Journal of Engineering
Volume 2016 (2016), Article ID 1674343, 10 pages
http://dx.doi.org/10.1155/2016/1674343

Research Article

Single VDTA Based Dual Mode Single Input Multioutput Biquad Filter

Rajeshwari Pandey, Neeta Pandey, and Navin Singhal

Department of Electronics and Communication Engineering, Delhi Technological University, Delhi 110042, India

Received 14 June 2016; Revised 9 September 2016; Accepted 3 October 2016

Academic Editor: Durga Misra

Copyright © 2016 Rajeshwari Pandey et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

This paper presents a dual mode, single input multioutput (SIMO) biquad filter configuration using single voltage differencing transconductance amplifier (VDTA), three capacitors, and a grounded resistor. The proposed topology can be used to synthesize low pass (LP), high pass (HP), and band pass (BP) filter functions. It can be configured as voltage mode (VM) or current mode (CM) structure with appropriate input excitation choice. The angular frequency () of the proposed structure can be controlled independently of quality factor (). Workability of the proposed biquad configuration is demonstrated through PSPICE simulations using 0.18 μm TSMC CMOS process parameters.

1. Introduction

The ever shrinking feature size of devices on ICs and consequential reduction of power supply voltage poses serious challenges to analog design such as reduced input common mode range, output swing, and linearity. This can be handled by operating in the current domain, as current mode circuits are designed for lower voltage swings. Therefore, over the last few decades, current mode (CM) processing has evolved as an alternative design technique [1] and has resulted in emergence of numerous active building blocks (ABBs) [2] such as differential difference current conveyor transconductance amplifier (DDCCTA) [3], current difference transconductance amplifier (CDTA) [4], current feedback operational amplifier (CFOA) [5], operational transresistance amplifier (OTRA) [6], differential input buffered transconductance amplifier (DBTA) [7], current difference buffered amplifier (CDBA) [8], current conveyor transconductance amplifier (CCTA) [9], and voltage differencing transconductance amplifier [10] which are used for realization of various signal processing and generation circuits. Among these, the voltage differencing transconductance amplifier (VDTA) is a recently introduced active element [11]. The VDTA is a voltage input current output ABB with two transconductance gain stages. It provides electronic tuning ability through its transconductance gains. Thus, the VDTA is one of the most suitable ABBs for easy and compact CMOS implementation [12] of signal processing and generating circuits.

Electronic filters are essential building block of communication and instrumentation systems. A variety of VDTA based biquadratic filters are available in literature [10–18] which can be classified as single input multioutput (SIMO) [11–14, 18], multi-input single output (MISO) [15–17], and multi-input multioutput MIMO [10] filter configurations. These filters can further be classified as voltage mode [10, 13, 17], current mode [11, 12, 14–16], and dual mode [18] structures. A detailed comparison of these structures is given in Table 1.

Table 1: Comparison of the proposed work with the previously reported work.

Ref.
Number of inputs
Simultaneous outputs
Standard filter functions
VM/CM
Active blocks used
Passive components
Orthogonal tunability of and

