A Novel Mixed-Mode Second-Generation Voltage Conveyor Based First-Order All-Pass Filter

A new plus-type second-generation voltage conveyor (VCII+) based first-order mixed-mode (MM) all-pass (AP) filter is proposed in this study. The proposed MM AP filter employs two VCII+s, three resistors and one grounded capacitor. It has low input and high output impedances for the current-mode selection while it has low input and low output impedances for the transimpedance-mode selection. The AP filter gain is unity for the current output while it is adjustable for the voltage output via a grounded resistor. However, a single passive component matching condition is needed for the proposed MM AP filter. Complete non-ideal analysis by taking into account all the parasitic resistors and non-ideal gains of the VCII+ is performed. The presented theory is verified through SPICE simulations by using supply voltage of ± 0.9 V and 0.18 μm Taiwan Semiconductor Manufacturing Company complementary metal oxide semiconductor technology parameters Nomenclature 1 Introduction Wide application areas in instrumentation and communication systems as quadrature oscillators, phase equalisers and delay equalisers have made the first-order all-pass (AP) filter design an important research topic [1–32]. The AP filters implemented by operational amplifiers (Op-Amps) suffer from low gain-bandwidth product of these active building blocks (ABBs). In the recent literature, as a result of numerous advantageous offered by the current-mode (CM) signal processing like simple circuitry, improved frequency performance, low voltage operation and so on, the realisations of a number of first-order AP filters using various CM ABBs [1–23, 26, 32] have been published. Literature survey shows that first-order AP filters using secondgeneration current conveyors (CCIIs) [1–9], current followers (CFs) [10], inverting CCIIs (ICCIIs) [11], differential voltage current conveyors (DVCCs) [12–14], dual-X CCIIs (DX-CCIIs) [15–20], extra-X current controlled conveyors (EX-CCCIIs) [21, 22], third-generation current conveyors (CCIIIs) [23], dual-X current conveyor transconductance amplifiers (DXCCTAs) [24, 25], current operational amplifiers (COAs) [26], MOS transistors [27], bipolar junction transistors (BJTs) [28, 29], operational transresistance amplifiers (OTRAs) [30], current differencing transconductance amplifiers (CDTAs) [31], voltage gain-controlled modified current feedback operational amplifiers (VGC-MCFOAs) [32] and so on have been reported so far. Some of the AP filters [1–29] can provide only CM operation while several AP filter topologies [30, 31] can realise only transimpedance-mode (TM) operation. Only one of [32] is mixedmode (MM). Also, some AP filters [7, 8, 11, 13, 23, 25–28, 30, 31] include a floating capacitor that is not suitable for integrated circuit (IC) fabrication. Several AP filter configurations [9, 13, 15, 24, 27] use more than one capacitor; accordingly, they occupy large chip area in IC process. Several AP filter circuits [8, 9, 28, 29, 31, 32] contain BJTs that are temperature dependent. Some of the AP filters [14, 32] need two input currents; thus, they need an extra circuitry. Some of the AP filters [12, 24, 32] do not use standard ABB. Several CM AP filter circuits [3, 7–9, 11, 13–17, 23, 26–28] do not provide both low input and high output impedances. Some TR AP filters [30, 31] do not realise both low input and low output impedances. Several AP filters [3, 15, 17, 24, 25, 31] have restrictions at high frequencies due to the use of operational transconductance amplifier [33] or a capacitor connection in series to the X terminal of the ABB [34]. Apart from these, some AP filters [35, 36] have been reported recently. In [37, 38], voltage conveyors as a new family of ABBs were introduced. Recently, in [39–41], a type of voltage conveyor namely second-generation voltage conveyor (VCII) has been employed to realise voltage output filters. Having a low impedance voltage output terminal, a low impedance current input terminal and a high impedance current output terminal [42], the VCII provides flexibility in the design of various types of the filters. In this paper, a new plus-type VCII (VCII+) based first-order MM AP filter is proposed. The proposed AP filter employs two VCII+s, three resistors and one grounded capacitor. By virtue of availability of low impedance current input, high impedance current output and low impedance voltage output terminals in the VCII+, a cascadable MM operation is possible without the use of any extra current and voltage buffers. Gain of the AP filter is unity for the current output while it is adjustable for the voltage output. Complete non-ideal analysis is performed by taking into account all the parasitic resistors and non-ideal gains of the VCII+. The presented theory is verified through SPICE simulations in which 0.18 μm supply voltage of ±0.9 V and Taiwan Semiconductor Manufacturing Company (TSMC) complementary metal oxide semiconductor (CMOS) technology parameters [43] are