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

Authors: Jiun-Wei Horng; Chun-Li Hou; Ching-Yao Tseng; Ryan Chang; Dun-Yih Yang
Journal: Active and Passive Electronic Components
 (2012)

---

## 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.


---

## Body

## 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 byvx=vy, izk=±ix and iy=0. Considering the proposed current-mode circuit in Figure 1, the current transfer function can be expressed as(1)IoutIin=Z2-2Z1Z2-Z1.Figure 1
The proposed cascadable current-mode circuit configuration.If the impedances of Figure1 are taken to be Z1=R1/(1+sCR1) and Z2=R2, a first-order circuit is obtained as shown in Figure 2. The current transfer function of Figure 2 is(2)IoutIin=sCR1R2+R2-2R1sCR1R2+R2-R1.Figure 2
The current-mode first-order filter.ForR1=R and R2=1.5R, (2) becomes(3)IoutIin=s-1/(3CR)s+1/(3CR).
This represents a first-order allpass function.ForR1=R and R2=2R, (2) becomes(4)IoutIin=ss+1/(2CR).
This represents a first-order highpass function.In Figure2, if the z12- output terminal of CCII(1) is eliminated, the transfer function becomes(5)IoutIin=-R1sCR1R2+R2-R1.ForR1=R and R2=2R, (5) becomes(6)IoutIin=-1/(2RC)s+1/(2CR).
This represents a first-order lowpass function.If the impedances of Figure1 are taken to be Z1=R1/(1+sC1R1) and Z2=(sC2R2+1)/sC2, a second-order circuit can be obtained as shown in Figure 3. The current transfer function of Figure 3 is(7)IoutIin=s2C1C2R1R2+s(C1R1+C2R2-2C2R1)+1s2C1C2R1R2+s(C1R1+C2R2-C2R1)+1.Figure 3
The current-mode second-order filter.ForR1=2R, R2=R and C1=C2=C, (7) becomes(8)IoutIin=2s2C2R2-sCR+12s2C2R2+sCR+1.
This represents a second-order allpass function.ForR1=R2=R and C1=C2=C, (7) becomes(9)IoutIin=s2C2R2+1s2C2R2+sCR+1.
This represents a second-order notch function.In Figure3, if the z12- output terminal of CCII(1) is eliminated, the transfer function becomes(10)IoutIin=-sC2R1s2C1C2R1R2+s(C1R1+C2R2-C2R1)+1.
This represents a second-order bandpass function.Because the input terminal of Figure1 is connected directly to the x-terminal of CCII(1) and the y-terminal of CCII(1) is grounded, the input terminal has the advantage of low input impedance. Because the Iout output terminal is taken out directly from the z12 and z22 terminals, the Iout 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(11)vx=αvy,iz=±βkix,
where βk=1-εki and εki(|εki|≪1) denotes the current tracking error, α=1-εv and εv(|εv|≪1) is the input voltage tracking error of a MOCCII. Reanalysis of the filter circuit in Figure 2 yields the following modified transfer functions:(12)IoutIin=sCR1R2β12+R2β12-R1α2(β12β21+β11β22)sCR1R2+R2-R1α2β21.
The cutoff angular frequency is obtained by(13)ωc=R2-R1α2β21CR1R2.
The active and passive sensitivities are low and obtained as(14)SCωc=-1,SR1ωc=-R2R2-R1α2β21,SR2ωc=-Sα2,β21ωc=R1α2β21R2-R1α2β21.
Reanalysis of the filter circuit in Figure 3 yields the following modified transfer functions:(15)IoutIin=s2C1C2R1R2β12+s(C1R1β12+C2R2β12-C2R1α2(β11β22+β12β21))+β12s2C1C2R1R2+s(C1R1+C2R2-C2R1α2β21)+1.The resonance angular frequency and quality factor are obtained by(16)ωo=1C1C2R1R2,Q=C1C2R1R2C1R1+C2R2-C2R1α2β21.
The active and passive sensitivities are low and obtained as(17)SC1,C2,R1,R2ωo=-12,SC1Q=-C1R1+C2R2-C2R1α2β212(C1R1+C2R2-C2R1α2β21),SC2Q=C1R1-C2R2+C2R1α2β212(C1R1+C2R2-C2R1α2β21),SR1Q=-C1R1+C2R2+C2R1α2β212(C1R1+C2R2-C2R1α2β21),SR2Q=C1R1-C2R2-C2R1α2β212(C1R1+C2R2-C2R1α2β21),Sα2,β21Q=C2R1α2β21C1R1+C2R2-C2R1α2β21.


## 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 MOCCII was realized by the CMOS implementation in Figure 4 [20] with the NMOS and PMOS transistor aspect ratios W/L=4.5u/0.9u and W/L=9u/0.9u, respectively.Figure 4
The CMOS MOCCII implementation.Figure5 represents the magnitude and phase responses of the first-order allpass filter in Figure 2, designed with fc=1.326MHz: C=20pF, R1=2kΩ and R2=3 kΩ. The power supply was ±1.25 V. The bias voltage is Vb=-0.6V. Figure 6 represents the magnitude and phase responses of the first-order highpass filter, designed with fc=1.989 MHz: C=20 pF, R1=2 kΩ, and R2=4 kΩ. Figure 7 represents the magnitude and phase responses of the first-order lowpass filter, designed with fc=3.979 MHz: C=20 pF, R1=1 kΩ, and R2=2 kΩ.Figure 5
Simulation results of the proposed current-mode first-order allpass filter.Figure 6
Simulation results of the proposed current-mode first-order highpass filter.Figure 7
Simulation results of the proposed current-mode first-order lowpass filter.Figure8 represents the magnitude and phase responses of the second-order allpass filter in Figure 3, designed with fo=2.814 MHz: C1=20 pF, C2=20 pF, R1=4 kΩ, and R2=2 kΩ. Figure 9 represents the magnitude and phase responses of the second-order notch filter, designed with fo=3.979 MHz: C1=20 pF, C2=20 pF, R1=2 kΩ, and R2=2 kΩ. Figure 10 represents the magnitude and phase responses of the second-order bandpass filter, designed with fo=3.979 MHz: C1=20 pF, C2=20 pF, R1=2 kΩ, and R2=2 kΩ.Figure 8
Simulation results of the proposed current-mode second-order allpass filter.Figure 9
Simulation results of the proposed current-mode second-order notch filter.Figure 10
Simulation results of the proposed current-mode second-order bandpass filter.A nonideal MOCCII model is shown in Figure11 [18]. It is shown that the real MOCCII has parasitic resistors and capacitors from the y- and z-terminals to the ground, and also, a series resistor at the input terminal x. 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 z, they introduce a pole at high frequency. This can explain why the simulations have nonideal frequency responses at high frequencies.Figure 11
The nonideal MOCCII model [18]. Rx=30Ω, Ry=17 MΩ, Rz1=577 kΩ, Rz2=572 kΩ, Cy=1.4 pF, Cz1=1.2 pF, Cz2=1.2 pF.


## 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.



---

*Source: 261075-2012-03-20.xml*