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Modelling and Simulation in Engineering
VolumeΒ 2012Β (2012), Article IDΒ 184829, 6 pages
http://dx.doi.org/10.1155/2012/184829
Research Article

Supplementary High-Input Impedance Voltage-Mode Universal Biquadratic Filter Using DVCCs

1Department of Electronics and Communications, Jaypee Institute of Information Technology, Noida 201304, India
2Department of Electronics Engineering, Z. H. College of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India

Received 9 April 2012; Accepted 12 July 2012

Academic Editor: AndrzejΒ Dzielinski

Copyright Β© 2012 Jitendra Mohan and Sudhanshu Maheshwari. 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

To further extend the existing knowledge on voltage-mode universal biquadratic filter, in this paper, a new biquadratic filter circuit with single input and multiple outputs is proposed, employing three differential voltage current conveyors (DVCCs), three resistors, and two grounded capacitors. The proposed circuit realizes all the standard filter functions, that is, high-pass, band-pass, low-pass, notch, and all-pass filters simultaneously. The circuit enjoys the feature of high-input impedance, orthogonal control of resonance angular frequency (πœ”o), and quality factor (Q) via grounded resistor and the use of grounded capacitors which is ideal for IC implementation.

1. Introduction

Analog filters are the basic building blocks and widely used for continuous-time signal processing. Application of analog filters employing current-mode active elements extends over a large number of fields [1]. The filter circuits may be used in phase-locked loop frequency modulation stereo demodulators, touch-tone telephone tone decoder, and cross-over networks in a three-way high fidelity loudspeaker [2, 3]. In the literature several voltage-mode biquadratic filters are presented which uses different types of current conveyors [4–28]. The voltage-mode filters with high-input impedance are of great interest because they can be easily cascaded to synthesize higher-order filters [7, 10, 13, 17, 26, 28]. In the literature there are a number of voltage-mode universal biquadratic filters with single-input multiple-outputs (SIMO) [4–12, 18] that are available. However, these reported circuits suffer from one or more of the following drawbacks:(i)excessive use of passive components [4, 6, 7];(ii)low-input impedance [5, 6, 8, 9, 11, 18];(iii)lack of orthogonal control over the resonance angular frequency (πœ”π‘œ) and quality factor (Q) [10, 12].

In this paper, a new voltage-mode universal biquadratic filter using three differential voltage current conveyors [29], two grounded capacitors, and three resistors is presented. The circuit realizes the entire standard filter functions, that is, high pass (HP), band pass (BP), low pass (LP), notch (NH), and all pass (AP) from the same circuit configuration. The circuit also possesses high-input impedance and provides orthogonal control of the πœ”π‘œ and Q via grounded resistor.

2. Differential Voltage Current Conveyor(DVCC)

The DVCC is first introduced long back as a modified current conveyor by Pal [30] and developed by Elwan and Soliman in 1997 [29]. It is a versatile building block, especially designed to handle differential and floating input signals [30, 31]. Using standard notation, the terminal relations of a DVCC are shown in Figure 1 and described by the following matrix equation: βŽ‘βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ£πΌπ‘Œ1πΌπ‘Œ2𝑉𝑋𝐼𝑍+πΌπ‘βˆ’βŽ€βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯⎦=⎑⎒⎒⎒⎒⎒⎒⎒⎒⎣⎀βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ¦βŽ‘βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ£π‘‰00000000001βˆ’10000010000βˆ’100π‘Œ1π‘‰π‘Œ2𝐼𝑋𝑉𝑍+π‘‰π‘βˆ’βŽ€βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯⎦.(1)

fig1
Figure 1: (a) Symbol of DVCC. (b) CMOS implementation of DVCC.

The difference of the π‘Œ1 and π‘Œ2 terminal voltages is conveyed to the X terminal; the current input at the X terminal is conveyed to the Z+, with the same polarity and Zβˆ’ terminal with inverse polarity. The DVCC is characterized by high-input impedance at the π‘Œ1 and π‘Œ2 terminals, high-output impedance at the Z+ and Zβˆ’ terminals, and low impedance at the 𝑋 terminal.