[10]
Two
Two
LP, HP, BP
VM
Two
Two C
No

[11]
One
Three
LP, HP, BP
CM
Two
Two C
No

[12]
One
Three
LP, HP, BP
CM
One
Two C; One R
Yes

[13]
One
Five
LP, HP, BP, NF, AP
VM
Two
Two C; Two R
Yes

[14]
One
Three
LP, HP, BP
CM
One
Two C
No

[15]
Three
One
LP, HP, BP, NF, AP
CM
Two
Two C
Yes

[16]
Three
One
LP, HP, BP, NF, AP
CM
One
Two C
No

[17]
Three
One
LP, HP, BP, NF, AP
VM
one
Two C
Yes

[18]
One
Three
LP, HP, BP
VM and CM
One
Three C; two R
Yes

Proposed work
One
Three
LP, HP, BP
VM and CM
One
Three C; one R
Yes

It may be noted from Table 1 that only a single VDTA based dual mode SIMO structure is available in literature and it uses five passive components. In this paper, a new single VDTA based SIMO-type dual mode biquad filter using four passive components is proposed. The proposed structure provides either voltage or current outputs through proper selection of input excitation. The proposed structure realizes three standard filter functions, namely, LP, HP, and BP, with independent and tuning feature. Proposed circuit configuration also offers low passive sensitivities. The rest of the paper is organised as follows: In Section 2, detailed circuit description is presented. The circuit behaviour in presence of nonidealities of VDTA has been analysed in Section 3 and deviation in filter parameters is enumerated. The functionality of the proposed filter has been confirmed through SPICE simulations using 0.18 μm TSMC CMOS process parameters and the results are presented in Section 4. Section 5 concludes the paper.

2. Circuit Description

The circuit symbol of the VDTA is shown in Figure 1 where and are the input terminals and , , and are the output terminals. The CMOS realization of VDTA [10] is shown in Figure 2. It consists of two transconductance (TC) stages, namely, input and output stages. The input TC stage converts the differential input voltage ( -,) into current through first TC gain () and the voltage at terminal () is converted to current () through second TC gain (). All VDTA terminals exhibit high impedance values [10]. The port relations are given in matrix form in

The TC gains, and , respectively, can be expressed as [10]

where is the transconductance value of the th transistor and is given by

In (3), is effective carrier mobility; is the gate oxide capacitance per unit area; and represent the dc bias current and the aspect ratio of the th MOS transistor, respectively.

Figure 1: Circuit symbol of VDTA.

Figure 2: The CMOS realization of VDTA [10].

The proposed dual mode SIMO filter is shown in Figure 3 which comprises of a single VDTA, three capacitors, and a resistor. With appropriate choice of input signal, it can be configured as either VM or CM structure.

Figure 3: Proposed VM and CM mode SIMO filter.

2.1. The VM Configuration

The filter configuration of Figure 3 operates in VM if input current is removed (). Routine analysis of the circuit yields voltage mode transfer functions given by

where

2.2. The CM Configuration

Removal of voltage source in Figure 3 results in CM filter topology. Analysis of the resulting topology leads to the following transfer function:

The angular frequency and quality factor for both the filter structures are given by

It may be observed from (7) and (8) that the parameters can be set to a desired value and can be controlled through independently.

It is relevant to mention here that the voltage outputs of the proposed structure are available at high impedance, which is invariably true for all available VDTA based voltage mode structures [10, 13, 17, 18]. It is therefore suggested that either the voltage output structures should be used to drive the high input impedance circuits or the output should be taken through buffers. Further, in CM operation, current outputs are available through passive elements and would require additional ABBs for accessing current at high impedance. However, it is also applicable to all single ABB based SIMO structures [12, 14, 18]. It may also be noted that in proposed structure can be accessed at high impedance by lifting the drain node of transistors and .

The passive sensitivities of and of the proposed filter structures can be expressed as given by (9) and their absolute values do not exceed unity in magnitude.

3. Nonideal Analysis

In this section, the effect of nonidealities of VDTA on the filter performance has been analysed. The nonidealities associated with VDTA based circuits may be divided into two groups. The first group concerns the finite voltage tracking errors and the second results from the presence of parasitics at all the terminals of VDTA.

3.1. Nonideality due to Tracking Error

Taking the tracking errors of the VDTA into account, the port relations expressed by (1) get modified as

where and are, respectively, the tracking errors for the first and second stages of the VDTA. In presence of and , the new expressions for and can be obtained as

It is evident that the values of , and deviate slightly from their ideal values. These changes may be accommodated by adjusting TC gains and through bias current of VDTA. However, the sensitivities of and with respect to and are quite low, as given by

3.2. Nonideality due to Parasitics

The nonideal model of VDTA is shown in Figure 4 wherein each terminal is characterized by finite parasitic impedance consisting of resistance in parallel with capacitance (; ; ; ; for , , , and terminals, resp.) [12]. The filter performance might deviate from ideal behaviour due to parasitics of VDTA. Thus, the filter structure of Figure 3 is to be analysed in the presence of parasitics. Using the nonideal model of VDTA, the proposed filter structure can be redrawn as shown in Figure 5.

