A Transconductance-Mode Multifunction Filter with High Input and High Output Impedance Nodes Using Voltage Differencing Current Conveyors (VDCCs)

The design of transconductance-mode multifunction biquad filter containing three input voltage nodes and single-output current node is proposed. Its circuit principle is emphasized on employing Voltage Differencing Current Conveyor (VDCC) to be an active building block. The proposed filter description uses three VDCCs co-working with two grounded capacitors and three grounded resistors. The synthesis of the proposed multifunction filter is based on avoidance of using multiple-output active elements to achieve commercially available integrated circuits for practical implementation. Additionally, without multiple-output active element, it can alleviate current tracking error from the current mirrors used in output ports. It also decreases the amounts of the transistors inside the active elements. The proposed multifunction filter offers all 5 filter functions, which are non-inverting Low-Pass (LP), non-inverting High-Pass (HP), noninverting Band-Pass (BP), non-inverting Band-Reject (BR) and also non-inverting All-Pass (AP) functions from same circuit topology under different circuit condition for input signals. Furthermore, the natural frequency for all filtering responses is independently achieved from the bandwidth or the quality factor of the proposed filter. For cascade-able connectivity, the output current port indeed provides a high impedance. In addition, the magnitude of the output current for all filtering functions can be resistively adjusted. The consideration for non-ideal case of the presented multifunction filter is also analyzed. The simulation and experimental results of the presented transconductance multifunction biquad filter based on VDCC practically implemented by the commercially available ICs, LM13700 and AD844 can validate the theoretical anticipation.

Abstract. The design of transconductance-mode multifunction biquad filter containing three input voltage nodes and single-output current node is proposed. Its circuit principle is emphasized on employing Voltage Differencing Current Conveyor (VDCC) to be an active building block. The proposed filter description uses three VDCCs co-working with two grounded capacitors and three grounded resistors. The synthesis of the proposed multifunction filter is based on avoidance of using multiple-output active elements to achieve commercially available integrated circuits for practical implementation. Additionally, without multiple-output active element, it can alleviate current tracking error from the current mirrors used in output ports. It also decreases the amounts of the transistors inside the active elements. The proposed multifunction filter offers all 5 filter functions, which are non-inverting Low-Pass (LP), non-inverting High-Pass (HP), noninverting Band-Pass (BP), non-inverting Band-Reject (BR) and also non-inverting All-Pass (AP) functions from same circuit topology under different circuit condition for input signals. Furthermore, the natural frequency for all filtering responses is independently achieved from the bandwidth or the quality factor of the proposed filter. For cascade-able connectivity, the output current port indeed provides a high impedance. In addition, the magnitude of the output current for all filtering functions can be resistively adjusted. The consideration for non-ideal case of the presented multifunction filter is also analyzed. The simulation and experimental results of the presented transconductance multifunction biquad filter based on VDCC practically im-plemented by the commercially available ICs, LM13700 and AD844 can validate the theoretical anticipation.

