General Mixed-Mode Single-Output DDCC-based Universal Biquad Filter

General Mixed-Mode Single-Output DDCC-based Universal Biquad Filter

Chen-Nong Lee1

1Department of Computer and Communication Engineering,

Taipei City University of Science and Technology, Taiwan, R. O. C.

Wen-Chih Yang2

2Department of Electrical Engineering, Taipei City University of Science and Technology,

Taiwan, R. O. C.

AbstractThis paper presents a general mixed-mode (including voltage, current, transadmittance, and transimpedance modes) universal filter using only three single- output differential difference current conveyors (DDCCs), two grounded capacitors, three grounded resistors, and one floating resistor. The proposed circuit can realize all four modes five universal filtering responses (lowpass, highpass, bandpass, notch, and allpass) from the same topology. The proposed circuit uses only single-output DDCCs with simpler implementation configuration than the multiple-output current- conveyors. This represents the attractive feature from chip area and power consumption point of view. Moreover, the proposed circuit has no need of component matching constraints for all five universal filtering responses in voltage and transadmittance modes. Furthermore, the proposed filter offers the following features: (i) using two grounded capacitors, (ii) no component- value constraints except the current/transimpedance allpass response, (iii) no need of extra inverting or non-inverting amplifiers, (iv) no need of extra current replicas degrading the final output impedance, and (v) low active and passive sensitivity performance. H-Spice simulation results confirm the theory.

KeywordsActive filters, differential difference current conveyors (DDCCs), general mixed-mode, universal biquad filter.

1. INTRODUCTION

   The applications and advantages in the designing general mixed-mode universal biquad filters have received considerable attentions in recent years. This is because general mixed-mode operations (including voltage-mode (VM), current-mode (CM), transadmittance-mode (TAM), and transimpedance-mode (TIM), i.e. four modes) such as TAM and TIM can play a very important role for transferring from VM to CM and vice versa, respectively. Therefore, the general mixed-mode universal biquad filters with input currents or/and voltages and output currents or/and voltages, are worthy of research and presented for the use of any filtering requirement, which is compatible with modern microelectronic systems applications, such as controls and voice and data communications, where consideration of size and weight make the use of inductors prohibitive.

   In the past several decades, many single-mode, dual-mode, or mixed-mode filters using different active elements have been presented [1-51]. The filters consist of more modes and filtering functions, meaning more applications for which they can be used. However, only several circuits [1-4, 6-8, 10, 12,

   15, 17, 22, 24, 25, 27, 31-34, 36, 38-40] can realize all five universal filtering functions (lowpass, highpass, bandpass,

   notch, and allpass) in VM, CM, TIM, and TAM. Such filters are referred to in this paper as general mixed-mode universal filter. The general mixed-mode universal filter structures employ at least four active elements in [1-4, 12, 15, 17, 25, 27,

   31, 32, 36, 39, 40] and need some matching conditions for realizing some VM or TAM filtering functions [1-4, 12, 15, 17, 25, 27, 36, 39, 40]. For example, in 2012, Lee proposed a multiple-mode (i.e. general mixed-mode) universal filter [25] using five operational transconductance amplifiers (OTAs) as active elements and two grounded capacitors (for second- order). The filter [25] can offer all five universal filtering functions in all the four possible modes. However, it needs component matching conditions for realizing VM and TAM allpass responses. In 2013, it has shown that the mixed-mode universal biquad filter [27] needs to use four multiple-output current controlled current conveyors (MOCCCIIs) and two grounded capacitors. However, it needs component matching conditions for realizing VM notch, allpass responses and TAM lowpass, notch, allpass responses. In 2016, two digitally programmable mixed-mode universal biquad filters were proposed in [31, 32], which can achieve many main advantages. However, the filter in [31] uses two multi-output second-generation current conveyors (MOCCIIs), six digitally programmable second-generation current conveyors (DPCCIIs) (i.e. eight active elements), four grounded resistors and two grounded capacitors. In [32], the filter uses followers with a minimal realization. However, the filter in [32] still needs to use seven current/voltage followers (i.e. seven active elements), three switches, three floating resistors, one grounded resistor, and two grounded capacitors. In 2018, Zanjani et al. proposed a mixed-mode Gm-C biquad filter [39] with independently electronic tunability. However, the filter needs to employ 19 inverters as operational transconductance amplifiers and two grounded capacitors. In 2018, Tsukutani et al. proposed a novel general mixed-mode universal biquad filter [40]. However, the biquad filter [40] needs to use five DVCCs, five grounded resistors, and two grounded capacitors. Few general mixed-mode universal biquad filter structures employ three active elements of simple implementation configuration [6-8, 10, 22, 24]. For example, in [24], the reported general mixed-mode biquad uses three differential difference current conveyors (DDCCs), two floating resistors, two grounded resistors, and two grounded capacitors. However, it needs component matching conditions for realizing VM, CM, TAM, and TIM allpass responses. In 2017, the reported general mixed-mode biquad filter [35] uses only