used. The advantages of the proposed VCII + based AP filter structure over the previously published works can be summarised as in the following: The proposed filter has low supply voltages, and dissipates lowpower. The proposed filter uses a grounded capacitor; thus, it is verysuitable for IC fabrication. Realisation of a floating capacitor requires poly2 CMOS process explained in [44]. The proposed filter provides output signal in both forms ofcurrent and voltage signals at high output impedance and low output impedance terminals, respectively. Hence, there is no requirement to use buffer stages at the outputs of the proposed filter. The proposed filter provides input current signal at low inputimpedance terminal. Thus, the input signal can be directly connected to the proposed filter without requiring a buffer. The proposed filter is compact and has a simple structure due tothe absence of extra voltage and current buffers at the outputs and input, respectively. The proposed filter can be easily cascaded at input and outputterminals. The proposed filter has the feature of MM operation. Capacitor of the proposed AP filter is not connected in seriesto the Z and or Y terminals (low impedance terminals); therefore, the proposed filter can be operated at high frequencies [34]. The proposed filter is novel because an AP filter based on theVCII has not been published so far. However, the proposed MM AP filter suffers from the following drawbacks: A single resistive matching condition is needed for the proposedAP filter. The proposed AP filter employs three resistors (minimum tworesistors are required). Organisation of this paper is as follows. After introduction given in Section 1, the VCII + is described in Section 2. In Section 3, the proposed AP filter topology is introduced. In Section 4, non-ideal analysis is presented. After simulation results are provided in Section 5, the paper is concluded in Section 6. 2 Description of the VCII+ Equation (1) shows the ideal relationships between terminal currents and voltages of the VCII+. Furthermore, symbolic representation of the VCII+ is demonstrated in Fig. 1 0 0 1 0 0 0 1 (1) 0 0 0 0 0 0 3 Proposed all-pass filter The proposed first-order MM AP filter topology is shown in Fig. 2. It is based on two VCII+s, three resistors and one grounded capacitor. The proposed AP filter circuit can be operated in MM. In other words, each of the AP outputs is available either a current signal at high impedance X terminal of the second VCII + (with ideal value of infinity) or a voltage signal at low impedance Z terminal of the second VCII + (with ideal value of zero). Therefore, there is no requirement of additional current and voltage buffers. The input is a current signal applied to Y terminal of the first VCII +. Its low impedance at Y terminal (with ideal value of zero) allows the direct application of a current signal to the Y terminal without Fig. 1 Symbolic representation of the VCII+ Fig. 2 Proposed first-order MM all-pass filter topology needing an extra current buffer. In addition to these, R3 can be chosen arbitrarily for the CM and TM operation. The AP filter outputs of Fig. 2 can be found as follows: due to the current buffering action between Y and X terminals, we have i1 = i2 = iin (2) The voltage at X1 terminal of the first VCII+, V1 is evaluated as R1 Viin (3) 1 + sCR1 Due to voltage buffering action between X and Z terminals of the first VCII+, V3 is equal to V1 and the voltage at Y terminal of the second VCII + is ideally zero; thus, iy2 is found as If it is considered that i3 = iy2 and using (2), (4) and (5), iAP is calculated as R1 (R1/RsCR1 iiiin = iin (6) R2(1 + sCR1) 1 + sCR1 If R1 = 2R2 is met, from (6), the output current is obtained as follows: sCR1 iAP = iin (7) 1 + sCR1 From (7), the following CM transfer function (TF) is obtained as iAP sCR1 H(s) = = (8) iin 1 + sCR1 where pole frequency, fo = 1/(2πCR1) is found. Also, phase response of the proposed AP filter is computed as φ(ωArctan(ωCR1) (9) Fortunately, as X terminals of the VCII+s are high impedance terminals, an extra current buffer is not needed to obtain iAP. The voltage produced at X terminal of the second VCII + is found as sCR1 V2 = R3iAP = R3 iin (10) 1 + sCR1 Due to the voltage buffering action between the X and Z terminals of the VCII+, V2 is transferred to Z terminal of the second VCII+. As a result, a TM TF is obtained as follows: VAP sCR1 = R3 (11) iin 1 + sCR1 Voltage output AP is available at Z terminal of the VCII+; consequently, an extra voltage buffer is not needed. Further, the gain can be adjusted by R3. 4 Non-ideal analysis Equation (12) shows the general relationships between terminal currents and voltages. Here, β is the current gain between Y and X1 terminals while η is the current gain between Y and X2 terminals. Also, α is the voltage gain between X1 and Z terminals. On the other hand, ry, rx1, rx2 and rz are, respectively, parasitic resistors at the Y, X1, X2 and Z terminals of the VCII+

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