3. Proposed Circuit

The proposed voltage-mode universal biquadratic filter is shown in Figure 2, employing three DVCCs, three resistors, and two grounded capacitors. The routine analysis of the proposed circuit in Figure 2 using (1) yields the filter transfer functions as 𝑉OUT1𝑉IN=1𝑠2𝐢1𝐢2𝑅1𝑅2+𝑠𝐢1𝑅3𝑉+1OUT2𝑉IN=𝑠2𝐢1𝐢2𝑅1𝑅2𝑠2𝐢1𝐢2𝑅1𝑅2+𝑠𝐢1𝑅3𝑉+1OUT3𝑉IN=𝑠𝐢1𝑅1𝑠2𝐢1𝐢2𝑅1𝑅2+𝑠𝐢1𝑅3𝑉+1OUT4𝑉IN=𝑠2𝐢1𝐢2𝑅1𝑅2+1𝑠2𝐢1𝐢2𝑅1𝑅2+𝑠𝐢1𝑅3𝑉+1OUT5𝑉IN=𝑠2𝐢1𝐢2𝑅1𝑅2βˆ’π‘ πΆ1𝑅1+1𝑠2𝐢1𝐢2𝑅1𝑅2+𝑠𝐢1𝑅3.+1(2) It can be seen from (2) that an LP response is obtained from 𝑉OUT1; HP response is obtained from 𝑉OUT2; BP response is obtained from 𝑉OUT3; NH response is obtained from 𝑉OUT4; if 𝑅3 = 𝑅1, AP response is obtained from 𝑉OUT5. In all the cases, the parameters πœ”π‘œ and Q of the filter can be found as πœ”o=ξ‚΅1𝐢1𝐢2𝑅1𝑅2ξ‚Ά1/2,1𝑄=𝑅3ξƒŽπ‘…1𝑅2𝐢2𝐢1.(3) From (3), the Q of the proposed filter can be controlled independently of πœ”π‘œ by varying 𝑅3. Since the input voltage signal is connected directly to the π‘Œ1 port of the DVCC (1) and the input current to the π‘Œ1 port is zero (πΌπ‘Œ1 = 0), the circuit has the feature of high-input impedance. Thus the proposed circuit is capable to realize all five standard filter functions simultaneously and without changing the circuit topology, unlike the previously proposed circuit in [26]. The circuit reported in [26] uses two floating resistors but the proposed circuit employs only one floating resistor. The circuit needs no component-matching conditions except for the all-pass filter realization.

184829.fig.002
Figure 2: Voltage-mode universal biquadratic filter.

Note that the proposed circuit uses two grounded capacitors at the 𝑍-terminal and three resistors at the 𝑋-terminal of the DVCCs. The design offers the feature of a direct incorporation of the shunt parasitic capacitances at the 𝑍-terminals and the series parasitic resistances at the 𝑋-terminal, as a part of the main capacitors (𝐢1 and 𝐢2) and resistors (𝑅1, 𝑅2, and 𝑅3).

4. Nonideal Analysis

Taking the nonidealities of the DVCC into account, the relationship of the terminal voltages and currents of the DVCC can be rewritten as βŽ‘βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ£πΌπ‘Œ1πΌπ‘Œ2𝑉𝑋𝐼𝑍+πΌπ‘βˆ’βŽ€βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯⎦=βŽ‘βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ£π›½0000000000π‘˜1βˆ’π›½π‘˜200000π›Όπ‘˜10000βˆ’π›Όπ‘˜2⎀βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ¦βŽ‘βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ’βŽ£π‘‰00π‘Œ1π‘‰π‘Œ2𝐼𝑋𝑉𝑍+π‘‰π‘βˆ’βŽ€βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯βŽ₯⎦,(4) where π›½π‘˜1(𝑠), π›½π‘˜2(𝑠) represent the frequency transfers of the internal voltage followers and π›Όπ‘˜1(𝑠), π›Όπ‘˜2(𝑠) represent the frequency transfers of the internal current followers of the kth-DVCC, respectively. They can be approximated by first-order low-pass functions, which can be considered to have a unity value for frequencies [30]. If this circuit is working at frequencies much less than the corner frequencies of π›½π‘˜1(𝑠), π›½π‘˜2(𝑠), π›Όπ‘˜1(𝑠), and, π›Όπ‘˜2(𝑠), namely, then π›½π‘˜1(𝑠) = π›½π‘˜1=1βˆ’πœ€π‘˜π‘£1 and πœ€π‘˜π‘£1(|πœ€π‘˜π‘£1β‰ͺ1|) denotes the voltage tracking error from the π‘Œ1 terminal to the 𝑋 terminal of the kth-DVCC; π›½π‘˜2(𝑠)=π›½π‘˜2=1βˆ’πœ€π‘˜π‘£2 and πœ€π‘˜π‘£2(|πœ€π‘˜π‘£2β‰ͺ1|) denotes the voltage tracking error from the π‘Œ2 terminal to the 𝑋 terminal of the kth-DVCC, π›Όπ‘˜1(𝑠)=π›Όπ‘˜1=1βˆ’πœ€π‘˜π‘–1, and πœ€π‘˜π‘–1(|πœ€π‘˜π‘–1β‰ͺ1|) denotes the current tracking error from the 𝑋 terminal to the 𝑍+ terminal; π›Όπ‘˜2(𝑠)=π›Όπ‘˜2=1βˆ’πœ€π‘˜π‘–2 and πœ€π‘˜π‘–2(|πœ€π‘˜π‘–2β‰ͺ1|) denotes the current tracking error from the 𝑋 terminal to the π‘βˆ’ terminal of the kth-DVCC.