   three current controlled current conveyor transconductance amplifiers (CCCCTAs) and two grounded capacitors. However, the circuit in [35] can not realize notch and allpass responses in TIM. Moreover, the CCCCTA is a complex active element.

   The applications and advantages in the designing current- conveyor-based active circuits have received considerable attentions [1, 2, 6-11, 13, 14, 18, 20-24, 26, 27, 30, 31, 33-35,

   37, 38, 40-50]. Especially, the differential difference current conveyor (DDCC) [49, 50] has the ability to perform the operations of the intrinsic voltage addition and subtraction [47, 48]. Therefore, it is very important for the design of general mixed-mode universal biquad filters [33]. Moreover, the DDCC has simplest implementation configuration in all of the other complex current conveyors, such as, fully differential current conveyor (FDCCII), current controlled current conveyor transconductance amplifiers (CCCCTA), differential difference current conveyor transconductance amplifier (DDCCTA), differential voltage current conveyor transconductance amplifier (DVCCTA), digitally programmable second-generation current conveyors (DPCCIIs), and dual X current conveyor differential input transconductance amplifier (DXCCDITA). The use of a FDCCII can be divided into two separate DDCCs. A CCCCTA can be produced by cascading a CCCII with an OTA. Similarly, a DDCCTA (or DVCCTA) also can be produced by cascading a DDCC (or DVCC) with an OTA. Therefore, each of them can be regarded as two basic active elements. In [13], Lee and Chang proposed a single FDCCII- based mixed-mode biquad filter [13]. The circuit [13] uses only a single FDCCII, three floating/grounded resistors, and two grounded capacitors. In 2017, the reported mixed-mode biquad filter [37] employs only a DXCCDITA and four passive components. Although single active element based mixed-mode biquad filters have been propose in [13, 37], both circuits [13, 37] are not general mixed-mode universal filters. Moreover, both used active elements (i.e. FDCCII and DXCCDITA) are complex active elements. There are three general mixed-mode universal biquad filters using two active elements [33, 34, 38]. In 2016, Lee proposed two general mixed-mode universal biquad filters [33, 34]. The filter in [33] uses one FDCCII, one DDCC, six grounded/floating resistors, and two grounded capacitors. The circuit has versatile input/output functions [33] which can offer all five universal filtering responses in single-input multiple-output (SIMO) and multiple-input single output (MISO) types, respectively. The circuit in [34] uses two plus-type FDCCIIs, five grounded/floating resistors, and two grounded capacitors. The circuit [34] has no need of any matching conditions which includes no need of component and input matching conditions. Similarly, in 2018, the reported mixed-mode biquad filter [38] also uses two FDCCIIs, four floating/grounded resistors and two grounded capacitors. Although the filters in [33, 34, 38] use only two active elements and can achieve many important advantages, it was shown that the use of the complex active elements and many resistors was unavoidable. In 2013 the reported mixed-mode [28] biquad filter employs only two voltage differencing transconductance amplifiers (VDTAs) and two grounded capacitors. The circuit can realize all five

   universal filtering functions in VM and TAM, but it [28] has not been operated in CM and TIM.

   In this paper, the proposed circuit uses only three single- output DDCC, two grounded capacitors, three grounded resistors, and one floating resistor, which can realize general mixed-mode (including VM, CM, TIM, and TAM) all five universal filtering responses (lowpass (LP), highpass (HP), bandpass (BP), notch (NH), and allpass (AP)) from the same topology. Over the last decade, the general mixed-mode universal filters have been presented in the literature [1-4, 6-8, 10, 12, 15, 17, 22, 24, 25, 27, 31-34, 36, 38-40]. With respect