Figure 4: Nonideal model of VDTA.

Figure 5: Nonideal filter structure.

Using routine analysis, and of the filter configuration of Figure 5 may be obtained as

where

The parasitic resistances associated with all terminals are practically too large making

Thus, (15) reduces to

By selecting external capacitances much larger than parasitic capacitances, (16) can be simplified as

Similarly, (17) can be simplified as

Substituting (19) and (20), it may thus be noted that (13) can be approximated to (7) which represents the ideal value of . Also putting (19), (20), and (21) in (14), may be expressed by (22) which is equal to its ideal value.

It may be concluded therefore that, by selecting external capacitances much larger than parasitic capacitances, the frequency response of the proposed structure would not be affected.

4. Simulation Results

The functionality of the proposed filter is validated through SPICE simulated using 0.18 μm TSMC process parameters which have been listed in Table 2 for ready reference. First, the DC transfer characteristic of the VDTA is validated which is followed by verification of both VM and CM filter responses. Subsequently, as a case study, the transient behaviour of BP filter (VM and CM) is studied and its total harmonic distortion (THD) variation is also observed.

Table 2: List of 0.18 μm CMOS process parameters used.

NMOS
LEVEL = 7+VERSION = 3.1 TNOM = 27 TOX = 4.1E-9+XJ = 1E-7NCH = 2.3549E17 VTH0 = 0.3672292+K1 = 0.5893162 K2 = 3.053194E-3K3 = 1E-3+K3B = 1.8246765 W0 = 1E-7NLX = 1.771394E-7+DVT0W = 0 DVT1W = 0 DVT2W = 0+DVT0 = 1.2540673 DVT1 = 0.3671218 DVT2 = 0.0374285+U0 = 2.3448599 UA = -1.473692E-9UB = 2.452512E-18+UC = 6.566514E-11 VSAT = 1.025312E5 A0 = 2+AGS = 0.4532362 B0 = 3.222688E-7B1 = 5E-6+KETA = -0.0109204 A1 = 0 A2 = 0.9744209+RDSW = 105 PRWG = 5PRWB = -0.2+WR = 1 WINT = 1.660932E-9 LINT = .520122E-8+XL = 0 XW = -1E-8DWG = -2.794177E-9+DWB = 7.839758E-9 VOFF = -0.091184 NFACTOR = 2.2684002+CIT = 0 CDSC = 2.4E-4 CDSCD = 0+CDSCBUTE = 0 ETA0 = 3.031184E-3 ETAB = 9.427488E-6+DSUB = 0.0153239 PCLM = 0.704686 PDIBLC1 = 2435533+PDIBLC2 = 2.76003E-3 PDIBLCB = -0.1 DROUT = 0.8035265+PSCBE1 = 4.372065E10 PSCBE2 = 2.518414E-9 PVAG = 0.0749313+DELTA = 0.01 RSH = 6.4 MOBMOD = 1+PRT = 0 UTE = -1.5 KT1 = -0.11+KT1L = 0 KT2 = 0.022 UA1 = 4.31E-9+UB1 = -7.61E-18 UC1 = -5.6E-11 AT = 3.3E4+WL = 0 WLN = 1 WW = 0+WWN = 1 WWL = 0 LL = 0+LLN = 1 LW = 0 LWN = 1+LWL = 0 CAPMOD = 2 XPART = 0.5+CGDO = 8.79E-10 CGSO = 8.79E-10 CGBO = 1E-12+CJ = 9.605878E-4 PB = 0.8 MJ = 0.3831903+CJSW = .643918E-10 PBSW = 0.8 MJSW = 0.1407086 +CJSWG = 3.3E-10 PBSWG = 0.8 MJSWG = 0.1407086+CF = 0 PVTH0 = -6.317463E-6 PRDSW = -.8440536+PK2 = 9.250773E-4 WKETA = 1.074587E-3 LKETA = -.453047E-3+PU0 = 4.3638022 PUA = -1.50117E-12 PUB = 0+PVSAT = 1.356677E3 PETA0 = 1.003159E-4 PKETA = -2.902589E-3

