# Voltage-Mode Universal Biquadratic Filter Using Single DVCC

Authors: Jiun-Wei Horng; Zih-Yang Jhao
Journal: ISRN Electronics
 (2013)

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## Abstract

A voltage-mode universal biquadratic filter using a differential voltage current conveyor (DVCC), two capacitors, and two resistors is presented. The proposed circuit has four input terminals and three output terminals and can realize all the standard filter functions, which are lowpass, bandpass, highpass, notch, and allpass filters, without changing the circuit topology. Three simultaneous output filter responses can be obtained from some derived filter types. The proposed circuit employs only one DVCC that simplifies the configuration.


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## Body

## 1. Introduction

Recently, there is a growing interest in designing current-conveyor- (CC-) or current-feedback-amplifier- (CFA-) based active filters. This is attributed to their high signal bandwidths, greater linearity, and larger dynamic range than OPAMP-based ones [1]. Note that a CFA is equivalent to a plus-type second-generation current conveyor (CCII) with a voltage follower [2].Active filters are so widely used in electronic systems, such as telecommunications, radar, consumer electronics, instrumentation systems, and military ordnance, [1, 3]. Many voltage-mode universal biquadratic filters with multi-inputs were proposed [4–10]. From the different combinations of injection of input voltage signals, voltage-mode lowpass, bandpass, highpass, notch, and allpass filters can be obtained without changing the circuit topology. However, these circuits require at least two active components. Moreover, the universal biquadratic circuits in [4, 7–9] require one more active component for the unity-gain inverting input in the allpass realizations. In 2002, Horng et al. proposed a universal biquad with four inputs using three resistors, two capacitors, and one CFA [11]. However, it still requires one more active component for the unity-gain inverting input in the allpass realization. Two voltage-mode universal biquads each with three inputs using two resistors, two capacitors, and one CCII were presented in [12, 13]. However, each of these two circuits requires one more active component for amplifying the input signal in the notch and allpass realizations. A voltage-mode universal biquadratic filter using single plus-type CCII (CCII+), two resistors, and two capacitors was presented in [14]. However, only two standard filter types can be obtained simultaneously in the same circuit.In this paper, a voltage-mode universal biquadratic filter circuit that has four input terminals and three output terminals is presented. It can realize all the standard filter functions, which is, lowpass, bandpass, highpass, notch, and allpass filters, without changing the circuit topology. With respect to the previous single active element universal biquad in Horng et al. [11], the proposed circuit employs less passive components does not need one more active component for the unity-gain inverting input in the allpass realization and the availability of two more simultaneous output filter responses from some derived filter types. With respect to the previous single CCII universal biquads in [12, 13], the proposed circuit does not need one more active component for amplifying the input signal in the notch and allpass realizations. With respect to the previous single CCII+ universal biquad in [14], one more simultaneous output filter response can be obtained from some derived filter types.


## 2. Proposed Circuit

The port relations of a CCII can be characterized byvx=vy,iz=±ix, and iy=0. The CCII has a disadvantage that only one of the input terminals has high-input impedance (the y terminal). The differential difference current conveyor (DDCC) [15] and DVCC [16] are extensions of the CCII and are specially defined to handle differential input voltage signals. Using standard notation, the port relations of a DDCC can be characterized by vx=vy1-vy2+vy3,izk=±ix, and iy1=iy2=iy3=0; the port relations of a DVCC can be characterized by vx=vy1-vy2,izk=±ix, and iy1=iy2=0. Considering the proposed voltage-mode circuit in Figure 1, the output voltage functions can be expressed as
(1)Vo1=((s2C1C2+sC2G1-sC2G2)Vin3+sC1G2Vin2cc+G1G2Vin1+(-sC1G2-G1G2)Vin4(s2C1C2+sC1G2))×(s2C1C2+s(C1G2+C2G1-C2G2)ccc+G1G2s2)-1,Vo2=(-sC2G2Vin3+(s2C1C2+sC1G2)Vin2c+(sC2G1+G1G2)Vin1-sC2G2Vin4(s2C1C2+sC1G2))×(s2C1C2+s(C1G2+C2G1-C2G2)ccc+G1G2s2)-1,Vo3=((-s2C1C2-sC2G1)Vin3+s2C1C2Vin2cc+sC2G1Vin1+(sC1G2-sC2G2+G1G2)Vin4(s2C1C2+sC1G2))×(s2C1C2+s(C1G2+C2G1-C2G2)ccc+G1G2s2)-1.Figure 1
The proposed voltage-mode universal biquad.From (1), we can see that thirteen circuit types can be obtained from Figure 1.(a)
IfVin2=Vin3=Vin4=0 (grounded), Vin1 = input voltage signal, a lowpass filter can be obtained at Vo1 and a bandpass filter can be obtained at Vo3.(b)
IfVin1=Vin3=Vin4=0 (grounded), Vin2 = input voltage signal, a bandpass filter can be obtained at Vo1 and a highpass filter can be obtained at Vo3.(c)
IfVin1=Vin2=Vin4=0 (grounded), Vin3 = input voltage signal and R2=R1, a highpass filter can be obtained at Vo1 and a bandpass filter can be obtained at Vo2.(d)
IfVin1=Vin2=Vin3=0 (grounded), Vin4 = input voltage signal and C2=C1, a bandpass filter can be obtained at Vo2 and a lowpass filter can be obtained at Vo3.(e)
IfVin2=Vin4=0 (grounded), Vin1=Vin3 = input voltage signal and R2 = R1, a notch filter can be obtained at Vo1, a lowpass filter can be obtained at Vo2, and a highpass filter can be obtained at Vo3.(f)
IfVin2=Vin4=0 (grounded), Vin1=Vin3 = input voltage signal and 2C2G2=C1G2+2C2G1, an allpass filter can be obtained at Vo1 and a highpass filter can be obtained at Vo3.(g)
IfVin2=Vin3=0 (grounded), Vin1=Vin4 = input voltage signal and R2=R1, a bandpass filter can be obtained at Vo1 and a lowpass filter can be obtained at Vo2.(h)
IfVin1=Vin4=0 (grounded), Vin2=Vin3 = input voltage signal and C2=C1, a highpass filter can be obtained at Vo2 and a bandpass filter can be obtained at Vo3.(i)
IfVin1=Vin3=0 (grounded), Vin2=Vin4 = input voltage signal and C2=C1, a lowpass filter can be obtained at Vo1, a highpass filter can be obtained at Vo2 and a notch filter can be obtained at Vo3.(j)
IfVin1=Vin3=0 (grounded), Vin2=Vin4 = input voltage signal and 2C2G2=2C1G2+C2G1, a lowpass filter can be obtained at Vo1 and an allpass filter can be obtained at Vo3.(k)
IfVin1=Vin2=0 (grounded), Vin3=Vin4 = input voltage signal, a bandpass filter can be obtained at Vo2.(l)
IfVin2=0 (grounded), Vin1=Vin3=Vin4 = input voltage signal, C2=C1, and R2=2R1, a highpass filter can be obtained at Vo1 and a lowpass filter can be obtained at Vo2.(m)
IfVin1=0 (grounded), Vin2=Vin3=Vin4 = input voltage signal, R2=R1, and C2=0.5C1, a highpass filter can be obtained at Vo2 and a lowpass filter can be obtained at Vo3.Thus, the circuit is capable of realizing all voltage-mode filter functions. Note that three standard filter responses can be obtained simultaneously from the circuit types (e) and (i).