   to the references [1-3, 31, 32, 40], the proposed biquad filter employs fewer active and passive elements. With respect to the references [4, 12, 15, 17, 25, 27, 36, 39], the proposed biquad filter employs fewer active elements. With respect to the references [7, 10], the proposed biquad filter uses active elements of same number but the proposed circuit has the following advantages: less component matching conditions, the use of only two grounded capacitors and no switches. With respect to the references [6, 8, 22, 24], the proposed biquad filter uses the same active elements (DDCCs) in same number but the proposed circuit has the following advantages: no need of component matching constraints for VM and TAM all five universal filtering responses and the use of only single-output DDCCs. Filters using only single-output DDCCs have the advantages: (i) no need of extra current replicas degrading the final output impedance, and (ii) simpler implementation configuration than multiple-output DDCCs. This represents the attractive feature from chip area and power consumption point of view. With respect to the references [33, 34, 38], the proposed biquad filter uses the DDCCs with far simpler implementation configuration than FDCCIIs.

2. PROPOSED CIRCUIT

   Fig. 1 shows the proposed general mixed-mode biquad filter structure using only three single-output DDCCs, two grounded capacitors, three grounded resistors, and one floating resistor, where Vin1, Vin2, Vin3 are the filter input voltages and Iin1, Iin2, Iin3 are the filter input currents whose setting determine the filter functions as shown later, Vout1 Vout2, Vout3, Vout4, and Iout are the filter voltage outputs and current output, respectively. Using standard notation, the port relations of a DDCC can be characterized by IY1 = IY2 = IY3 = 0, VX = VY1 VY2 +VY3, IZ+= +IX and IZ-= -IX. The current output has very high output impedance.

   If Iin1 = Iin2 = Iin3 = 0, and Vin2= 0 , Vin1 = Vin3 is given by the single input signal, circuit analysis yields the following VM filtering responses:

   Vout1

   Vin

   Vout2

   Vin

   Vout3

   Vin

   Vout4

   Vin

   s2C1C2 G1G2

   s2C1C2 sC1G2 G1G2

   s2C1C2

   s2C1C2 sC1G2 G1G2

   sC1G2

   s2C1C2 sC1G2 G1G2 G1G2

   s2C1C2 sC1G2 G1G2

   VM notch (3)

   VM highpass (4)

   VM bandpass (5)

   VM lowpass (6)

   Examining (3) and (5) show that the voltage difference between Vout1 and Vout3 yields an allpass filtering response.

   Vout1 Vout3 s2C1C2 sC1G2 G1G2

   VM allpass (7)

   Vin s2C1C2 sC1G2 G1G2

   Fig. 1. Proposed general mixed-mode biquad filter structure.

   Part I: VM and TAM universal biquad filters with three inputs and one output

   Note that it is no need to impose component choice for realizing any filtering responses. Moreover, no inverting or non-inverting amplifiers (for special input signals) are needed in the realizations.

   Part III: CM and TIM universal biquad filters with three inputs and one output

   If Vin1 = Vin2 = Vin3 = 0, and Iin1 , Iin2 , Iin3 are given by the input signals, circuit analysis for Fig. 1 yields the following CM and TIM universal transfer functions:

   If Iin1 = Iin2 = Iin3 = 0, and Vin1 , Vin2 , Vin3 are given by the

   Iout

   s2C1C2G4Iin1 sC1G3G4Iin2 G2G3G4Iin3

   2

   input signals, circuit analysis for Fig. 1 yields the following VM and TAM universal transfer functions:

   s C1C2G3 sC1G2G3 G1G2G3

   CM universal transfer function (8)

   s2C1C2Vin1 sC1G2Vin2 G1G2Vin3

   s2C C I sC G I G G I

   Vout1

   Iout

   s2C1C2 sC1G2 G1G2

   VM universal transfer function (1)

   s2C1C2G4Vin1 sC1G2G4Vin2 G1G2G4Vin3

   s2C C sC G G G

   Vout1 1 2 in1 1 3 in2 2 3 in3

   s2C1C2G3 sC1G2G3 G1G2G3

   TIM universal transfer function (9)

   Specializations of the numerator in (8) and (9) result in the

   1 2 1 2 1 2

   TAM universal transfer function (2)

   Specializations of the numerator in (1) and (2) result in the following VM and TAM five universal filtering responses from voltage-output and current-output as below.

