Mixed-Mode Universal Filter Using OTAs

Montree Kumngern and Somyot Junnapiya Department of Telecommunications Engineering, Faculty of Engineering,

King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand E-mail: kkmontre@kmitl.ac.th

Abstract—This paper presents an electronically tunable versatile biquadratic filter. Unlike the typical voltage-mode and current-mode filter, the proposed filter can realize voltage-mode, current-mode, transconductance-mode and transresistance-mode transfer functions without changing the circuit topology, called a mixed-mode filter. The proposed structure employs six operational transconductance amplifiers, two grounded capacitors and one external resistor that provides following advantages: realization of low-pass, band-pass, high-pass, band-stop and all-pass filter responses; orthogonal control of the natural frequency and the quality factor; employment of grounded capacitors which is more suitable for integrated circuit implementation; low active and passive sensitivities. Simulation results are also given to confirm the presented theory.

Keywords-biquad filter; mixed-mode circuit; analog signal processing; operational transconductance amplifier

I. INTRODUCTION The universal biquad filters are defined as second-order

filter topologies, where the following five standard transfer functions are available; i.e., low-pass (LP), band-pass (BP), high-pass (HP), band-stop (BS) and all-pass (AP), which plays an important role in the fields of analog signal processing. They could be applied in the implementation of phase-locked loop frequency modulation stereo demodulation, touch-tone telephone tone decode, cross-over network used in a three-way high-fidelity loudspeaker [1], [2]. As a result, a number of universal filters based on different design techniques have been developed in the literature; see, for example, [2]-[17]. In [2]-[6], universal filters using current conveyors were proposed. However, these circuits suffer from the lack of the electronic tunability.

Operational transconductance amplifiers (OTAs) have received considerable attention because of the advantage of some advantages in the circuit design such a high potential of electronic tunability, a wide tunable range, a wide signal bandwidth and powerful ability to generate various circuits. Moreover, OTA-based circuits require no resistors and, therefore, are highly suitable for integrated circuit (IC) implementation [15]. Beside, the active filters employing grounded capacitors are very beneficial from the point of view of IC implementation [18]. Several universal biquad filters using OTAs were proposed [7]-[16]. Considering the reported universal filters in [7]-[12], the circuits in [7]-[11] use grounded capacitors, but these structures do not provide five standard filtering functions. While the circuit in [12] provides

five standard filtering functions and enjoys low sensitivities, but it uses floating capacitor. The circuits in [13], [14] uses only active devices, but they use two kinds of active components (OTA and op-amp). The active filters using low active components are more suitable for IC implementation and they also reduced the power consumption and the area of chip when they build in form IC. Recently, mixed-mode universal filters using OTAs were proposed [16], [17]. However, only one standard filter function can be obtained in each filter realization.

In this paper, a mixed-mode universal biquadratic filter using six OTAs, two grounded capacitors and one resistor with one input and seven output or two inputs and eight outputs is presented. The use of grounded capacitors makes the proposed circuit suitable for IC implementation. The proposed filter can realize voltage-mode, current-mode, transconductance-mode, transresistance-mode LP, BP, HP, BS and AP filters from the same configuration. The natural frequency ( o) and the quality factor (Q) can be orthogonally controlled by setting the circuit components. The natural frequency can also be controlled electronically by changing the transconductance values of OTAs. The active and passive sensitivities of the circuit are low. PSPICE simulation results are performed to confirm the theoretical analysis.

II. PROPOSED CIRCUIT The circuit symbol of the operational transconductance

amplifier (OTA) is shown in Fig. 1. The characteristic of ideal OTA can be described by

21mo VVgI (1)

when Io is the output current, gm is the transconductance gain, and V1 and V2 are the non-inverting voltage and the inverting input voltage, respectively.

Figure 1. Circuit symbol of OTA.

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Proceedings of the 2012 IEEE International Conference onCyber Technology in Automation, Control and Intelligent Systems

May 27-31, 2012, Bangkok, Thailand

Figure 2. The addition/subtraction circuit using OTAs.

Fig. 2 shows the addition/subtraction circuit using OTAs. Referring to [19], this circuit may be called a “pool circuit”. Assuming OTA1 and OTA2 are identical, the voltage Vo can be expressed as

321o VVVV

Thus, the circuit in Fig. 2 can be operated as the addition and subtraction voltage signals.

The proposed mixed-mode universal filter is shown in Fig. 4. It consisted of six OTAs, two grounded capacitors and one resistor. Since all the capacitors are grounded, thus the circuit is beneficial to an IC implementation [18]. If Iin1=Iin2=0, Vin is applied by the input signal, the transfer functions can be expressed as

m2m11m2m111212

m2m11

in

o1

ggGggsCGCCsggG

VV (3)

m2m11m2m111212

m211

in

o2

ggGggsCGCCsgGsC

VV (4)

m2m11m2m111212

1212

in

o3

ggGggsCGCCsGCCs

VV (5)

m2m11m2m111212

m2m111212

in

o4

ggGggsCGCCsggG GCCs

VV (6)

m2m11m2m111212

m2m11m2111212

in

o5

ggGggsCGCCsggGgGsCGCCs

VV (7)

m2m11m2m111212

m2m111

in

o1

ggGggsCGCCsggGsC

VI (8)

m2m11m2m111212

m21212

in

o2

ggGggsCGCCsgGCCs

VI

. (9)

Thus, the voltage-mode LP, BP, HP and BS filters are obtained at the node voltages Vo1, Vo2, Vo3 and Vo4, respectively, and the voltage-mode AP filter is obtained at the node voltage Vo5 if G1=gm3, where G1=1/R1. Also the transconductance-mode BP and HP filters can be obtained at the terminals Io1 and Io2, respectively.

