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New electronically-controllable lossless grounded and floating inductance simulation circuits have been proposed employing Voltage Differencing Transconductance Amplifiers (VDTA). The proposed grounded inductance (GI) circuit employs a single VDTA and one grounded capacitor whereas the floating inductance (FI) circuit employs two VDTAs and one grounded capacitor. The workability of the new circuits has been verified using SPICE simulation with TSMC CMOS 0.18 μm process parameters.

Several circuits and techniques for the simulation of grounded and floating inductance employing different active elements such as operational amplifiers, current conveyors, current controlled conveyors, current feedback operational amplifiers, operational mirrored amplifiers, differential voltage current conveyors, current differencing buffered amplifiers, current differencing transconductance amplifiers, operational transconductance amplifiers (OTAs) have been reported in the literature see [1-33] and the references cited therein. Many active elements have been introduced by Biolek, Senani, Biolkova and Kolka in [

The symbolic notation of the VDTA is shown in _{P} and V_{N} are input terminals and Z, X^{+} and X^{–}^{ }are output terminals. All terminals of VDTA exhibit high impedance values [

The proposed grounded and floating inductance circuits are shown in Figures 2 and 3 respectively.

A routine circuit analysis of the circuit shown in

The circuit, thus, simulates a grounded inductance with the inductance value given by

which is electronically controllable by either or.

On the other hand, analysis of the new FI circuit shown in

which proves that the circuit simulates a floating lossless electronically-controllable inductance with the inductance value given by

Considering the various VDTA non-ideal parasitics i.e., the finite X-terminal parasitic impedance consisting of a resistance in parallel with capacitance and the parasitic impedance at the Z-terminal consisting of a resistance in parallel with capacitance.

The non-ideal input impedance for the circuit shown in

From Equation (6) a non-ideal equivalent circuit of the grounded inductor is derivable which is shown in

Where, , , and

From the above, the sensitivities of L_{GI} with respect to various active and passive elements are found to be

, , , (7)

Similarly, for the circuit shown in

with

and (8)

The non-ideal equivalent circuit of floating inductor of

where and

The various sensitivities of L_{FI} with respect to active and passive elements are:

, ,

, (9)

Taking g_{m}_{1} = g_{m}_{2} = 631.702 μA/V, C_{z} = C_{Z} = 0, R_{x} = R_{z}_{ }= ∞ and C = 0.01nF, these sensitivities are found to be (1, 0, 0, 0, 1, 1) and (1, 0, –1, –1) for Equations (7) and (9) respectively. Thus, all the passive and active sensitivities of both grounded and floating inductance circuits are low.

The workability of the proposed simulated inductors has been verified by realizing a band pass filter (BPF) as shown in Figures 6 and 7.

The transfer function realized by this configuration is given by

from where it is seen that bandwidth and centre frequency both are independently tunable, the former by R_{1} and the latter by any of the transconductances g_{m}_{1}, g_{m}_{2} and C_{2}.

The transfer function realized by the configuration shown in

with

and

In this case, bandwidth is tunable by R_{0} whereas centre frequency can be tuned by C_{0}.

Performance of the new simulated inductors was verified by SPICE simulations. CMOS-based VDTA from [_{m}_{1} = g_{m}_{2} = 631.7 μA/V. From the frequency response of the simulated grounded inductor (

To verify the theoretical analysis of the application circuits shown in Figures 6 and 7, these configurations have also been simulated using CMOS VDTAs. The component values used were for _{1} = 5 pF, C_{2} = 0.01 nF, R_{1} = 1.58 kΩ and for _{0} = 0.01 nF, C_{1} = 5 pF, R_{0} = 1.58 kΩ. The VDTAs were biased with ±0.9 volts D.C. power supplies with I_{B}_{1} = I_{B}_{2} = I_{B}_{3 }= I_{B}_{4} = 150 μA. Figures 10 and 11 show the simulated filter responses of the BP filters. A comparison of the other

previously known grounded and floating inductance simulators has been presented in

The above results, thus, confirm the validity of the applications of the proposed grounded and floating simulated inductance circuits.

New electronically-controllable circuits of lossless grounded and floating inductance have been proposed employing VDTAs. The proposed grounded inductance circuit employs only one VDTA and one grounded capacitor. On the other hand, the floating inductance configuration uses two VDTAs and one grounded capacitor, requires realization conditions for floatation. A comparison of the other previously known grounded and floating inductance simulators has been presented in