   1. Highpass: Vin1 = Vin , and Vin2 = Vin3 = 0 (grounded).

   2. Lowpass: Vin3 = Vin , and Vin1 = Vin2 = 0 (grounded).

   3. Bandpass: Vin2 = Vin , and Vin1 = Vin3 = 0 (grounded).

   4. Notch: Vin1 = Vin3 = Vin , and Vin2 = 0 (grounded).

   5. Allpass: Vin1 = Vin2 = Vin3 = Vin

   Note that it is no need to impose component choice for realizing any filtering responses. Moreover, no inverting or non-inverting amplifiers (for special input signals) are needed in the realizations.

   following CM and TIM five universal filtering responses from current-output and voltage-output as below.

   1. Highpass: Iin1 = Iin , and Iin2 = Iin3 = 0.

   2. Lowpass: Iin3 = Iin , and Iin1 = Iin2 = 0.

   3. Bandpass: Iin2 = Iin , and Iin1 = Iin3 = 0.

   4. Notch: Iin1 = Iin3 = Iin , and Iin2 = 0.

   5. Allpass: Iin1 = Iin2 = Iin3 = Iin, and G1 = G2 = G3

   In (iv), a low-pass notch and a high-pass notch can be obtained by tuning the grounded conductances G1 or G3. Note that it is no need to impose component choice except CM/TIM allpass response. Moreover, no inverting amplifiers (for special input signals) are needed in the realizations.

   Inspection of (1) to (9) show that, in all cases the parameters 0, 0/Q, and Q are given by

   Part II: VM universal biquad filter with one input and four

   0

   G1G2

   C1C2

   (10)

   outputs

   0 G2

   (11)

   Q C2

   Q C2G1

   S

   S

   (12)

   The active and passive sensitivities of 0 and Q are:

   C1G2

   0

   G1 ,G2

   0

   S

   S

   C1 ,C2

   0

   S

   S

   1 ,3 ,12 ,32

   0.5

   (19)

   From (10) and (11), the parametrs 0 and 0/Q can be orthogonally adjustable by tuning the grounded resistor R2 for 0/Q first and then resistor R1 for 0 without disturbing

   S

   S

   Q

   C2 ,G1

   Q C1,G2

   Q

   S

   S

   3,12 ,32

   SQ 0.5

   1

   (20)

   S

   S

   parameter 0/Q. However, (10) and (12) show that the parameters 0 and Q are interactive. The technique to obtain the non-interactive filter parameter control can be suggested as follows [44]. For the fix-valued capacitors, the 0 can be

   SQ 1 (21)

   13

   , , ,

   , , ,

   adjusted arbitrarily without disturbing Q by simultaneously changing resistor R1 and grounded resistor R2 and keeping the G1/G2 constant. On the other hand, the parameter Q can be tuned arbitrarily without disturbing 0 by simultaneously

   SG0,G , , , , ,

   3 4 2 11 13 21 22

   3 4 2 11 13 21 22

   SQ

   0

   23 31 33

   0

   (22)

   (23)

   increasing 1/R1 and grounded R2 and keeping the product

   G1G2 constant.

3. NONIDEAL ANALYSIS

   Taking the tracking errors of the single-output DDCC into account, the relationship of the terminal voltages and currents can be written as: IY1 = IY2 = IY3 = 0, VX = 1(s)VY1 2(s)VY2 + 3(s)VY3, IZ ± = ±(s)IX, where (s) and (s) represent the

   frequency transfers of the internal current and voltage followers of the DDCC. They can be approximated by the first order lowpass functions [33, 42, 45-50]. For frequencies much less than the corner frequencies of the DDCC, all (s) and (s) are real quantities of magnitudes slightly less than one [33, 42, 45-50]. Assuming the circuit works at frequencies much less than the corner frequencies of (s) and (s), namely, (s) =

   = 1i and i (i << 1) denotes the current tracking error of the

   DDCC and (s) = = 1v and v (v << 1) denotes the voltage tracking error of the DDCC. Taking into account the

   non-idealities of the DDCC(1), DDCC(2) and DDCC(3), we obtain the non-idealities as below:

   G3 ,G4 ,2 ,11 ,21 ,22 ,23 ,31 ,33

   From (19) to (23), the proposed general mixed-mode universal biquad filter has low active and passive sensitivities (not larger than unity in absolute value).

