# MO-CCCCTA-Based Floating Positive and Negative Inductors and Their Applications

Authors: Neeta Pandey; Rishik Bazaz; Rahul Manocha
Journal: Journal of Electrical and Computer Engineering
 (2011)

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## Abstract

This paper introduces a floating inductance simulation using multiple output current controlled current conveyer transconductance amplifier (MO-CCCCTA). The simulated inductor retains minimum requirement of passive elements as only one-grounded capacitance is used for one inductor. PSPICE simulation has been done and included to ensure the validity of the approach. A few applications have also been included to substantiate the usability of the proposed circuit.


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## Body

## 1. Introduction

The current mode (CM) have received major consideration in the recent past owing to their various advantages like higher bandwidth, greater linearity, higher dynamic range, and lower power consumption which makes them a better candidate for analog circuits than their voltage mode counterparts. Furthermore, since signals are represented by current, a much lower voltage is required as compared with the voltage-mode signal processing. This makes the current mode circuits suitable for low-voltage designs. With recent introduction of second-generation current controlled conveyors (CCCII) [1], current conveyor transconductance amplifier (CCTA) [2], and MO-CCCCTA [3], current conveyors' applications have been extended to the domain of electronically adjustable functions.Despite the fact that a spiral inductor can be realised in VLSI circuits, the need for improvement cannot be ignored. It has many disadvantages, namely, space usage, cost, and robustness. Many analog functional blocks (AFBs) have already been reported for active simulation of inductors to extract benefits of passive prototypes [4–25]. These AFBs include Operational Transconductance Amplifiers (OTAs) [4, 8, 18], Current Feedback Opamps (CFOAs) [20], current conveyors and current controlled conveyors [7–12, 14, 15, 18, 19, 22–24], Operational Transresistance Amplifier [13], Current Differencing Buffered Amplifier [16], Current Backward Transconductance Amplifier [17], Differential Difference Current Conveyor [21], and Voltage Differencing Differential Input Buffered Amplifiers [25]. The study of floating inductor simulators [4, 7–11, 14–25] shows that the circuits suffer from one or more disadvantages: use of more than one active element [4, 7–11, 14, 15, 18–20, 22–25], overuse of passive elements [7, 9–11, 16–22], lack of electronic tunability [7, 9–11, 16, 19–22], and use of floating capacitance [6–11, 14, 15, 21, 22].Negative inductance plays a significant role in cancellation as well as compensation of parasitic inductances. Actively simulated negative inductors have various applications(i)
in microwave circuits for impedance matching;(ii)
in compensation of bond wire in high-speed/low-power integrated circuits (ICs) because of reduced noise margin.Some active realisation of negative inductance has also been reported in the literature [4, 17, 18, 23, 24]. These too suffer from the weaknesses as enumerated earlier. The magnitude of both the inductors is linearly proportional to the frequency in both cases. It is the phase which differentiates the two. The positive inductor has a phase of +90°, while the negative inductor has a phase of −90°. MO-CCCCTA is a modified version of earlier introduced CCTA and CCCII. MO-CCCCTA has been employed owing to the various advantages such as output current gain controllability, resistorlessness, and compactness in chip area.In this paper, we present electronically controllable floating inductance simulations using MO-CCCCTA as active component. The circuit construction comprises only single MO-CCCCTA block and a grounded capacitor, which is suited for IC fabrication. The inductor value can be electronically tuned by input bias currents of the MO-CCCCTA. The performances of the proposed circuits are simulated with PSPICE, and they showed good agreement with ideal passive counterparts. Some applications such as fifth order low-pass filter, RLC band-stop filter and inductance nullifying circuit, are also given to demonstrate the usefulness of the proposed element.


## 2. Functional Block Description

The MO-CCCCTA as shown in Figure1 is characterized by the port relations [3] of (1). The MO-CCCCTA has a finite input resistance RX at the X input terminal and an additional transconductance gm amplifier in the output side(1)[IYVXIZ±IO±]=[0000RX100±100000±gm0][IXVYVZVO].
The parasitic resistance RX and the transconductance gm can be controlled by bias currents Ib1 and Ib2, respectively.  A BJT-based MO-CCCCTA is illustrated in Figure 2, and the intrinsic resistance (RX) and transconductance (gm) are expressed as(2)RX=VT2Ib1,gm=Ib22VT,
where Ibi (i=1, 2) and VT are the bias currents and the thermal voltage, respectively.Figure 1
The functional symbol of MO-CCCCTA.Figure 2
A possible bipolar implementation of the MO-CCCCTA.


## 3. Inductor Design

The proposed positive floating inductor is shown in Figure3, and its negative configuration is shown in Figure 4. Using the routine analysis of the circuit, the impedance may be calculated as(3)Zin=sRXCgm.
The equivalent positive inductance value in terms of bias current is(4)Leq=CVT2Ib1Ib2.
Similarly, the equation for negative inductance is(5)Leq=-CVT2Ib1Ib2.Figure 3
Proposed floating positive inductance.Figure 4
Proposed floating negative inductance.


