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One-Input Five-Output Voltage-Mode Universal Biquadratic Filter Using Single-Ended 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 & somyot@telecom.kmitl.ac.th

Abstract—This paper presents a new high-input impedance electronically tunable voltage-mode universal filter with one input and five outputs employing eight single-ended operational transconductance amplifiers and two grounded capacitors. The proposed circuit can simultaneously realize voltage-mode low-pass, band-pass, high-pass, band-stop and all-pass filter without inverting-type input signals and component-matching conditions requirements. The natural frequency and the quality factor can be orthogonally controlled. The natural frequency can also be electronically tuned. The active and passive sensitivities of the circuit are low. Simulation results are provided to demonstrate the theoretical analysis.

Keywords–biquadratic filter; voltage-mode circuit; operational transconductance amplifier; analog signal processing

I. INTRODUCTION 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 [1].

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 FM stereo demodulation, touch-tone telephone tone decode, cross-over network used in a three-way high-fidelity loudspeaker [2]. As a result, a number of universal filters based on different design techniques have been developed in the literature; see, for example, [1]-[21]. In [2]-[8], universal filters using current conveyors were proposed. However, these circuits suffer from the lack of the electronic tunability. Several universal biquad filters using OTAs were proposed in [9]-[21]. The second-order voltage-mode active filters with high-input impedance are of great interest because several cells of this kind can be directly connected in cascade to implement higher order filters [7], [8]. Beside, the use of grounded capacitors is very beneficial from the point of view of IC implementation [22]. Considering the reported single input and multiple outputs (SIMO) universal filters in [9]-[17], the circuits in [9]-[14]

employing grounded capacitors, but these structures do not provide five standard filtering functions. While the circuit in [15] provides five standard filtering functions and enjoys low sensitivities, but it uses floating capacitor. The circuits in [16], [17] uses only active devices, but they use two kinds of active components (OTA and op-amp). Compared with multiple-input universal filters [18]-[20], the SIMO universal filters can simultaneously realize LP, BP, HP, BS and AP filter without changing the connection of the input signals and also without imposing any restrictive conditions on the input signals which of special interests in this paper.

Therefore, a voltage-mode universal biquad filter with one input and five outputs using eight single-ended OTAs and two grounded capacitors is presented in this paper. The proposed filter can realize voltage-mode LP, BP, HP, BS and AP filters from the same configuration without inverting-type input signals and component-matching condition requirements. Furthermore, the proposed circuit provides high input impedance which is directly connected in cascade to implement higher order filters. The natural frequency and the quality factor can be orthogonally controlled. Also the natural frequency can be electronically tuned. Simulation results using PSPICE program are given to show the performance of the filter and verify the theory.

II. CIRCUIT DESCRIPTION

Figure 1. Circuit symbol of OTA.

Figure 2. The addition/subtraction circuit using OTAs.

978-1-4673-2493-9/12/$31.00 ©2012 IEEE 430

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Figure 3. Proposed voltage-mode universal filter using single-ended OTAs.

The circuit symbol of the OTA is shown in Fig. 1. The characteristic of ideal OTA can be described by

( )21mo VVgI −= (1)

where 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.

Fig. 2 shows the addition/subtraction using two OTAs. Referring to [23], this circuit may be called a “pool circuit”. Assuming OTA1 and OTA2 are identical, the voltage Vo can be expressed as

321o VVVV +−= . (2)

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

The proposed universal filter is shown in Fig. 3. It consisted of only eight single-ended OTAs and two grounded capacitors. It should be noted that the use of grounded capacitors is very suitable for IC implementation [22]. The voltage transfer functions of Fig. 3 can be expressed as

m2m1m21212

m2m1

in

o1

gggsCCCsgg

VV

++= (3)

m2m1m21212

m21

in

o2

gggsCCCsgsC

VV

++= (4)

m2m1m21212

m2m1m21212

in

o3

gggsCCCsgggsCCCs

VV

+++−−= (5)

m2m1m21212

m2m1212

in

o4

gggsCCCsggCCs

VV

+++= (6)

m2m1m21212

212

in

o5

gggsCCCsCCs

VV

++= . (7)

