A Voltage Gain-Controlled Modified CFOA And Its Application in Electronically Tunable Four-Mode All-Pass Filter Design

This paper presents a new active building block (ABB) called voltage gain-controlled modified current feedback amplifier (VGC-MCFOA) based on bipolar junction transistor technology. The versatility of the new ABB is demonstrated in new first-order all-pass filter structure design employing single VGC-MCFOA, single grounded capacitor, and three resistors. Introduced circuit provides all four possible transfer functions at the same configuration, namely current-mode, transimpedancemode, transadmittance-mode, and voltage-mode. The pole frequency of the circuit can be easily tuned by means of DC bias currents. The theoretical results are verified by SPICE simulations based on bipolar transistor arrays AT&T ALA400CBIC-R process parameters. Keywords—Voltage gain-controlled modified CFOA, MCFOA, electronically tunable filter, four-mode circuit, all-pass filter.


I. INTRODUCTION
After the second-generation current conveyor (CCII) was introduced by Sedra and Smith in 1970 [1], it became the most versatile active building block (ABB) used for analog signal processing and the is basic ABB of many other active elements such as the composite current conveyor [2] done by an interconnection of two CCIIs, which was recently introduced as modified current feedback operational amplifier (MCFOA) [3]- [7] or the conventional CFOA [8] (CCII followed by unity gain voltage buffer -UGVB).It should be noted that, the MCFOA is different from the conventional CFOA defined in [8], since the W terminal current of the MCFOA is copied to the Y terminal in the opposite direction.However, it is well known that the Y-terminal current of the conventional CFOA is equal to zero.Short list of additional CCII-based ABBs is the following: the second-generation current-controlled conveyor (CCCII) [9], where the intrinsic resistance of X-terminal can be tuned, the differential difference CC (DDCC) [10] and its more versatile derivative the so-called universal current conveyor (UCC) [11]- [14], the dual-X CCII (DXCCII) [15], which is an interconnection of CCII and inverting CCII N. Herencsar, J. Koton, and K. Vrba are with the Department of Telecommunications, Faculty of Electrical Engineering and Communication, Brno University of Technology, Purkynova 118, 612 00 Brno, Czech Republic (phone: +420-541149190; fax: +420-541149192; e-mails: {herencsn, koton, vrbak}@feec.vutbr.cz;web: http://publicationslist.org/herencsar).
A. Lahiri is with the 36-B, J and K Pocket, Dilshad in which the Y-terminal is joined, the current differencing buffered amplifier (CDBA) [16] employing current differencing unit (CDU) based on two CCIIs and UGVB, or the universal voltage conveyor (UVC) [17] based on two CCIIs and differential UGVB.
Recently the further research has been focused on CCIIbased ABBs employing operational transconductance amplifier (OTA) [18] at their output stage.Probably the most known active element from this group is the current differencing transconductance amplifier (CDTA) [19], but other versatile elements such as the current-conveyor transconductance amplifier (CCTA) [20], where CCII is followed by an OTA, the differential-input buffered and transconductance amplifier (DBTA) [21] in which an interconnection of two CCIIs are followed by UGVB and OTA, the current follower transconductance amplifier (CFTA) [22], which employs a CCII with grounded Y-terminal and an OTA, the current backward transconductance amplifier (CBTA) [23], which is a specific interconnection of CCII and OTA, or the z-copy currentcontrolled current inverting transconductance amplifier (ZC-CCCITA) [24] have also received considerable attention.
In this paper we present a novel ABB called voltage gain-controlled modified current-feedback operational amplifier (VGC-MCFOA).The VGC-MCFOA joins the voltage gain control feature of the VCG-CCII in the conventional MCFOA [3]- [7].To demonstrate the usefulness of the VGC-MCFOA, a new first-order all-pass filter (AFP) structure is proposed, which operates in current-mode (CM), transimpedance-mode (TIM), transadmittance-mode (TAM), and voltage-mode (VM), respectively.To prove the theoretical analysis, SPICE simulations based on bipolar transistor arrays AT&T ALA400-CBIC-R process parameters are given.

II. CIRCUIT DESCRIPTION
The voltage gain-controlled modified current feedback operational amplifier (VGC-MCFOA) is a five-terminal ABB and its circuit symbol is shown in Fig. 1(a).Compared to the conventional MCFOA presented in [3]- [7], its voltage transfer from the Y to X terminal can be easily electronically tuned by means of the voltage gain h.Hence, the relations between the individual terminals of the VGC-MCFOA can be described by the following hybrid matrix: The frequency-dependent non-ideal current gains α j for j = {1, 2, 3} and voltage gains β k for k = {1, 2} are ideally equal to unity.Using a single-pole model [4], they can be defined as: where α oj and β ok are DC current and voltage gains of the element, respectively.The bandwidths 1/τ αj and 1/τ β k on the order of a few gigarad/s in current technologies are ideally equal to infinity.At low and medium frequencies i.e., f (2) and (3) turn to: where ε αij and ε β vk are the current and voltage tracking errors, whereas |ε αij | 1 and |ε β vk | 1, respectively.The basic idea for implementation of the proposed VGC-MCFOA is shown in Fig. 1(b), where the OTA 1 and OTA 2 are used to control the voltage gain h and two CCII+/represent the conventional MCFOA.Subsequently, the bipolar implementation of the VGC-MCFOA is shown in Fig. 1(c).The voltage gain control stage is formed by two simple differential pair amplifiers (transistors Q 1 -Q 6 ) and transistors Q 7 -Q 32 form the two CCII+/-based MCFOA, respectively.Here it is worth mentioning that the voltage gain control of VCG-CCII [29] was implemented using the same technique.For the implementation in Fig. 1(b) the voltage gain h can be expressed as: where g m1,2 = IB1 2VT and g m5,6 = IB2 2VT .Here, the V T is the thermal voltage (approximately 26 mV at 27 • C) and the I B1 and I B2 are control currents adjusting the transconductances g m1,2 and g m5,6 , respectively.Therefore, the voltage gain h in (6) can be given as: From (7) it is obvious that the proposed VGC-MCFOA can be easily adjusted electronically by either I B1 and/or I B2 currents.