Introduction
Analog active filters are essential parts for analog signal processing systems, they are widely employed in many applications, such as communications, audio systems, instrumentation and measurement system, control systems, mobile telecommunication systems [1]. Most of analog filters are designed in second-order system, because second-order (or biquad) filter can be obtained completely by five filtering transfer function forms: Low-Pass (LP), High-Pass (HP), Band-Pass (BP), Band-Reject (BR) and All-Pass (AP). The second-order multifunction filter offers many filtering transfer function forms in the same configuration without modifying circuit scheme. It has obtained significant encouragement and became an interesting research topic. Among several types of the multifunction filters, the Multiple-Input Single-Output (MISO) multifunction filter is an attractive circuit and has been designed over the years [2]. Additionally, Current-Mode (CM) multifunction filters whose desired parameters are electronically adjusted by relative currents provide several benefits, for example, low power consumption, greater linearity, larger input dynamic range, wider bandwidth, or smaller number of components compared to circuits in voltage-mode configuration using in voltage-mode active devices such as conventional operational amplifiers [3], [4] and [5].
The filter proposed in [26] and the filter proposed in [27] provide 5 standard function responses comprises only of 1 VDCC cooperating with 1 resistor and 2 capacitors. The filter in [26] consists of 1 VDCC, 2 resistors and 2 capacitors and offers 3 standard functions (LP, HP and BP). The outstanding feature is that the natural frequency and the quality factor can be electronically adjusted. In addition, the adjustment of the quality factor of the second filter in [26] can be achieved without disturbing the natural frequency. Unfortunately, the output voltage terminal is not in low impedance, thus for practical implementation, a voltage buffer is inevitably needed for cascade configuration.
Subsequently, a 1 input 4 output voltage-mode filter proposed in [28] consisting of 1 VDCC, 2 resistors and 2 capacitors, its natural frequency and the quality factor of are tuned with electronic method, where the quality factor is adjusted without disturbing the natural frequency. This voltage-mode filter, however, does not provide low impedance architecture. Later, the current-mode filter using 1 VDCC, 1 dual-output current amplifier, 1 resistor and 2 grounded capacitors was presented in [29]. Its natural frequency is also electronically controlled as well as the quality factor. Moreover, the input and output impedances are ultimately perfect for current-mode architecture without requirement of a current buffer. Unfortunately, the mentioned filter offers only LP, HP, and BR function responses. Additionally, the circuit configuration needs the multipleoutput building blocks, which requires more transistors in internal architecture, leading to higher power consumption and more circuit complexity.
The 3 input 1 output current-mode filters composed of 1 VDCC, 1 grounded resistor and 2 grounded capacitors were introduced in [30] and [31]. They offer 5 filter responses while the natural frequency and quality factor are electronically adjustable. As well, the output impedance in current node is high, appropriating for current-mode cascade connection, without any current buffer requirement. The filter introduced in [30], however, requires the multiple-output VDCC. Also, the VDCC based current-mod filter in [31] requires the matching condition for the lowpass filter response.
The single input two output current-mode filters consist of 2 VDCCs, 2 grounded resistors and 2 grounded capacitors were introduced in [32] and [33]. Two output filtering responses are simultaneously obtained while other filtering responses are obtained by summing the input and output currents together. The natural frequency and quality factor are orthogonal adjustable. Moreover, the output impedance in current node is high, appropriating for current-mode cascade connection without any current buffer requirement. However, these require the multiple-output VDCC. Also, these VDCC based current-mode filters require the matching condition for the HP response in [32] and for HP, BR and AP responses in [33]. The comparison of the previous biquad filters and proposed filter using VDCC as active element is shown in Tab. 1.
In this article, a 3 input 1 output transconductancemode multifunction filter emphasizing on use of VD-CCs is proposed. The circuit configuration comprises 3 VDCCs, 3 grounded resistors and 2 grounded capacitors. The features of the proposed filter are that it can be further chip fabrication including offthe-shelf configuration. Additionally, the natural frequency is independently controlled from the quality factor by electronic method. The PSpice simulation and experimental results achieved from the pro-posed transconductance-mode filter are in corresponding with the theoretical expectation.
The article is organized as follows; Sec. 2. describes principle of operation, the basic principle of the used active elements, VDCC is introduced. The presented transconductance-mode multifunction biquad filter is subsequently explained. Non-ideal analysis of the proposed filter affected from the voltage and current transfer errors is introduced in Sec. 3. Section 4. introduces the simulation and experimental results to prove the different performances of the presented biquad filter. Section 5. provides the conclusion.

