# Voltage Mode Universal Biquad Using CCCII

Authors: Ashish Ranjan; Sajal K. Paul
Journal: Active and Passive Electronic Components
 (2011)

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## Abstract

This paper proposes a multi-input single-output (MISO) second-order active-C voltage mode (VM) universal filter using two second-generation current-controlled current conveyors (CCCIIs) and two equal-valued capacitors. The proposed circuit realizes low pass, band pass, high pass, all pass, and notch responses from the same topology. The filter uses-minimum number of passive components and no resistor which is suitable for IC Design. The filter enjoys low-sensitivity performance and exhibits electronic and orthogonal tunability of pole frequency (ω0) and quality factor (Q0) via bias current of CCCIIs. PSPICE simulation results confirm the theory.


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## Body

## 1. Introduction

Analog filters are very important signal processing circuits, which find wide applications in communication, instrumentation, and control engineering [1]. During last one decade or so, there has been substantial emphasis to realize multiple-input single-output (MISO) voltage mode universal filter [2–9] as they permit realization of multiple filter functions with the same topology, and hence there is a possibility to design filters with less number of active and passive components. It also brings versatility and simplicity to the design of circuits and systems and drops down the cost. The investigation of the recently reported literature on MISO voltage mode filter [2–9] reveals the following:(i)
the use of excessive number (three or more) of current conveyors in [2–4, 6, 8],(ii)
the use of excessive passive components in [9],(iii)
requireing complex and different matching constraints in [5, 9] for all pass and notch responses, hence not suitable for IC implementation,(iv)
Not completely extendible from second-generation current conveyor (CCII) to CCCII-based topology in [2–4, 6, 8, 9]; hence, resistors cannot be eliminated from these topologies,(v)
the absence of electronic tunability of filter parameters in [2–4, 6, 8, 9],(vi)
electronic tunability is possible in [7] if resistance R1 and R2 in [7] are replaced by the addition of some active devices such as JFET,(vii)
input impedance is low for all the responses in [9], which is not desirable for VM filter. Hence, additional circuitry will be required for cascading,(viii)
no orthogonal control of pole frequency (ω0) and quality factor (Q0) in [9].It is well accepted that the configurations possessing inbuilt electronic tunability [10] property can easily be adapted for signal processing in integrated circuits environment. The basic second-generation current conveyor (CCII) does not have in built tuning property, whereas second-generation current-controlled current conveyor (CCCII) has, owing to the adjustability of intrinsic resistance at port X of CCCII by bias current [10]. In this paper, an MISO universal voltage mode filter based on CCCII is presented. The proposed filter uses two CCCIIs and two equal-valued capacitors and no resistor. It permits to obtain all responses of universal filter such as low pass, band pass, high pass, notch, and all pass from the same topology. Although it uses two CCCIIs, but it is free from most of the shortcomings discussed above. The PSPICE simulation results verify the theoretical values.


## 2. Circuit Description

The circuit symbol of the double-output second-generation current-controlled conveyor (DOCCCII) is shown in Figure1. The port relationship of a DOCCCII is given as follows:(1)IY=0,VX=VY+IX|RX|,IZ±=±IX,
where the positive and negative sign defines a positive and a negative CCCII, respectively. Here, RX, the intrinsic series input resistance of the conveyor at X port, is electronically tunable via I0 of the CMOS-based CCCII shown in Figure 2 and RX may be defined as [11](2)Rx=1gm2+gm4,gmi=2βiI0(i=2,4),βi=ε0εinsμiWitoxLi,
where gm2 and gm4 are the transconductances of M2 and M4, respectively. The proposed voltage mode universal filter circuit is shown in Figure 3.Figure 1
Block diagram of DOCCCII.Figure 2
Internal structure of DOCCCII.Figure 3
Voltage mode universal filter.Analyzing the circuit as shown in Figure3, we get the transfer function as(3)Vout=N(S)D(S),
where(4)N(S)=Vin1+SCRX1Vin2-SCRX1Vin3+(S2C2RX1RX2+SCRX1)Vin4,D(S)=S2C2RX1RX2+SCRX1+1.
Table 1 shows the availability of each filter response and corresponding selection of Vin1, Vin2, Vin3, and Vin4. It may be noted that there is no component-matching constraint for obtaining any filter response.Table 1
TheVin1, Vin2, Vin3, and Vin4 values selection for each filter function response.
Filter responseInputsV0Vin1Vin2Vin3Vin4Low-pass filter1000High-pass filter0011Band-pass filter0010All-pass filter1−111Notch filter1011Thus, the proposed topology can be viewed as four-input single-output voltage mode universal filter. The filters are characterized by(5)ω0=1C1RX1RX2,ω0Q0=1CRX2,Q0=RX2RX1.
The above equation reveals that ω0 can be independently controlled keeping Q0 unchanged by simultaneously changing RX1 and RX2 and keeping quotient RX1/RX2 constant for all responses. Similarly, Q0 can be independently controlled keeping ω0 unchanged by simultaneously changing RX1 and RX2 and keeping product RX1RX2 constant for all responses. The resistances RX1 and RX2 can easily be adjusted to the required values by externally controlling the bias currents (I01 and I02) of DOCCCII/CCCII. The pole frequency (ω0) can also be adjusted electronically by controlling bias current (I01) of DOCCCII without disturbing ω0/Q0. The passive sensitivity of ω0 and Q0 is given as(6)SRX1ω0=SRX2ω0=-12,SCω0=-1,SCQ0=0,SRX1Q0=-SRX2Q0=-12.
As the value of sensitivities are within unit, the sensitivity performance is low for the proposed topology.


## 3. Simulation Results

The proposed voltage mode second-order universal filter circuit is simulated with PSPICE using 0.35μm AMS CMOS-based CCCII circuit given in Figure 2 [11] with supply voltage of ±2.5 volts and aspect ratio of transistors as given in Table 2.Table 2
MOS dimensions used in the circuit.
TransistorsW (μm)L (μm)M1, M220.35M3, M460.35M5, M6, M7302M8, M9102M10, M11, M14, M15101M12, M13, M16, M17301The filter is designed for a pole frequency off0=1.4 MHz and quality factor Q0=1 by using C=0.5 nF and I01=I02=200 μA. Figures 4, 5, and 6 show the simulation and theoretical results for low-pass, high-pass, and band-pass responses, respectively. It is evident that the simulated results agree well with the theoretical values. The gain and phase responses of notch and all-pass filters are shown in Figures 7 and 8, respectively. To judge the quality of the output, total harmonic distortion (%THD) is obtained for the band-pass filter as shown in Figure 9. The %THD is well within the acceptable limit of 5% [12]. Response as shown in Figure 9 reveals that the output is of good quality.Figure 4
Low-pass filter response.Figure 5
High-pass filter response.Figure 6
Band-pass filter response.Figure 7
Notch-filter response.Figure 8
All-pass filter response.Figure 9
Variation of %THD of output voltage versus input voltage.


## 4. Conclusions

In this paper, a new second-order voltage mode universal filter topology is proposed. The topology uses single dual-output current-controlled current conveyor (DOCCCII), a current controlled current conveyor (CCCII), and two equal-valued capacitors. The proposed filter structure uses minimum number of passive components and no resistor. It removes most of the shortcomings of the topologies in [2–9].



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*Source: 439052-2011-06-05.xml*