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New voltage-controlled floating inductors employing CFOAs and an analog multiplier have been presented which have the attractive features of using a canonic number of passive components (only two resistors and a capacitor) and not requiring any component-matching conditions and design constraints for the intended type of inductance realization. The workability and applications of the new circuits have been demonstrated by SPICE simulation and hardware experimental results based upon AD844-type CFOAs and AD633-type/MPY534 type analog multipliers.

Voltage-controlled-resistors and a variety of other voltage-controlled impedances are useful elements in the realization of electronically-controllable filters and oscillators and have been investigated in past using a variety of active elements such as op-amps, operational transconductance amplifiers, operational mirrored amplifiers, current conveyors and current feedback op-amps, for instance, see [

A recent paper [^{1} to realize lossless VC-FI providing inductance value proportional to an external control voltage V_{c}. On the other hand, the second circuit of [_{c}. The circuits proposed in [

The purpose of this article is to present four new circuits which, in contrast to the circuits of [

The proposed circuits, which employ canonic number of only two resistors and a grounded capacitor (GC) for realizing lossless VC-FIs, are shown in ^{2} of an analog divider (as in the circuits of

and

Thus, the circuits realize an equivalent floating inductance_{2} = R_{3} to realize the intended type of VC-FI, the circuits of

Consider now the circuits of

These circuits, therefore, realize an equivalent VC-FI of value

Lastly, it must also be noticed that in contrast to the circuits of

To check the workability of the proposed circuits, all the VC-FIs were tested by utilizing them in the realization of a second-order voltage-controllable notch filter as shown in _{c} for the notch filter when it was realized by using the VC-FI of

In the simulations, AD844 type CFOAs were used which were biased with ±12 V DC power supplies. The simulation results of

For verifying the practical validity of the proposed VC-FI formulations, we present here the results of the hardware implementation of a voltage-controlled band reject filter (shown in _{1} = 1 k Ω, R_{2} = 1 k Ω, C_{1} = 1.0 nF, R_{0} = 680 Ω to obtain f_{0} = 5.2 kHz and bandwidth = 5.58 kHz. V_{c} was varied from 1 to 10 volts to vary the center frequency. An exemplary frequency response for V_{c} = 1 volt is shown in _{0} with respect to V_{c} has been shown in

The SPICE simulation results of

Four new lossless VC-FIs are introduced which employ a canonical number of passive components (namely, only one GC and two resistors) and realize the intended type of floating inductances without any conditions/design constraints. This is in contrast to the recently reported circuits of [

The workability of the new circuits as VC-FIs and the variability of the inductance value through an external control voltage V_{c} were demonstrated by SPICE simulation results of a notch filter, as well as through experimental results of another voltage-con- trolled notch filter.

It is expected that the proposed new circuits may find applications in situations requiring voltage-controlled inductors.

Lastly, it may be mentioned that the realization of many other grounded/floating, positive/negative and generalized linear voltage controlled impedances, based upon the ideas contained in [

and

respectively. The circuits of _{1}, R_{2} and C_{0} by impedances Z_{1}, Z_{2} and Z_{3} respectively.

Furthermore, the negative floating impedances are realizable from the configurations of

Senani, R., Bhaskar, D.R., Tripathi, M.P. and Jain, M.K. (2016) Canonic Realizations of Voltage- Controlled Floating Inductors Using CFOAs and Analog Multipliers. Circuits and Systems, 7, 3617-3625. http://dx.doi.org/10.4236/cs.2016.711306

In the context of the analysis and citations of references in [

1) The analysis of Section 2 at pages 192-193 of [_{eq} is correctly characterized by either the following y-matrix [

or equivalently, by the following transmission matrix [

Thus, a straight forward analysis of the circuit of

Therefore, the circuit of _{2} = R_{3}.

On the other hand, the circuit of _{1} = R_{2}. Therefore, the conditions _{1} + R_{2}) = R_{3} as given by the authors at page 193 of [

2) While comparing their propositions of ^{3} as reference 17, which is extremely surprising since this unpublished reference is not an open literature and was, therefore, definitely not available to the authors of [^{3} was quoted in the acknowledgement of reference [

3) Making a Hartley oscillator using an ideal op-amp is anomalous since inductor L_{1}, due to being connected directly from the output of the ideal op-amp to ground, will not appear in any open loop transfer function (or loop gain) or the characteristic equation of the circuit. A resolution to this anomaly has recently been provided in [