Thus, the proposed filter can realize the LP, BP, AP, BS and HP filters at the node voltages Vo1, Vo2, Vo3, Vo4 and Vo5, respectively. The filter provides high impedance input terminal

which it enables easy cascadability for high-order filter applications. It should be noted that no inverting-type input signals and on component-matching conditions requirements are imposed for realizing five types of standard biquadratic function. The natural frequency (ωo) and the quality factor (Q) are given by

21

m2m1o CC

ggω = (8)

2m1

1m2

CgCgQ = . (9)

Letting gm1=gm2=gm, the circuit parameters ωo and Q are simply rewritten, respectively, as

21mo CC

1gω = (10)

2

1

CCQ = . (11)

It is evident from equations (10) and (11) that the parameter ωo can be tuned by changing the transconductance gain gm and parameter Q can be given by setting (C1/C2)1/2. This means that the parameters ωo and Q can be orthogonally controlled. The parameters ωo and Q sensitivities are given by

5.0SS o

2

o

1

ωC

ωC −== , 1S o

m

ωg = (12)

5.0SS QC

QC 21

=−= . (13)

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

The CMOS implementation of single-ended OTA can be shown in Fig. 4. It uses only four MOS transistors and one current source. Assuming transistors M1 and M2 are matched and operated in saturation region, the transconductance gain gm can be expressed by

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Figure 4. CMOS implementation of single-ended OTA.

( ) abcoxm I W/LμCg = (8)

where Iabc is the bias current, μ 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 gain gm can be tuned by varying the biasing current Iabc.

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

simulations. The OTAs given in Fig. 4 were realized by using 0.35 μm CMOS process from TSMC and W/L = 5 μm/ 1 μm and W/L = 10 μm/ 1 μm for nMOS and pMOS devices, respectively [21]. The power supplies are selected as VDD = −VSS = 1.65 V. The biasing currents for OTA3 to OTA8 are chosen as 20 μA. As an example design, the capacitors C1 = C2 = 10 pF and the biasing currents Iabc1 = Iabc2 = 50 μA (gm = 181.97 μS) 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 LP, BP, BS and HP of the proposed filter are shown in Fig. 5. In this figure, the pole frequency of 2.84 MHz and the power consumption of 0.8 mW are obtained.

Gai

n, d

B

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

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

Gai

n, d

B

Figure 7. Simulated frequency responses of BP filter when Iabc is varied.

Fig. 6 shows the simulated frequency responses of the gain and phase characteristics of the AP filter. It is observed from Figs. 5 and 6 that the proposed filter performs five standard biquadratic filtering functions well. Fig. 7 shows the simulated a BP filter response when the biasing currents Iabc (i.e., Iabc=Iabc1=Iabc2) were simultaneously adjusted for the values of 1, 5, 20 and 100 μA while keeping C1 = C2 = 10 pF. This result is confirmed by equation (10).

In order to test the input dynamic range of the proposed filter, the simulation has been repeated for a sinusoidal input signal at fo = 2.84 MHz. Fig. 8 shows that the input dynamic range of the BP response with Iabc1=Iabc2= 50 μA and C1 = C1 = 10 pF, which extends up to amplitude of 250 mV (peak) without signification distortion. In this figure, total harmonic distortion (THD) of 3.6 % is obtained.

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Time, s28.0 28.4 28.8 29.2 29.6 30.0

-300

-200

-100

0

100

200

300

inputoutput

Figure 8. The input and output waveforms of the BP response for

a 2.84 MHz sinusoidal input voltage of 250 mV (peak).

IV. CONCLUSIONS In this paper, a new electronically tunable single input and

five outputs voltage-mode universal filter using eight OTAs and two grounded capacitors is proposed. It has the following properties: (i) It uses grounded capacitor which is suitable for IC implementation. (ii) It can realize the LP, BP, HP, BS and AP filter responses without inverting-type input signals and component-matching conditions requirements. (iii) The parameter ωo and Q can be orthogonally controlled. (iv) The parameter ωo can be electronically tuned. (v) It provides low active and passive sensitivities. (vi) The proposed structure is suitable for IC implementation as either a CMOS technology or a bipolar technology. PSPICE simulators are given to demonstrate the effectiveness of our schemes. The simulation results obtained were found to be in good agreement with the theory.

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