2.
Principle of the Proposed Circuit

Active Building Block Used in This Design
The design of transconductance-mode multifunction filter emphasizing on the use of VDCC as the active function block is realized in the paper. So, a brief description of this active element is disclosed in this section.
The internal structure of VDCC for CMOS implementation was initially introduced 2014 by Firat et al [11]. The VDCC is a five-terminals active element. The input and output terminals represent as P, N, Z, X and W terminals. The input voltage terminals, P and N offer the high impedance, where the output current terminals, Z and W achieve high impedance. The voltage output terminal, X is a low impedance. For the conventional VDCC, there are two W terminals called W n and W p which provide the output currents in opposite directions. For our design, the VDCC containing only single W terminal is required to achieve practical circuit implementation via commercially available integrated circuits. In addition, avoidance of multiple output terminals can reduce the effect of the current tracking error at W terminal and can additionally decrease the number of transistors inside of VDCC structure. Fig. 1 shows the VDCC circuit symbol including its electrical equivalent circuit. The VDCC ideal electrical characteristics are explained in Eq. (1).
where g m represents the transconductance of VDCC. The internal construction of VDCC in this design is implemented using the commercially available Integrated Circuits (ICs) as depicted in Fig. 2(a). It comprises LM13700 as an OTA [34] and AD844 as a current conveyor [35]. This implementation comprises only one terminal without the requirement of W p or W n terminal which it can alleviate current tracking error from the current mirrors used in output ports. The g m for this implementation is obtained as: where I B is bias current, V T is the thermal voltage of approximately 26 mV at a room temperature. It can be seen from Eq. (2) that the g m is electronically controllable. In Fig. 2(b), the bias current I B can be simply generated from Microcontroller Unit (MCU). As shown in Fig. 2 Fig. 3(a) (Fig. 3(b) [30] and [33], two output filtering responses (LP and HP) are simultaneously obtained while other filtering responses are obtained by summing the input and output currents together. *** The cascade-ability is achieved without using additional buffers at both input and output nodes.

Proposed Transconductance-Mode Multifunction Filter with Electronic Controllability
The proposed electronically controllable transconductance-mode multifunction second order filter is depicted in Fig. 3. It is composed of three VDCCs, three resistors and two capacitors which are connected to ground. It is clear from the circuit in Fig. 3 that the realization of presented filter does not need the VDCC with containing multiple W terminals (W n or W p ), which is different to the VDCC based current-mode filter proposed in [29] and [30]. From the mentioned principle, the employed VDCC in this design is more suitable to be implemented by employing the commercially available ICs as depicted in Fig. 2. The high input voltage nodes, V 1 , V 2 and V 3 are at terminal p of VDCC 1 , VDCC 2 and VDCC 3 , respectively. The single output current is Io exhibiting a high impedance at the current output terminal. With reference to Fig. 3 and assuming ideal VDCC as shown in Eq. (1), the output current: I o corresponding to V 1 , V 2 , and V 3 are is obtained by: From Eq. (3), the natural frequency (ω 0 ) of the presented three input voltage and single input voltage filter is obtained as: Also, the quality factor (Q) is provided to be: From Eq. (4) and Eq. (5), if R 1 = R 2 = R and g m2 = g m3 = g m , the natural frequency modified to be: The quality factor in Eq. (5) becomes: Equation 6 and Eq. (7) verify that the control of the f 0 can be independently set from the Q via resistor R and transconductance g m , respectively. Additionally, the natural frequency is not temperature sensitive. Also, if g m and g m1 are simultaneously tuned, the quality factor is not temperature sensitive. The transconductance gain for all filtering functions is given by: Derivation of 5 filter functions can be achieved from Eq. (3) as follows: • By feeding the input signal voltage to node V 2 and connecting nodes V 1 and V 3 to ground, the noninverting transconductance-mode transfer function for the LP filter is obtained.
• By feeding the input signal voltage to node V 3 and connecting nodes V 1 and V 2 to ground, the noninverting transconductance-mode transfer function for the HP filter is obtained.
• By feeding the input signal voltage to node V 1 and connecting nodes V 2 and V 3 to ground, the noninverting transconductance-mode transfer function for the BP filter is obtained.
• By feeding the input signal voltage to node V 2 and connecting nodes V 1 and V 3 to ground, the noninverting transconductance-mode transfer function for the BR filter is obtained.
• By feeding the input signal voltage to nodes V 2 , V 3 and feeding the inverting signal voltage to node V 1 , the non-inverting transconductance-mode transfer function for the AP filter is obtained. Thus, the inverting unity voltage amplifier is needed for AP filter.