PMOS
LEVEL = 7+VERSION = 3.1 TNOM = 27 TOX = 4.1E-9+XJ = 1E-7 NCH = 4.1589E17 VTH0 = -0.38888+K1 = 0.5636481 K2 = 0.0308017 K3 = 0+K3B = 7.400372 W0 = 1E-6 NLX = 1.385693E-7+DVT0W = 0 DVT1W = 0 DVT2W = 0+DVT0 = 0.5846878 DVT1 = 0.2165736 DVT2 = 0.1+U0 = 3.6325808 UA = 1.459877E-9 UB = 1.18636E-21+UC = -1E-10 VSAT = 2E5 A0 = 1.7849198+AGS = 0.3754547 B0 = 3.172437E-7 B1 = 7.280105E-7+KETA = 0.0156934 A1 = 0.3222966 A2 = 0.3+RDSW = 196.7345438 PRWG = 0.5 PRWB = -0.1589203+WR = 1 WINT = 0 LINT = 2.702835E-8+XL = 0 XW = -1E-8 DWG = -2.627805E-8+DWB = 1.03876E-9 VOFF = - 0.0927458 NFACTOR = 2+CIT = 0 CDSC = 2.4E-4 CDSCD = 0+CDSCB = 0 ETA0 = 0.145648 ETAB = -0.0543017+DSUB = 0.9610783 PCLM = 2.0812378 PDIBLC1 = 7.131255E-4 +PDIBLC2 = 0.0185628 PDIBLCB = -9.170788E-4 DROUT = 0+PSCBE1 = 3.206374E9 PSCBE2 = 9.279285E-10 PVAG = 15+DELTA = 0.01 RSH = 7.3 MOBMOD = 1+PRT = 0 UTE = -1.5 KT1 = -0.11+KT1L = 0 KT2 = 0.022 UA1 = .31E-9+UB1 = -7.61E-18UC1 = -5.6E-11 AT = 3.3E4+WL = 0 WLN = 1 WW= 0+WWN = 1 WWL = 0 LL = 0+LLN = 1LW = 0 LWN = 1+LWL = 0 CAPMOD = 2 XPART = 0.5+CGDO = 6.41E-10CGSO = 6.41E-10 CGBO = 1E-12+CJ = 1.136354E-3 PB = 0.8459606 MJ = 0.4088875+CJSW = 2.255183E-10 PBSW = 0.832695 MJSW = 0.3342249+CJSWG = 4.22E-10 PBSWG = 0.832695 MJSWG = 0.3342249+CF = 0 PVTH0 = 4.532819E-3 PRDSW = 7.6587079+PK2 = 3.513392E-3 WKETA = 0.0251295LKETA = -2.32504E-3+PU0 = -.4738884 PUA = -8.40745E-11 PUB = 1E-21+PVSAT = -50 PETA0 = 1E-4 PKETA = -2.114056E-3

4.1. The DC Transfer Characteristic

The VDTA structure shown in Figure 3 [10] with supply voltages of ±0.9 V is used for simulation. The same aspect ratios of the MOS transistors are used as given in [10]. The DC transfer characteristic of the VDTA, as shown in Figure 6, is plotted for  μA, which resulted in  μ A/V.

Figure 6: The DC transfer characteristics of the VDTA.

4.2. Frequency Response

The LP, HP, and BP filter responses for both VM and CM filter structures with  MHz and are shown in Figures 7(a) and 7(b), respectively. The passive components were chosen as  nF and  KΩ. The tuning of gain expression for low pass filter with respect to is shown in Figure 7(c).

(a)

(b)

(c)

Figure 7: Frequency response at  MHz and . (a) VM topology. (b) CM topology. (c) VM LP filter depicting gain tuning with .