Figure 3. Proposed mixed-mode universal filter using OTAs.

If Vin=0 (grounded), Iin2=0 and Iin1 is applied by input signal current, the transresistance-mode transfer functions can be expressed as

m2m11m2m112112

m2m1

in1

o1

ggGggsCCCGsgg

IV (10)

m2m11m2m112112

m21

in1

o2

ggGggsCCCGsgsC

IV (11)

m2m11m2m112112

212

in1

o3

ggGggsCCCGsCCs

IV (12)

m2m11m2m112112

m2m11212

in1

o4

ggGggsCCCGsggGCCs

IV (13)

m2m11m2m112112

m2m11m21212

in1

o5

ggGggsCCCGsggGgsCCCs

IV (14)

Also if Vin=0 (grounded), Iin1 and Iin2 are the input signal currents, the current-mode transfer functions can be expressed as

120

Iabc

V2 V1

M1 M2

+Io

MpMp Mp

VSS

VDD

Mp

Mn Mn

Mp

Mn

(a)

-Io

V1 V2

M1 M2

IoMp Mp

Iabc

VSS

VDD

(b)

Mp

Mn

Figure 4. CMOS implementation of OTAs for Fig. 3; (a) OTA1-OTA2,

and (b) OTA3-OTA6

m2m11m2m112112

m2m11

in1

o1

ggGggsCCCGsggsC

II (15)

m2m11m2m112112

2112

in1

o2

ggGggsCCCGsCCGs

II (16)

m2m11m2m112112

m2m112112

in1

o3

ggGggsCCCGsggGCCGs

II (17)

m2m11m2m112112

m2m11m2m112112

in

o3o1

ggGggsCCCGsggGggsC CCGs

III (18)

m2m11m2m112112

m2m11

in

o3o2

ggGggsCCCGsggG

III (19)

Thus, the current-mode BP, HP and BS filters are obtained at the terminals Io1, Io2 and Io3, respectively, when Iin1 is applied by input signal current. Also the current-mode AP filter is obtained at Io1+Io3 when Iin1=Iin2=Iin. The current-mode LP filter is obtained at Io2+Io3 when Iin1=Iin2=Iin where G1=gm2. Therefore, from equations (3)-(19), the proposed filter can be

realized current-mode, voltage-mode, transconductance-mode, transresistance-mode transfer functions and hence the named “mixed-mode filter”. The natural frequency ( o) and the quality factor (Q) are given by

21

m2m1o CC

gg (20)

2m2m1

21 Cgg

CGQ . (21)

From equations (20)-(21), the parameter o can be tuned by changing the transconductance values gm1 and gm2 when C1=C2 while the parameter Q can be given by setting G1 when C1=C2 and gm1=gm2. Thus, the proposed universal filter has orthogonal controlling capability for the circuit parameters Q and o. The parameters o and Q sensitivities are given by

5.0SS o

2

o

1 CC , 5.0SS o

m2

o

m1 gg (22)

5.0SSSS Qg

Qg

QC

QC m2m112

, 1S o

1G . (23)

The active and passive sensitivities are within unity in magnitude. Thus, the active and the passive sensitivities are low.

The CMOS implementations of OTAs used in Fig. 3 are shown in Fig. 4. Assuming transistors M1 and M2 are matched and operated in saturation region, the transconductance gain (gm) can be expressed by

abcoxm I W/LCg (24)

where Iabc is the bias current, is the carrier mobility, Cox is the gate oxide capacitance per unit area, W and L are the channel width and length, respectively. Thus, the transconductance value can be controlled by the biasing current Iabc.

III. SIMULATION RESULTS The proposed circuit of Fig. 3 was simulated using PSPICE

simulations. The CMOS OTAs given in Fig. 4 were realized by using 0.35 m CMOS process from TSMC and W/L = 5 m /1

m and W/L = 10 m / 1 m for nMOS and pMOS transistors, respectively [20]. The power supplies are selected as VDD =

VSS = 1.65 V. The biasing currents for OTA3 to OTA8 are chosen as 20 A. As an example design, the capacitors C1 = C2 = 10 pF, R1 = 5.5 k and the biasing currents Iabc1 = Iabc2 = 50

A (gm = 181.97 S) are given. This setting has been designed to obtain the LP, BP, HP, BS and AP filter responses with fo 2.89 MHz and Q 1. The simulated responses of the HP, BP, BS and LP of the proposed filter are shown in Fig. 5 when Vin is applied by input signal. In this figure, the pole frequency of 2.87 MHz and the power consumption of 1.57 mW are obtained. Fig. 6 shows the simulated frequency responses of the gain and phase characteristics of the AP filter. It is observed from both figures that the proposed filter performs five standard biquadratic filtering functions well.

121

Gai

n, d

B

Figure 5. Simulated LP, BP, HP and BS responses.

Frequency, MHz0.01 0.1 1.0 10 100

-40

-20

0

20

40

-400

-300

-200

-100

-0

Gain, dB Phase, degree

gainphase

Figure 6. Simulated gain and phase responses of AP filter.

IV. CONCLUSIONS In this paper, a new electronically tunable mixed-mode

universal filter using six OTAs, two grounded capacitors and one resistor is proposed. It has the following properties: (i) realization of voltage-mode, current-mode, transconductance-mode, transresistance-mode without changing circuit topology, (ii) simultaneous realization of the LP, BP, HP, BS and AP filter responses, (iii) no need to employ inverting-type input signals, (iv) employment of two grounded capacitors, (v) orthogonal control of the parameters o and Q, (vi) electronic control of the parameter o, (vii) provision of low active and passive sensitivities.

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