Non-Ideal Consideration
The non-ideal effect of the active element, VDCC on the functionalities of the presented transconductancemode multifunction biquad filter is considered. Eq. (9) shows the non-idealities of VDCC.
where β represents a voltage gain error from the input voltage terminal, Z to the output voltage terminal, X and α represents a current gain error from the input current terminal, X to the output current terminal, W . Taking the non-idealities of VDCC into account and routine analysis, the non-ideal output current of the presented multifunction biquad filter is re-written as: From Eq. (3), the natural frequency non-ideal case is given as: while, the quality factor for non-ideal case is defined as: It can be noticed from Eq. (11) and Eq. (12), that the voltage/current gain errors in the VDCC directly affect the magnitudes of natural frequency as well as quality factor. Thus, the practically accuracy design of the VDCC must be strictly considered to alleviate the mentioned non-ideal phenomenon. For example, in transistor level design, the high-performance current mirrors are suited to use in the active building blocks.

Simulation and Experimental Results
To evaluate and prove several functionalities of the presented transconductance-mode versatile filter with electronic controllability, we provide both program simulation and experimental procedures in this section.
Primarily, the simulation via PSpice was achieved by using the macro model parameters (level 3) of two commercial integrated circuits LM13700 (OTA) and AD844 (CCII) to investigate the workability of the designed transconductance-mode multifunction filter employing the practical realization of the VDCCs as shown in Fig. 2(a). The simulation setting was done as follows; DC bias currents for g m1 , g m2 and g m3 were set to I B1 = I B2 = I B3 = 100 µA, while the values of the passive device in the proposed versatile filter were chosen as R 1 = R 2 = 1.51 kΩ and C 1 = C 2 = 1 nF, the presented transconductance-mode filter was biased by a symmetrical ±5 VDC. Based on device values selected above, the theoretical f 0 calculated from Eq. 4 and the theoretical Q calculated from Eq. 5 are gained respectively to f 0 = 105.45 kHz, Q = 1 and the transconductance gain is 0.662 mS.   The simulation result of frequency response for LP, HP, BP, and BR filtering functions achieved from the presented scheme is shown Fig. 4. The simulated f 0 from this simulation is approximately 100 kHz. The deviation of simulated and theoretical value of the natural frequency is about 5.45 %. This deviation stems from the non-ideal effect of VDCC (voltage and current gain errors) as shown in Eq. (10), Eq. (11) and Eq. (12).
The simulation result of AP filtering response which functions as phase shifter is illustrated in Fig. 5. It is found from this result that the simulated gain response is almost constant for whole frequency range, while the phase variation of the output current is changed from 0 • to −360 • . All mentioned simulation results confirm that the presented transconductance-mode second order filter provides five filtering functions for the same configuration.   The control of Q value without changing the f 0 was proved by the simulation result of frequency response depicted in Fig. 6. In this simulation, the bias current I B1 was set for four values, 25 µA, 50 µA, 100 µA and 200 µA. Additionally, the tuning of the Q value can be also controlled without changing the f 0 by simultaneously setting the bias currents I B2 = I B3 = I B as the simulation shown in Fig. 7. In this result, I B2 = I B3 = I B was adjusted for four values as 50 µA, 100 µA, 200 µA, and 400 µA. The tuning of the f 0 without affecting the Q was proved as depicted in Fig  The simulated sinusoidal signal output current in time-domain for band-pass filtering function is depicted in Fig. 9 when resistor R 3 was set for three values as, 1 kΩ, 2 kΩ, and 4 kΩ, the sinusoidal input voltage with 40 mV p-p , f = 100 kHz was fed at input voltage node. This simulation result confirms that the output current amplitude of the presented transconductance-mode filter is controlled via R 3 . Total Harmonic Distortion (THD) investigation of the proposed transconductance-mode multifunction filter obtained in Fig. 10 was simulated (f = 100 kHz).  To investigate the practical workability of the proposed transconductance-mode filter, the experiment was also setup by using LM13700 and AD844. The used power supply voltage was ±5 V. The hardware setup was achieved by choosing C 1 = C 2 = 1 nF, all resistors were set to be 1.5 kΩ, and all bias currents were 110 µA. The 1.5 kΩ Resistance Load (RL) was connected to the output current node. So, the filter output responses were measured at voltage dropped at RL. Using mentioned element values, the obtained natural frequency as analyzed in Eq. (4) and the quality factor as analyzed in Eq. (5), this yields f 0 = 106.1 kHz and Q = 1. The measured frequency responses of the proposed transconductance-mode filter for the LP, HP, BP, and BR functions are shown in Fig. 11. The experimental natural frequency is approximately 104.7 kHz. The deviation of experimental and expected values of the natural frequency is about 1.32 %. Considering the simulation result in Fig. 4 and the experiment result in Fig. 11 it is found that the experimental HP response is affected from the wiring at low frequency.  For AP function, the inverting input is required. In experiment, inverting amplifier with unity gain was constructed from a AD844 and two resistors with same resistance value (1.5 kΩ). The frequency response of phase and gain of AP function are depicted in Fig. 14. From the experimental results in Fig. 13 and Fig. 14, it is found that the designed transconductance-mode filter offers five filtering responses as theoretically expected in Subsec. 2.2. The expected and measured gain responses of the filter are trivially different at low and high frequencies due to the effects of non-ideal properties of VDCC, as analyzed in Sec. 3.