Taking the tracking errors of the nonideal DVCC into account, the denominator of (2) becomes 𝐷(s)=𝑠2𝐢1𝐢2𝑅2𝛼22𝑅3𝛼11+𝑅1𝛽12βˆ’π‘…3𝛼11𝛽21ξ€Έ+𝑠𝐢1𝑅3𝛽22𝛽31𝛼11𝛼22+𝛽12𝛽22𝛽32.(5) The parameters πœ”π‘œ and Q from (5) can be rewritten as πœ”π‘œ=𝛽12𝛽22𝛽32𝐢1𝐢2𝑅2𝛼22𝑅3𝛼11+𝑅1𝛽12βˆ’π‘…3𝛼11𝛽21ξ€Έξƒͺ1/2,1𝑄=𝑅3𝛽31𝛼11𝐢2𝑅2𝛽12𝛽32𝑅3𝛼11+𝑅1𝛽12βˆ’π‘…3𝛼11𝛽21𝐢1𝛽22𝛼22ξƒͺ1/2.(6) The active and passive sensitivities of the proposed SIMO voltage-mode filter are derived from (6). These are as follows: π‘†πœ”π‘œπΆ1,𝐢2,𝑅21=βˆ’2,π‘†πœ”π‘œπ‘…11=βˆ’2𝑅1𝛽12𝑅3𝛼11+𝑅1𝛽12βˆ’π‘…3𝛼11𝛽21ξ€Έ,π‘†πœ”π‘œπ›½22,𝛽32=βˆ’π‘†πœ”π‘œπ›Ό22=12,π‘†πœ”π‘œπ›½12=12𝑅3𝛼11βˆ’π‘…3𝛼11𝛽21𝑅3𝛼11+𝑅1𝛽12βˆ’π‘…3𝛼11𝛽21ξ€Έ,π‘†πœ”π‘œπ‘…3,𝛼111=βˆ’2𝑅3𝛼11ξ€·1βˆ’π›½21𝑅3𝛼11+𝑅1𝛽12βˆ’π‘…3𝛼11𝛽21ξ€Έ,π‘†πœ”π‘œπ›½21=12𝑅3𝛼11𝛽21𝑅3𝛼11+𝑅1𝛽12βˆ’π‘…3𝛼11𝛽21ξ€Έ,𝑆𝑄𝐢2,𝑅2=βˆ’π‘†π‘„πΆ1=12,𝑆𝑄𝛽32=βˆ’π‘†π‘„π›½22,𝛼22=12,𝑆𝑄𝑅1=12𝑅1𝛽12𝑅3𝛼11ξ€·1βˆ’π›½21ξ€Έ+𝑅1𝛽12ξ€Έ,𝑆𝑄𝑅3,𝛼11=ξ€·βˆ’2𝑅1𝛽12βˆ’π‘…3𝛼11ξ€·1βˆ’π›½21ξ€Έξ€Έ2𝑅3𝛼11ξ€·1βˆ’π›½21ξ€Έ+𝑅1𝛽12ξ€Έ,𝑆𝑄𝛽31𝑆=βˆ’1,𝑄𝛽12=12𝑅3𝛼11+2𝑅1𝛽12βˆ’π‘…3𝛼11𝛽21𝑅3𝛼11+𝑅1𝛽12βˆ’π‘…3𝛼11𝛽21ξ€Έ,𝑆𝑄𝛽211=βˆ’2𝑅3𝛼11𝛽21𝑅3𝛼11ξ€·1βˆ’π›½21ξ€Έ+𝑅1𝛽12ξ€Έ.(7) From the results it is evident that the sensitivities are low and within unity in absolute value. Thus the proposed circuit can be classified as insensitive as all the active and passive sensitivities are less than or equal to unity [28].