It may be observed from (7) and (8) that can be tuned by changing either capacitance values () or the transconductances (). The transconductance variation can be obtained through bias current adjustment. The tuning can be accomplished through without affecting . The orthogonal adjustment of and is shown by plotting the BP responses for  KHz, 1 MHz, and 10 MHz while keeping fixed at 1. The responses for VM and CM structures are shown in Figures 8(a) and 8(b), respectively. Similarly, the simulation results for , 1, and 5 when remains constant at 1 MHz, for VM and CM topologies, are shown in Figures 9(a) and 9(b), respectively. It is evident from Figures 8 and 9 that and are orthogonally tunable.

(a)

(b)

Figure 8: BP responses for  KHz, 1 MHz, and 10 MHz keeping fixed at 1 for (a) VM and (b) CM topology.

(a)

(b)

Figure 9: BP responses for , 1, and 5 with  MHz for (a) VM and (b) CM topology.

Another set of simulations have been carried out to examine frequency response limitations of the proposed structure. Low pass current mode response is used for illustration. The simulations conditions on bias currents are kept the same as reported in the beginning while the capacitor values are changed and corresponding theoretical and simulated pole frequencies are noted and listed in Table 3. It may be noted that there is a close match between theoretical and simulated pole frequencies when the values of external capacitors are chosen to be sufficiently greater than parasitic capacitances. However, a significant deviation is seen when external capacitances are selected close to parasitics (tens of fF order). Further, it is also observed that parasites limit frequency range because their pole frequencies are much lower than those for tracking errors.

Table 3: The % frequency deviation for CM LP filter.

Capacitor value
Theoretical
Simulated
% frequency deviation

0.1 nF
1.01231 MHz
1.06 MHz
4.5

0.01 nF
10.1231 MHz
10.639 MHz
4.8

1 pF
101.231 MHz
108.854 MHz
7.0

0.1 pF
1.01231 GHz
886.833 MHz
12.3

0.01 pF
10.1231 GHz
2.269 GHz
77.0

1 fF
101.231 GHz
2.76 GHz
97.3

4.3. Transient Response

The time domain behaviour of the VM BP filter is also studied by applying three sinusoidal frequency components: a low frequency signal of 1 MHz, a high frequency component of 100 MHz, and the third component of 10 MHz which is of the BP filter. The input signal is shown in Figure 10(a) and its frequency spectrum is depicted in Figure 10(b). The transient response of the filter and the associated frequency spectrum are shown in Figures 11(a) and 11(b), respectively. It may be noted that the frequency components other than are significantly attenuated.

(a)

(b)

Figure 10: (a) The voltage input transient signal and (b) its frequency spectrum.

(a)

(b)

Figure 11: (a) The voltage output transient signal and (b) its frequency spectrum.

To observe the transient response of CM BP filter, it is driven by an input current signal consisting of three frequency components: 1 KHz, 10 KHz, and 100 KHz. The BP filter is designed for an  KHz. The related results are depicted in Figures 12 and 13 which clearly show that the signals outside the bandwidth of BP filter are significantly attenuated.

(a)

(b)

Figure 12: (a) The current input transient signal and (b) its frequency spectrum.

(a)

(b)

Figure 13: (a) The current output transient signal and (b) its frequency spectrum.

To check the quality of the output of BP filter, the percentage total harmonic distortion (%THD) with the sinusoidal input signal is obtained as shown in Figure 14. It is observed from Figure 14(a) that the %THD remains considerably low [19] for input signal values up to 500 mV for VM topology. Similarly, it may be noted from Figure 14(b) that the %THD is well below 7% for current signals up to 200 μA. The simulated value of power dissipation, in both VM and CM operations, is observed to be 0.54 mW.

(a)

(b)

Figure 14: THD variation of BP filter against amplitude of the applied sinusoidal signal at 159 KHz (a) voltage mode and (b) current mode.

5. Conclusion

A single VDTA based dual mode SIMO biquad which realizes LP, HP, and BP responses has been proposed in this paper. The proposed biquad is a SIMO structure and can be configured as voltage mode or current mode with appropriate input excitation selection. The angular frequency and the quality factor of the proposed configuration can be controlled in a noninteractive manner. The filter is electronically tunable. The filter structure functionality is verified through SPICE simulations and both frequency and transient responses are studied.

Competing Interests

The authors declare that they have no competing interests.

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