LP
(c) 400 kHz. The tuning of the Q factor without affecting the f 0 as expected in Eq. (5) was experimentally tested. The experimental result of Q tuning is shown in Fig. 15 where the DC bias current I B1 was adjusted for four values as 65 µA, 110 µA and 240 µA. The tuning of the natural frequency without affecting quality factor as theoretical expected in Eq. (6) was proved as the result shown in Fig. 16, where the resistors R 1 = R 2 = R were set for three values, 1 kΩ, 1.5 kΩ, and 3 kΩ, the natural frequencies obtained from the experiment are located at 151.4 kHz, 104.7 kHz and 52.48 kHz, respectively. The measured input and output transient responses for BP, HP, LP, BR, and AP filter are illustrated in Fig. 15, Fig. 16, Fig. 17, Fig. 18 and Fig. 19, respectively. In mentioned experiment, the 20 mV p-p sinusoidal wave with three values of frequency (30 kHz, 100 kHz and 400 kHz) was applied as input.

Conclusion
The transconductance-mode multifunction second order filter with high input voltage nodes and high output current node has been introduced in this contribution. The proposed filter uses 3 VDCCs without multipleoutput to avoid circuit complexity and high power consumption as the active elements cooperating with 3 grounded resistors and 2 grounded capacitors. The standard 5 filter functions can be obtained by suitable input selections. The natural frequency and the quality factor can be adjusted electronically/orthogonally by controlling the bias currents of the VDCCs, while the output amplitude can be resistively adjusted. Additionally, the natural frequency is not temperature sensitive Also, if g m and g m1 are simultaneously tuned, the quality factor is not temperature sensitive The several performances of the presented versatile filter are demonstrated by both simulation and experimental results, they depict the workability of the presented versatile filter as expected. In addition to using in monolithic chip architecture, based on VDCC implemented from the commercially available ICs, the proposed multifunction filter is also appropriate for off-the-shelf implementation.