5. Simulation Results

The performance of the proposed voltage-mode universal biquadratic filter in Figure 2 is verified using the PSPICE simulation program. The MOS transistors are simulated using 0.35 μm CMOS process parameters given in Table 1. The aspect ratios of the transistors used in the simulation are given in Table 2. The supply voltages and biasing voltage are given by 𝑉+=2V, π‘‰βˆ’=βˆ’1.9V, 𝑉𝑏1=βˆ’1.23 V, and 𝑉𝑏2=βˆ’1.15 V, respectively. The proposed circuit is designed for 3.18 MHz and Q = 1 by choosing 𝑅1=𝑅2=𝑅3=5 kΞ© and 𝐢1=𝐢2=10 pF. Figure 3 shows the simulated gain responses for the LP, HP, and BP filters and agrees well with the designed values. Figures 4 and 5 show the simulated gain and phase responses for the NH and AP filters. Next, Q tuning of BP filter at constant frequency of 3.18 MHz is shown in Figure 6. The circuit of Figure 2 is designed for Q values of 1, 5, and 10 with 𝑅3 values as 5 kΞ©, 1 kΞ©, and 500 Ω, respectively, with 𝐢1=𝐢2=10 pF and 𝑅1=𝑅2=5 kΞ©.

tab1
Table 1: TSMC 0.35 μm CMOS process parameters.
tab2
Table 2: Aspect ratios of the MOS in Figure 1.
184829.fig.003
Figure 3: Gain plots of LP, HP, and BP filters for Q = 1 at 3.18 MHz.
184829.fig.004
Figure 4: Gain and phase plots of NH filter for Q = 1 at 3.18 MHz.
184829.fig.005
Figure 5: Gain and phase plots of AP filter for Q = 1 at 3.18 MHz.
184829.fig.006
Figure 6: Q tuning (Q = 1, 5, and 10) of BP filter at 3.18 MHz.

To test the input dynamic range of the proposed filter, the simulation of the HP filter as example has been repeated for a sinusoidal input signal at 3.18 MHz. Figure 7 shows the input dynamic range of the HP filter which extends upto amplitude 200 mV (peak to peak) without significant distortion. In Figure 8, the total harmonic distortion (THD) of the 𝑉OUT2 output voltage is given at 3.18 MHz operation frequency. Figure 9 shows the INOISE and ONOISE simulated amplitude-frequency responses of the proposed LP filter at 𝑉OUT1.

fig7
Figure 7: Input (a) and HP output (b) signal waveforms to demonstrate the ac dynamic range at 𝑉OUT2.
184829.fig.008
Figure 8: THD variation with 𝑉IN for HP filter at 𝑉OUT2.
184829.fig.009
Figure 9: The input and output referred noise spectral densities of the proposed LP filter at 𝑉OUT1.

6. Conclusion

The voltage-mode universal biquadratic filter realizes all the standard filter functions by employing three DVCCs and five passive components. It offers high-input impedance, which permit the use of circuits in cascade without requiring any impedance-matching device. Moreover, the proposed circuit enjoys the following features: orthogonal control of πœ”π‘œ and Q, low active and passive sensitivity, and the direct incorporation of parasitic resistance and parasitic capacitance at the X-terminal and Z-terminal of the respective DVCCs, as a part of main resistor and capacitor. So, the new circuit will enhance the existing knowledge on the voltage-mode universal biquadratic filter. PSPICE simulations with TSMC 0.35 μm process confirm the theoretical prediction.

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