Switched Capacitor Biquad Filter Using CDTA ()

Meeti Dehran, Indu Prabha Singh, Kalyan Singh, Rabindra Kumar Singh

Department of Electrical and Electronic Engineering, Kamla Nehru Institute of Technology (KNIT), Sultanpur, India.

Department of Physics and Electronics, R.M.L. University, Faizabad, India.

epartment of Electronics and Communications Engineering, Shri Ramswaroop Memorial Group of Professional Colleges (SRMGPC), Lucknow, India.

**DOI: **10.4236/cs.2013.46057
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Department of Electrical and Electronic Engineering, Kamla Nehru Institute of Technology (KNIT), Sultanpur, India.

Department of Physics and Electronics, R.M.L. University, Faizabad, India.

epartment of Electronics and Communications Engineering, Shri Ramswaroop Memorial Group of Professional Colleges (SRMGPC), Lucknow, India.

A switched capacitor biquad filter using current differencing transconductance amplifier (CDTA) is presented in this paper. The proposed circuit employs only one CDTA, two virtually grounded capacitors and one switched capacitor. It is a resistorless circuit, so it is beneficial to IC implementation in terms of space consideration. The proposed circuit is a second order single input multiple output (SIMO) current-mode filter. This filter can simultaneously realize all basic filter functions high pass, low pass and band pass responses without any component-matching conditions. All the active and passive sensitivities are low. The natural angular frequency (*ω*_{0}) and quality factor (*Q*) of proposed filter can be electronically controlled. Owing to current mode operation it consumes less power. PSPICE simulation results are used to verify the theoretical analysis.

Keywords

Current Differencing Transconductance Amplifier (CDTA); Biquad Filter; Current-Mode Circuit

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Dehran, M. , Singh, I. , Singh, K. and Singh, R. (2013) Switched Capacitor Biquad Filter Using CDTA. *Circuits and Systems*, **4**, 438-442. doi: 10.4236/cs.2013.46057.

1. Introduction

Since the introduction of the current differencing transconductance amplifier (CDTA) in 2003, it has been acknowledged to be a versatile current-mode active building block in designing analog circuits [1]. This device with two current inputs and two kinds of current output provides an easy implementation of current-mode active filters [2]. It also exhibits the ability of electronic tuning by the help of its transconductance gain (g_{m}). All these advantages together with its current-mode operation nature make the CDTA a promising choice for realizing the current-mode filters. As a result, a variety of CDTA applications has also been considered by various researchers.

The work in [2] introduces universal biquad filters which can simultaneously realize lowpass (LP), highpass (HP) and bandpass (BP) current responses. However, they suffer from the use of a large number of passive components. On the other hand, a lowpass filter circuit using CDTAs is proposed in [3]. However, this configuration is restricted for only lowpass transfer function design and it also requires an additional passive resistor. In [4], the CDTA-based current-mode single-input threeoutput filter is reported. It permits the realization of only three basic filter functions LP, BP, and HP responses simultaneously at high impedance output. While the circuit proposed in [5] requires four CDTAs, and an external passive resistor for its realization. In [6], a universal current-mode biquad, providing four basic transfer functions (low-pass, band-pass, high-pass, and band-reject) simultaneously is described. However, this circuit labors with the following drawbacks: 1) only the output current of the low-pass section flows to an independent load. All the remaining output currents flow through the working impedances and thus they cannot be directly utilized without negative influence on the filter behavior. 2) The additional resistor R_{3} does not represent any increase of the filter versatility and thus it can be removed from the filter structure without decreasing its functionality. The paper published in [7] employed two CDTA to perform all three basic filter functions. Second order filter using single CDTA is published in [8,9]. The paper proposed in [8] provides only BP and HP outputs or LP and BP responses after interchanging RC network to CR. The filter introduced in [9] uses single CDTA and provides several transfer functions depending on the position of applied input current, but at low frequency.

In this paper, a current-mode filter, consisting of a single CDTA, two grounded capacitors and one switched capacitor is used to realize the filter. It provides the advantage of using switched capacitor instead of a resistor that is beneficial to IC implementation in terms of space consideration. The proposed circuit can be used as high pass, low pass, and band pass filter. PSPICE simulation results are used to verify the performance of the proposed circuit.

2. CDTA

Digital signal processing is becoming increasingly more powerful while advances in IC technology provide compact efficient implementation of its algorithms on silicon chips. Although many types of signal processing have indeed moved to digital domain, analog circuits are fundamentally necessary in many of today’s complex, high performance systems. This is caused by the reality that naturally occurring signals are analog. Therefore analog circuits act as a bridge between the real world and digital systems. In the beginning, operational amplifiers were the main building blocks for analog circuit design. Unfortunately, their limited performance such as bandwidth, slew-rate etc. led the analog designer to search for other possibilities and other building blocks. As a result, new current-mode active building blocks such as Operational Transconductance Amplifiers (OTA), second generation Current Conveyors (CCII), Current-Feedback Op-Amps (CFOA), Differential Voltage Current Conveyor (DVCC), Differential Difference Current Conveyor (DDCC), third-generation Current Conveyor (CCIII), Dual X Current Conveyors (DXCCII), Current Controlled Current Conveyors (CCCII), Current Differencing Buffered Amplifier (CDBA) And Current Differencing Transconductance Amplifier (CDTA) receive considerable attention due to their larger dynamic range and wider bandwidth. Employing these new active elements for analog design and using CMOS technology for implementation, the circuit designers obtained new possibilities to solve their problems. CDTA device is a synthesis of the well-known advantages of the CDBA and an output transconductance amplifier to facilitate the implementation of currentmode analog signal processing.