### 3.1. Effect of Nonidealities

The frequency performance of the inductor may deviate from the ideal ones due to nonidealities. The nonidealities may be categorized in two groups: transfer errors and parasites. The first comes from transfer errors in internal current and voltage transfers of MO-CCCCTA and their frequency dependence and can be written as(6)[IYVXIZ±IO±]=[0000RXβ00±α00000±γgm0][IXVYVZVO],
where the coefficients β=1-εv, α±=1-εi±; εv and εi± denote voltage and current tracking errors from Y to X terminal and X to Z terminal, respectively. The coefficient γ denotes current gain from Z terminal to O terminal. The second group of nonidealities comes from parasites of MO-CCCCTA comprising of resistances and capacitances connected in parallel at terminals Y, Z, and O (i.e., RY, CY, RZ, CZ, RO, CO). The effects of these parasites on inductor behaviour depend strongly on circuit topology. In the presence of these parasites, the capacitor C in circuits of Figures 3 and 4 modifies to C//CZ//RZ. Considering the nonidealities outlined above, (4) and (5) modify, respectively to(7)sLeq=(sCeq+GZ)VT2αγIb1Ib2,(8)sLeq=-(sCeq+GZ)VT2αγIb1Ib2,
where Ceq=C//CZ and GZ=1/RZ.It may be noted that the impedance value deviates from the ideal one due to nonunity values ofα, β, and γ.  The values of α, β, and γ are simulated to, respectively, as 0.973, 0.999, and 0.998. The maximum operating frequency will be influenced by parasitic resistance at Z port as the parasitic capacitance at Z port may be accommodated in external capacitor. The parasitic resistances and capacitances for MO-CCCCTA are simulated to be RY=749 kΩ, CY=6.89 pF; RZ=789 kΩ, CZ=4.03 pF; RO=1.70 MΩ, CO=3.3 pF, respectively. It may be noted that by selecting C≫CZ, the   effect of parasitic capacitance may practically be ignored. However, a zero (1/RZCeq) is introduced in impedance of (7) and (8) which limits the lower frequency operation.The current and voltage transfer functions, apart from having nonunity values, also have poles at high frequencies. However, the maximum frequency of operation will be limited by poles of voltage (fβ) and current (fα,fγ) and transfers which are simulated to be 70.09 MHz, 33.7 MHz, and 78.85 MHz for the MO-CCCCTA of Figure 2. The effect can, however, be ignored if the operating frequencies are chosen sufficiently smaller than voltage and current transfer pole frequencies of the MO-CCCCTA.


### 3.2. Comparison

Survey of the literature till date on floating inductors reveals that two or more active blocks are required for implementation except those available in [16, 17, 21], where a single active block is required as that of presented work. It reveals that our work is comparable with the works of [16, 17, 21]. Hence we compare our work with [16, 17, 21].Requirement of Passive Components:
(1)
The total number of passive components is more than one in [16, 17, 21], whereas the proposed topologies use a single passive component.(2)
Floating passive components are used in [21] which is not considered good from IC implementation viewpoint.Electronic Tunability:
(1)
There is no electronic tunability in [16, 21].(2)
Though tunability is available in [17] through one bias current, the proposed topology has more flexibility as the inductance value can be tuned via two bias currents of MO-CCCCTA.


## 3.1. Effect of Nonidealities

The frequency performance of the inductor may deviate from the ideal ones due to nonidealities. The nonidealities may be categorized in two groups: transfer errors and parasites. The first comes from transfer errors in internal current and voltage transfers of MO-CCCCTA and their frequency dependence and can be written as(6)[IYVXIZ±IO±]=[0000RXβ00±α00000±γgm0][IXVYVZVO],
where the coefficients β=1-εv, α±=1-εi±; εv and εi± denote voltage and current tracking errors from Y to X terminal and X to Z terminal, respectively. The coefficient γ denotes current gain from Z terminal to O terminal. The second group of nonidealities comes from parasites of MO-CCCCTA comprising of resistances and capacitances connected in parallel at terminals Y, Z, and O (i.e., RY, CY, RZ, CZ, RO, CO). The effects of these parasites on inductor behaviour depend strongly on circuit topology. In the presence of these parasites, the capacitor C in circuits of Figures 3 and 4 modifies to C//CZ//RZ. Considering the nonidealities outlined above, (4) and (5) modify, respectively to(7)sLeq=(sCeq+GZ)VT2αγIb1Ib2,(8)sLeq=-(sCeq+GZ)VT2αγIb1Ib2,
where Ceq=C//CZ and GZ=1/RZ.It may be noted that the impedance value deviates from the ideal one due to nonunity values ofα, β, and γ.  The values of α, β, and γ are simulated to, respectively, as 0.973, 0.999, and 0.998. The maximum operating frequency will be influenced by parasitic resistance at Z port as the parasitic capacitance at Z port may be accommodated in external capacitor. The parasitic resistances and capacitances for MO-CCCCTA are simulated to be RY=749 kΩ, CY=6.89 pF; RZ=789 kΩ, CZ=4.03 pF; RO=1.70 MΩ, CO=3.3 pF, respectively. It may be noted that by selecting C≫CZ, the   effect of parasitic capacitance may practically be ignored. However, a zero (1/RZCeq) is introduced in impedance of (7) and (8) which limits the lower frequency operation.The current and voltage transfer functions, apart from having nonunity values, also have poles at high frequencies. However, the maximum frequency of operation will be limited by poles of voltage (fβ) and current (fα,fγ) and transfers which are simulated to be 70.09 MHz, 33.7 MHz, and 78.85 MHz for the MO-CCCCTA of Figure 2. The effect can, however, be ignored if the operating frequencies are chosen sufficiently smaller than voltage and current transfer pole frequencies of the MO-CCCCTA.


