m1 or g m2 while keeping the product of g m1 and g m2 as constant. Thus, both filter parameters are orthogonal electronically tunable.

IV. NON IDEAL EFFACTS AND SENSITIVITY ANALYSIS
To see the effect of non ideal tracking errors of VDTA on the performace of the proposed CM structure, the current-voltage equations of VDTA can be rewritten as: Where β 1 and β 2 are the tracking errors of the VDTA and deviated from unit value. The proposed circuit of Fig.3 have been further reanalysed by taking the above non ideal errors into account. On re-analysing, the nonideal filter transfer functions and its filter parameters can be derived as follow.
Above equations can conclude that the filter parameters such as pass band gain, ω 0 and Q 0 may be slightly deviated from ideal ones due to effect of tracking errors of VDTA. Furthermore, the active and passive sensitivities of ω 0 and Q 0 for the proposed filter in Fig.3 is determined as follow which results in low (with in unity in magnitude) active and passive sensitivities of ω 0 and Q 0 .  (12) V. SIMULATION RESULTS In order to check the performance, the presented filter shown in Fig. 3 was implemented using CMOS realization of VDTA (as shown in Fig. 2) with transistors W/L ratio calculated as given in Table. II and simulations were made using PSPICE along with 0.18µm CMOS process parameters from TSMC. To design the proposed filter of pole frequency of 3.93 MHz at Q 0 =1, the circuit was set with biasing voltage of V DD = -V SS = 1.5V and the biasing currents were chosen so that g m1 =g m2 ≈496.2µA/V (I B1 =I B2 =53µA). The passive components value were calculated as R=2KΩ, C 1 =C 2 =20pF. Fig.4 shows the simulated versus ideal current gain responses of LP, HP, BP, and BR for the proposed biquad filter of Fig. 3. The simulated gain responses given in Fig. 4 show good agreement with ideal responses. The total power consumption of the filter was obtained as 1.41mW. With the same component value setting, the simulated gain and phase response of AP filters are also depicted in Fig.5.
Further simulations to prove the electronic tuning capability of ω 0 independent of Q 0 for the proposed circuit were also done. For this purpose, various BP responses at different set of g m1 = g m2 = 304.82µA/V, 496.2µA/V, 681.6µA/V, 963.9µA/V (by simultaneously variations in g m1 and g m2 ) are plotted in Fig. 6 which result in pole frequency (f 0 ) variations of the circuit as 2.30 MHz, 3.93MHz, 5.6MHz, and 8.10MHz without changing Q 0 (=1). Similarly, the simulation results showing the tuning feature of Q 0 independent of ω 0 for the circuit is also shown in Fig. 7 which were obtained by maintaining the product of g m1 and g m2 to be a constant as (I B1 =93.3 µA, I B2 =30µA), (I B1 =70 µA, I B2 =40µA), (I B1 = 53µA, I B2 =53µA), and (I B1 =40µA, I B2 =70µA) resulting Q 0 = 0.72, 0.83, 1, and 1.16 respectively, at constant pole frequency of 3.93MHz.
The transient behavior of the proposed CM circuit is also investigated by applying an input sinusoidal current signal at f 0 = 500 KHz with peak to peak amplitude of 80 µA and measuring the output at LP filtering response (when I 1 =I 2 =0 and I 3 =I in ,). Fig.8 shows the corresponding transient behavior of the LP output signal. The percentage of total harmonic distortion of Fig. 8 is 1.67. The dependence of the output harmonic distortion of LP current output on varying frequency in the range of 500 KHz to 4500 KHz of sinusoidal current input signal at constant peak to peak amplitude of 40µA is illustrated in Figure 9 which results the THDs within 3% acceptable limits.
Further to observe the effect of passive component mismatching on the filter's performance, Monte-Carlo analysis has been performed. To measure the impact, the CM BP output was simulated with 10% Gaussian deviation in C 1 = C 2 = 20 pF for 500 concurrently runs. Corresponding simulated results of BP response are shown in Fig.10. Fig. 10a, shows the magnitude response whereas Fig.10b shows the statistical results in the form of histogram where the simulated mean, median and standard deviation were obtained as 4.17MHz, 4.17MHz and 160.009KHz, respectively which conclude that with respect to the simulated pole frequency of 3.93 MHz, the proposed filter is less sensitive to the change in capacitive value and thus offers good passive sensitivity of the circuit.

VI. CONCLUSION
A new three input single output CM biquad universal filter based on single active element has been proposed in this paper which also consits of only three grounded passive elements and can realizes all five filtering functions such as LP, BP, HP, BR and AP. To prove the workability of the proposed biquad filter in all aspect, extensive PSPICE simulation results are also made. In addition, the proposed circuit has also number of the benefits as discussed below.
i. Requiring no inverted type and/or scaled type current input signal(s) to realize any filtering functions. ii. Using only grounded passive elements which make the circuit suitable for IC fabrication point of view.
iii. Using only minimum number of active element. iv. Exhibiting low active and passive sensitivities. v. Consuming low power of 1.41mW. vi. Providing orthogonal current tuning capability tunability of filter parameters. vii. Providing the canonical structure as it requires only two grounded capacitors.