The electrical symbol of the CDTA is shown in Figure 1.

The terminal relation of the CDTA can be characterized by the following set of Equation (1).

Figure 1. Electrical symbol of CDTA.

(1)

Where P and n are input terminals;

z and ±x are output terminals;

g_{m} is the transconductance gain;

And Z_{z} is external impedance connected at the terminal z.

According to above equation, the current flowing out of the terminal z (I_{z}) is a difference between the currents through the terminals p and n (I_{p} - I_{n}). The voltage drop at the terminal z is transferred to a current at the terminal x (I_{x}) by a transconductance gain (g_{m}), which is electronically controllable by an external bias current (I_{B}). These currents, which are copied to a general number of output current terminals x, are equal in magnitude but flow in opposite directions.

The (CDTA) is composed of a unity-gain current source controlled by the difference of two input currents and a multi-output transconductance amplifier providing electronic tuning ability through its transconductance gain (g_{m}). Therefore, this device is quite suitable for the synthesis of current-mode filters with electronically tunability properties. Moreover, the use of the CDTA as an active element provides the circuit implementations with a reduced number of passive elements, thereby leading to compact structures in some applications. All these advantages together with its current-mode operation nature make the CDTA a promising choice for implementing the current-mode continuous-time signal processing circuits consecutively.

Figure 2 shows a CMOS realization of the CDTA element [10]. The transistors M1 to M17 form the input DCCCS stage and M21 to M28 form the dual-output transconductor stage Aspect ratios of the transistors in Figure 2 are given in Table 1.

3. Proposed Circuit

The proposed current-mode multifunction filter employing CDTA, two grounded capacitors and a switched capacitor is shown in Figure 3.

Since all the grounded capacitors are employed, the circuit is suitable for IC implementation [11,12]. The switched capacitor (SC) functions as a resistor and re-

Figure 2. CDTA CMOS implementation from [10].

Table 1. Aspect ratios of the transistors.

duces the required space for the fabrication. The SC is compatible with CMOS technology. The proposed circuit is able to perform the basic filter functions i.e. low pass, high pass, band pass. The low pass, high pass and band pass current outputs have been shown in Figure 3. From routine calculations for the proposed filter, the current responses can be given by:

Figure 3. Biquad filter using CDTA element.

(2)

(3)

(4)

Bandwidth (BW), natural frequency (ω_{0}) and quality factor (Q) are given by

(5)

From Equation (5), the parameter ω_{0} can be controlled by transconductance g_{m} independently of bandwidth. The transconductance values can be changed through adjusting the biasing current of the CDTA.

From the expression of Equation (5), the sensitivities of ω_{0} and Q to variations in various parameters is given as

(6)

Hence all the sensitivities are low as calculated in Equation (6).

The value of the capacitor C_{3} used in switched capacitor is calculated using the formula given as

(7)

Where, R is the equivalent resistance value of the switched capacitor and f is the frequency of clock signal (Φ_{1}) and (Φ_{2}), applied at two mosfets (M30, M31) of switched capacitor.

4. Simulation Results

The performance of the proposed filter is verified using the simulation in PSpice. According to the analysis from Sections 2 and 3, the single input excitation is given. The CDTA model employing the n-well CMOS process TSMC 0.35 mm is used. The transconductanceis set to 888 µS via a bias current of 40 µA.

As an example design, the capacitors C1 = C2 = 10 pF, C_{3} = 2.96 pF and the biasing current I_{bias} = 40 μA are given. This setting has been designed to obtain the LP, BP and HP, filter responses. The simulated responses of the BP, LP and HP of the proposed filter are shown in Figure 4. Both the natural frequency and the quality factor are in accordance with the proposed values.

5. Conclusion

A 2nd-order single input multiple output (SIMO) current-mode filter employing a single CDTA is described in the paper. The natural angular frequency ω_{0} and the bandwidth ω_{0}/Q can electronically be controlled by ad-

(a)(b)(c)

Figure 4. Response of biquad filter using CDTA element. (a) Low pass response; (b) High pass response; (c) Band pass response.

justing the transconductance gain g_{m} of the CDTA. The simulated responses with PSPICE have been used to prove the theory. It possesses the properties as the following: 1) employment of only grounded capacitors which is suitable for IC implementation; 2) ability of realizing the LP, BP, and HP filter responses without any componentmatching condition; and 3) Electronic control of the parameter ω_{0}. The switched capacitor has good linearity. The PSPICE simulation results demonstrate the close agreement with the presented theory.

Conflicts of Interest

The authors declare no conflicts of interest.

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