## 3.2. Comparison

Survey of the literature till date on floating inductors reveals that two or more active blocks are required for implementation except those available in [16, 17, 21], where a single active block is required as that of presented work. It reveals that our work is comparable with the works of [16, 17, 21]. Hence we compare our work with [16, 17, 21].Requirement of Passive Components:
(1)
The total number of passive components is more than one in [16, 17, 21], whereas the proposed topologies use a single passive component.(2)
Floating passive components are used in [21] which is not considered good from IC implementation viewpoint.Electronic Tunability:
(1)
There is no electronic tunability in [16, 21].(2)
Though tunability is available in [17] through one bias current, the proposed topology has more flexibility as the inductance value can be tuned via two bias currents of MO-CCCCTA.


## 4. Simulation Results and Discussions

To validate the theoretical predictions, the proposed circuits are simulated with SPICE using schematic of MO-CCCCTA, as given in Figure2, and PR100N and NR100N bipolar transistors [26]. The DC supply voltage of 1.5 V is used. The bias current values are Ib1=50 μA and Ib2=200 μA for all the simulations. Figures 5 and 6 show the transient responses obtained from the proposed simulated inductors. The impedances of the proposed circuit with respect to frequency, which are compared to ideal inductor, are also shown in Figure 7. It can be seen that the circuit can be used up to several megahertz. At a high-frequency range, the proposed inductors degrade their performances. Figure 8 shows impedance phase plot.Figure 5
Transient response for positive inductor.Figure 6
Transient response for negative inductor.Figure 7
Magnitude plot for proposed floating inductor.Figure 8
Phase plot for proposed inductor.Parametric simulation by varying the two bias currents was also done. Figures9 and 10 show the variation in impedance magnitude for different Ib1 and Ib2, respectively. It is confirmed that the simulated inductance values can be adjusted by corresponding input bias currents.Figure 9
Variation of impedance withIb1.Figure 10
Variation of impedance withIb2.


## 5. Applications

To illustrate the use of proposed floating inductor, various applications like band-stop filter and fifth order low-pass filter were simulated. All the circuits have been simulated using PSPICE. The passive RLC 5th order low-pass filter as shown in Figure11 was taken as reference. The circuits are designed for half power frequency ω-3dB=10 Mrad/s or 1.59 MHz.  Then after scaling the different component values are C=475.2 pF and C′=1.538 nF. The capacitance required in the floating inductance block is 0.73 nF each. Each circuit is denormalized by source resistance R=RX, which is realized using the same MO-CCCCTA AFB. The magnitude response of the proposed circuit has been shown in Figure 12. The simulated results show close conformity with the theoretical results. The magnitude response of the active low-pass filter closely follows its passive implementation.Figure 11
5th order low pass filter.Figure 12
Magnitude response of 5th order filter.A band-stop filter with center frequency of 600 KHz was also simulated. Time domain response was also carried out. The filter model is shown in Figure13, and its magnitude response is shown in Figure 14. The input signal comprised of three frequencies of 10 KHz, 100 KHz, and 600 KHz. Signal amplitude was 10 mV each. The transient response with its spectrum for input and output is shown in Figure 15, which clearly shows that the 600 KHz signal is significantly attenuated.Figure 13
Band-stop filter.Magnitude response of band-stop filter.
(a)(b)Transient response and its spectrum (a) input and (b) output.
(a)(b)The third application is the inductance compensation circuit as shown in Figure16. The transient response has been shown in Figure 17. It can be observed that the positive inductance in the circuit has been nullified by the simulated negative floating inductor as there is very low phase lag between current and voltage.Figure 16
Inductance-nullifying circuit.Figure 17
Transient response of inductor-nullifying circuit.


## 6. Conclusion

The novel floating positive and negative inductors with electronic tunability employing only single MO-CCCCTA have been introduced in this paper. The proposed inductors can be easily and widely tuned using bias current values. The simulated results of active and passive circuits match to a wide range of operation. The proposed inductors have been employed in construction of low-pass filter, band-stop filter and inductance-nullifying circuit. PSPICE simulation has been used to verify the functionality of various circuits.



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*Source: 150354-2011-09-19.xml*