## 3. Nonideality Analysis of the DVCC

Taking into consideration the DVCC nonidealities, the port relations of DVCC can be expressed as(2)vx=α1vy1-α2vy2,iz=±βkix,
where βk=1-εki and εki(|εki|≪1) denotes the current tracking error from x terminal to zk terminal of a DVCC, α1=1-εv1 and εv1(|εv1|≪1) is the input voltage tracking error from y1 terminal to x terminal of a DVCC, and α2=1-εv2 and εv2(|εv2|≪1) is the input voltage tracking error from y2 terminal to x terminal of a DVCC. The denominator of the nonideal output voltage function for Figure 1 becomes
(3)D(s)=s2C1C2+s(C1G2α2β2+C2G1-C2G2α1β1)+G1G2α2β2.
The resonance angular frequency and quality factor are obtained by
(4)ωo=G1G2α2β2C1C2,Q=C1C2G1G2α2β2C1G2α2β2+C2G1-C2G2α1β1.
The active and passive sensitivities are low and obtained by
(5)SG1,G2,α2,β2ωo=-SC1,C2ωo=12,SC1Q≅C2G1-C1G2-C2G22(C1G2+C2G1-C2G2),SC2Q≅C1G2+C2G2-C2G12(C1G2+C2G1-C2G2),SG1Q≅C1G2-C2G1-C2G22(C1G2+C2G1-C2G2),SG2Q≅C2G1+C2G2-C1G22(C1G2+C2G1-C2G2),Sα1,β1Q≅C2G2C1G2+C2G1-C2G2,Sα2,β2Q≅C2G1-C1G2-C2G22(C1G2+C2G1-C2G2).


## 4. Simulation Results

HSPICE simulations were carried out to demonstrate the feasibility of the proposed circuits using 0.18μm, level 49 MOSFET from TSMC. The DVCC was realized by the CMOS implementation in Figure 2 [17] with the NMOS and PMOS transistor aspect ratios W/L=4.5u/0.9 u and W/L=9u/0.9 u, respectively. The supply voltages are V+=+0.9V,V-=-0.9V, and Vb=-0.38V.Figure 2
The CMOS DVCC implementation.Figures3(a)–3(c) represent the simulated frequency responses for the notch (Vo1), lowpass (Vo2), and highpass (Vo3) filters of Figure 1, respectively, designed with Vin2=Vin4=0 (grounded), Vin1=Vin3= input voltage signal, Q=1, and fo=318.3kHz: C1=C2=50pF and R1=R2=10kΩ.Simulated frequency responses of Figure1 designed with Vin2=Vin4=0 (grounded), Vin1=Vin3 = input voltage signal, C1=C2=50pF, and R1=R2=10kΩ: (a) notch filter (Vo1), (b) lowpass filter (Vo2), and (c) highpass filter (Vo3).
(a)
(b)
(c)Figures4(a) and 4(b) represent the simulated frequency responses for the allpass (Vo1) and highpass (Vo3) filters of Figure 1, respectively, designed with Vin2=Vin4=0 (grounded), Vin1=Vin3 = input voltage signal, Q=1.414, and fo=450.16kHz: C1=C2=50pF,R1=10kΩ, and R2=5kΩ.Simulated frequency responses of Figure1 designed with Vin2=Vin4=0 (grounded), Vin1=Vin3= input voltage signal, C1=C2=50pF,R1=10kΩ, and R2=5kΩ: (a) allpass filter (Vo1), and (b) highpass filter (Vo3).
(a)
(b)


## 5. Conclusions

In this paper, a new voltage-mode universal biquadratic filter has been presented. The new voltage-mode circuit with four input terminals and three output terminals employs two capacitors, two resistors, and one DVCC. The new circuit has the features of using only four passive components and does not need one more active component in the realizations of notch and allpass filters and the availability of three simultaneous output filter responses from some derived filter types (types (e) and (i)).



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*Source: 125746-2013-03-10.xml*