4. H-SPICE SIMULATIONS

   The CMOS implementations of the single-output plus-type DDCC are shown in Fig. 2 [42, 49]. Note that, the DDCC has simpler implementation configuration than the FDCCII, VDTA, DDCCTA, DVCCTA, CCCCTA, DPCCII, and

   DXCCDITA. Moreover, the single-output DDCC has no need of applying the realization of current replicas. Therefore, the proposed circuit has the advantage: no need of extra current replicas degrading the final output impedance. To verify the theoretical analysis of the proposed general mixed-mode universal biquad filter, the H-SPICE simulations with the NMOS transistor aspect ratios (W/L=5m/1m) and PMOS transistor aspect ratios (W/L=10m/1m) of Fig. 2, using the TSMC 0.25m process for the proposed circuit of Fig. 1, were

   IY1 IY 2 IY 3 0 ,

   IZ 1IX

   IY1 IY 2 IY 3 0 ,

   IZ 2IX

   IY1 IY 2 IY 3 0 ,

   VX 11VY1 12VY 2 13VY 3 ,

   for DDCC(1) (13)

   VX 21VY1 22VY 2 23VY 3 ,

   for DDCC(2) (14)

   VX 31VY1 32VY 2 33VY 3 ,

   performed with the component values: C1 = C2 = 4pF and R1 =

   R2 = R3 = R4 = 10k, for the general mixed-mode universal filtering responses, leading to a center frequency of f0 = 3.9789MHz and quality factor of Q = 1. Their supply voltages are VDD =Vss = 1.25V, Vb1 = 0.4V, and Vb = 0.41V. Fig.

   3 presents the simulated bandpass, lowpass, highpass, notch, and allpass amplitude-frequency responses of the proposed general mixed-mode biquad filter (operated in TAM with the

   IZ

   3IX

   for DDCC(3) (15)

   normalized transadmittance magnitude = 20 log |10000Iout / Vin| dB due to R = 10 k). Fig. 4 presents the simulated allpass phase-frequency responses of the proposed general mixed-

   The denominator of the non-ideal general mixed-mode

   universal biquad transfer function becomes

   mode biquad filter (operated in TAM). Although not included in this paper, it can be shown that the other modes simulated

   D(s) s2 s

   G213

   C233212

   • G1G2 C1C2131232

   (16)

   results (with the normalized magnitude) are very similar to the above simulated results. As can be seen, there is a close agreement between theory and simulation.

   The 0 and Q of the non-ideal mixed-mode biquad are:

   0

   Q

   G1G2 C1C2131232

   1 31232G1C2

   (17)

   (18)

   13

   1G2C1

   Fig. 2. The CMOS implementation of the single-output plus-type DDCC.

   10

   0

   -10

   magnitude(db)

   magnitude(db)

   -20

   -30

   -40

   -50

   -60

   5 6 7 8

   10 10 10 10

   frequency(Hz)

   Fig. 3. Amplitude-frequency responses of the proposed general mixed-mode universal biquad filter with normalized TAM signals (, simulated BP; ×, simulated LP; , simulated HP; , simulated NH; , simulated AP; and

   , theoretical curve ).

   100

   50

   0

   phase(degree)

   phase(degree)

   -50

   -100

   -150

   -200

   -250

   -300

   -350

   4 5 6 7

   10 10 10 10

   frequency(Hz)

   Fig. 4. Allpass phase-frequency responses of the proposed general mixed- mode universal biquad filter with TAM operation (, simulated phase; and

   ,theoretical curve).

5. CONCLUSIONS

Only using three single-output DDCCs, two grounded capacitors, three grounded resistors, and one floating resistor, to design a general mixed-mode universal biquad filter is

presented in this paper. Filters using active elements with simple implementation configuration, such as single-output DDCCs, have the advantages of the lowest cost, power dissipation, chip area, and noise. Filters using single-output active elements, such as single-output DDCCs, have the advantage: no need of extra current replicas degrading the final output impedance. The proposed circuit can be operated in general mixed-mode (i.e. VM, CM, TAM, and TIM) and can realize all five universal filtering responses (lowpass, highpass, bandpass, notch, and allpass) in the general mixed- mode applications without changing the filter topology. Moreover, the proposed circuit has no need of component matching constraints for VM and TAM all five universal filtering responses. Furthermore, the proposed general mixed- mode circuit still enjoys many main advantages: using two grounded capacitors attractive for integration, no inverting or non-inverting amplifiers for special input signals, no component-value constraints except the CM/TIM allpass responses, high output impedance, and low active and passive sensitivities. H-Spice simulations with TSMC 0.25m process confirm the theoretical predictions.

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