A. Ideal Case Study
The proposed four-mode APF is shown in Fig. 2. Considering the ideal VGC-MCFOA (i.e.α j and β k are unity), based on the input selected two following cases can be considered: Case I: If I in1 = I in2 = I in , V in = 0 (grounded), and assuming R 2 = R 3 = R, then we can obtain the following transfer functions (TFs): (9) Case II: If the input of the APF is V in , I in1 = I in2 = 0, and assuming R 1 = R 2 = R, then for the circuit the following TFs can be obtained: Thus, from Eqs. ( 8)-( 11) it is seen that by suitable selection of input and output all four possible modes, i.e. current-, transimpedance-, transadmittance-, and voltage-mode firstorder APF can be realized with the same circuit topology.
The phase responses of TFs in ( 8) and ( 9) are calculated as follows: and phase responses of TFs in (10) and ( 11) are given as: Hence, the phases of TFs in ( 8) and ( 9) alter from 180 • to 0 • while according to (10) and (11) the phase shift change between 0 • to -180 • , respectively.
Consequently, the zero (ω z ) and pole (ω p ) frequencies of all four TFs can be found as: From Eqs. ( 14) and ( 15) it is clearly seen that the pole/zero frequency values can be easily tuned by means of the bias currents I B1 and/or I B2 .

B. Non-Ideal Analysis
Taking into account non-idealities of the VGC-MCFOA, TFs ( 8) and ( 9) in Case I of the convert to: and non-ideal phase responses from TFs ( 16) and ( 17) can be expressed as: The zero and pole frequencies in Eq. ( 14) change to: ) From Eq. ( 19), the active and passive sensitivities of zero and pole frequencies are given as: S and it is evident that the sensitivities of active parameters and passive components for ω (CM,TIM)z and ω (CM,TIM)p are at maximum unity in relative amplitude.The same study can also be done for the Case II with similar results.

IV. SIMULATION RESULTS
First, the proposed VGC-MCFOA in Fig. 1(c) has been further investigated in SPICE software.In the design the transistor model parameters NR100N (NPN) and PR100N (PNP) of bipolar arrays ALA400-CBIC-R from AT&T were used Fig. 3. Model of the VGC-MCFOA including parasitic elements 1.272 pF [31].The DC supply voltages are +V CC = −V EE = 2.5 V. Bias current I O = 400 µA has been chosen and I B1 , I B2 were set to 101 µA and 100 µA, respectively, to obtain voltage gain h = 1 precisely.The maximum values of terminal voltages and terminal currents without producing significant distortion were determined to be ±106.7 mV and ±16.23 mA, respectively.Evaluated DC current and voltage gains, f -3dB frequencies of transfers, and values of the X and W terminal parasitic resistances (in series) and Z and Y terminal parasitic resistances and capacitances (in parallel) shown in Fig. 3 are given in Table I.The total power dissipation of the proposed VGC-MCFOA was found to be 23.1 mW.Simulated voltage gain h responses between Y and X terminals is demonstrated in Fig. 4. In case of (A), the external bias current I B1 has been varied in large interval from 10 µA to 1 mA (equal to gain h = 0.1 to 10) at constant I B2 = 100 µA.From Fig. 4 it can be clearly seen that due to the above mentioned non-idealities of the VGC-MCFOA, the obtained voltage gain is in reduced range 0.101÷8.71.Hence, to overcome the the large variation of control current I B1 and simultaneously obtain the same gain range i.e. h = 0.1 to 10, the control current I B1 has been varied in reduced interval  THD variation of the proposed APF for both currentand transimpedance-mode responses against applied input current at f 0 = 29.9kHz 2.95; 8.46} to set the pole frequency of the proposed circuit as f 0 ≈ {10.2; 29.9; 100; 300} kHz.Using the INOISE and ONOISE statements, the input and output noise behavior with respect to frequency has also been simulated, as it is shown in Fig. 6.The output noise and equivalent input noise at pole frequency (f 0 ∼ = 29.9kHz) were found as 86.13 nV/ √ Hz and 93.38 pA/ √ Hz, respectively.The THD variation for both responses with respect to amplitude of the applied sinusoidal input current at pole frequency of 29.9 kHz (filter parameter: I B1 = 101 µA) is shown in Fig. 7.An input with the amplitude of 30 µA yields for both responses THD values of 1.59%.From the simulations it is evident that the gain and phase characteristics of the filter are in good agreement with theory and the deviations are caused by the non-idealities of the active element used.
V. CONCLUSION In this paper, a novel ABB called voltage gain-controlled MCFOA, which joins the voltage gain control feature of the voltage and current gain CCII in the conventional MCFOA.The usefulness of the tunable feature in the introduced VGC-MCFOA is demonstrated in four-mode first-order all-pass filter design.Since the capacitor in the circuit is grounded, the proposed filter is attractive for integration.The pole frequency can successfully be tuned in wide frequency range by means of external bias currents.The SPICE simulations confirm the theoretical assumptions.