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Active and Passive Electronic Components

Volume 2012 (2012), Article ID 261075, 6 pages

http://dx.doi.org/10.1155/2012/261075

## Cascadable Current-Mode First-Order and Second-Order Multifunction Filters Employing Grounded Capacitors

Department of Electronic Engineering, Chung Yuan Christian University, Chung-Li 32023, Taiwan

Received 28 November 2011; Accepted 28 December 2011

Academic Editor: Daisaburo Takashima

Copyright © 2012 Jiun-Wei Horng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A configuration for realizing low input and high output impedances current-mode multifunction filters using multiple output second-generation current conveyors (MOCCIIs) is presented. From the proposed circuit configuration, first-order allpass, highpass, lowpass and second-order allpass, notch, bandpass filters can be obtained. The simulation results confirm the theoretical analysis.

#### 1. Introduction

Current conveyors (CCs) are receiving much attention for their potential advantages such as inherent wider signal bandwidths, simpler circuitry and larger dynamic range [1, 2]. Current-mode active filters with low input impedance and high output impedance are of great interest because they can be directly connected in cascade to implement higher order filters [3, 4]. Several current-mode first-order allpass filters using various active components have been reported. Some circuits use two second-generation current conveyors (CCIIs) to realize such a first-order allpass filter function with high output impedance [5]. However, the number of passive components they used are not canonical. Some first-order circuits use one active component [6, 7]. However, their input impedances are not low. Some first-order circuits use one active element, one capacitor, and one resistor [8–10]. However, these circuits have not the advantage of low input impedance and the capacitors they used are not grounded. In 2007, Metin et al. [11] propose a current-mode first-order allpass filter using two CCIIs, two grounded resistors and one grounded capacitor with low input and high output impedances. In 2009, Lahiri and Chowdhury [12] proposed a current-mode first-order allpass filter using one current differencing transconductance amplifier (CDTA) and one grounded capacitor with low input and high output impedances. As the function of CDTA can also be replaced by two CCII and one operational transconductance amplifier (OTA) [12], if the structure of [12] is constructed by CCIIs and OTA, it requires two CCIIs and one OTA.

In this paper, a new current-mode circuit configuration with low input and high output impedances uses two multiple output second-generation current conveyors (MOCCIIs) is presented. The first-order allpass, highpass, and lowpass filters can be obtained from the proposed circuit configuration.

Several current-mode universal biquadratic filters with single-input and multioutput were presented in the literature [13–15]. However, the input impedances of the circuits in [13, 14] are high. Moreover, at least three CCIIs are required in [14, 15]. Several current-mode universal biquadratic filters with multi-input terminals using current conveyors are presented [16, 17]. However, the input impedances of these circuits are high at most of their input terminals.

In this paper, from the proposed circuit configuration, the second-order allpass, notch, and bandpass filters can also be obtained. All proposed circuits use only grounded capacitors that are attractive for integrated circuit implementation [19].

#### 2. Proposed Circuits

Using standard notation, the port relations of a MOCCII can be characterized by , and . Considering the proposed current-mode circuit in Figure 1, the current transfer function can be expressed as

If the impedances of Figure 1 are taken to be and , a first-order circuit is obtained as shown in Figure 2. The current transfer function of Figure 2 is

For and , (2) becomes This represents a first-order allpass function.

For and , (2) becomes This represents a first-order highpass function.

In Figure 2, if the output terminal of CCII(1) is eliminated, the transfer function becomes

For and , (5) becomes This represents a first-order lowpass function.

If the impedances of Figure 1 are taken to be and , a second-order circuit can be obtained as shown in Figure 3. The current transfer function of Figure 3 is

For , and , (7) becomes This represents a second-order allpass function.

For and , (7) becomes This represents a second-order notch function.

In Figure 3, if the output terminal of CCII(1) is eliminated, the transfer function becomes This represents a second-order bandpass function.

Because the input terminal of Figure 1 is connected directly to the -terminal of CCII(1) and the -terminal of CCII(1) is grounded, the input terminal has the advantage of low input impedance. Because the output terminal is taken out directly from the and terminals, the output terminal has the advantage of high output impedance. The proposed first-order and second-order filters employ only grounded capacitors. The use of grounded capacitors is attractive for integrated circuit implementation [19].

#### 3. Nonideality Analysis of the MOCCIIs

Taking into consideration the MOCCII nonidealities, the port relations of MOCCII can be expressed as where and denotes the current tracking error, and is the input voltage tracking error of a MOCCII. Reanalysis of the filter circuit in Figure 2 yields the following modified transfer functions: The cutoff angular frequency is obtained by The active and passive sensitivities are low and obtained as Reanalysis of the filter circuit in Figure 3 yields the following modified transfer functions:The resonance angular frequency and quality factor are obtained by The active and passive sensitivities are low and obtained as

#### 4. Simulation Results

HSPICE simulations were carried out to demonstrate the feasibility of the proposed circuits using 0.18 *μ*m, level 49 MOSFET from TSMC. The MOCCII was realized by the CMOS implementation in Figure 4 [20] with the NMOS and PMOS transistor aspect ratios and , respectively.

Figure 5 represents the magnitude and phase responses of the first-order allpass filter in Figure 2, designed with MHz: pF, kΩ and kΩ. The power supply was ±1.25 V. The bias voltage is V. Figure 6 represents the magnitude and phase responses of the first-order highpass filter, designed with MHz: pF, kΩ, and kΩ. Figure 7 represents the magnitude and phase responses of the first-order lowpass filter, designed with MHz: pF, kΩ, and kΩ.

Figure 8 represents the magnitude and phase responses of the second-order allpass filter in Figure 3, designed with MHz: pF, pF, kΩ, and kΩ. Figure 9 represents the magnitude and phase responses of the second-order notch filter, designed with MHz: pF, pF, kΩ, and kΩ. Figure 10 represents the magnitude and phase responses of the second-order bandpass filter, designed with MHz: pF, pF, kΩ, and kΩ.

A nonideal MOCCII model is shown in Figure 11 [18]. It is shown that the real MOCCII has parasitic resistors and capacitors from the - and -terminals to the ground, and also, a series resistor at the input terminal . The parasitic resistances of MOCCII become effective at very low frequency. This can explain why Figures 6 and 10 have nonideal frequency responses at low frequencies. Because there are parasitic resistance and capacitance at the output terminal , they introduce a pole at high frequency. This can explain why the simulations have nonideal frequency responses at high frequencies.

#### 5. Conclusions

A new cascadable current-mode circuit configuration using two MOCCIIs is presented. The proposed circuit has the advantages of low input and high output impedances. By choosing appropriate passive components, the first-order allpass, lowpass, highpass or second-order allpass, notch, bandpass filters can be obtained. All proposed filters use only grounded capacitors.

#### Acknowledgment

The authors would like to thank the reviewers for their suggestions.

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