Realization of New Electronically Controllable Grounded and Floating Simulated Inductance Circuits Using Voltage Differencing Differential Input Buffered Amplifiers

A new active circuit is proposed for the realisation of lossless grounded and floating inductance employing Voltage Differencing Differential Input Buffered Amplifiers (VD-DIBAs). The proposed grounded simulated inductance circuit employs two VD-DIBAs and a single-grounded capacitor whereas the floating simulated inductance circuit employs three VD-DIBAs and a grounded capacitor. The circuit for grounded inductance does not require any realization conditions whereas in case of floating inductance, only equality of two transconductances is needed. Some sample results demonstrating the applications of the new simulated inductors using VD-DIBAs have been given to confirm the workability of the new circuits.


The Proposed New Configurations
The schematic symbol and equivalent model of the VD-DIBA are shown in Figures 1(a) and 1(b) [26].The model includes two controlled sources: the current source controlled by differential voltage (V + -V − ), with the transconductance g m , and the voltage source controlled by differential voltage (V z -V v ), with the unity voltage gain.The VD-DIBA can be described by the following set of equations: The proposed configurations are shown in Figures 2 and 3, respectively.
Active and Passive Electronic Components VD-DIBA  [26].A routine analysis of the circuit shown in Figure 2 results in the following expression for the input impedance The circuit, thus, simulates a grounded inductance with resulting value given by On the other hand, an analysis of the circuit shown in Figure 3 yields which proves that the circuit simulates a floating lossless inductance with resulting inductance value given by Note that ensuring g m1 = g m3 requires only the equality of the two DC bias currents of the VD-DIBAs which can be easily implemented in practice

Nonideal Analysis and Sensitivity Performance
Let R z and C z denote the parasitic resistance and parasitic capacitance of the Z terminal.Taking into account the nonidealities of the VD-DIBA, namely, ) are voltage tracking errors of the VD-DIBA.
For the circuit shown in Figure 2, the input impedance will become The non-ideal equivalent circuit of the grounded inductor is shown in Figure 4 The sensitivities of L with respect to active and passive elements are  For the circuit shown in Figure 3 the input-output currents and voltages relationship is given by: ).The non-ideal equivalent circuit of floating inductor is shown in Figure 5: Figure 6: BPF realized by the new grounded simulated inductor.

Verification of the Workability of the New Proposed Grounded/Floating Inductance Configurations
The workability of the proposed simulated inductors has been verified by realizing a band pass filter (BPF) and band reject filter (BRF), respectively.Figure 6 shows the schematics for the realization of a BPF, using the new simulated grounded inductor.
The transfer function realized by this configuration is given by Figure 7 shows the schematics for the realization of a BRF, using the proposed floating inductor circuit.The transfer function realized by this configuration is given by The performance of the new simulated inductors was evaluated by PSPICE simulations.Since VD-DIBA is not a commercially available IC, a possible implementation of VD-DIBA using commercially available devices is shown in Figure 8.A CMOS-based OTA as shown in Figure 17 and CFOA SPICE macromodel of AD844 to realise VD-DIBAs as per the schematic of Figure 8 were used to determine the frequency response of the grounded and floating simulated inductors.The following values were used for grounded inductor C = 16.65 pF, g m1 = g m2 = 258.09 1 uA/V, for floating inductor C = 16.65 pF, g m1 = g m3 = 258.091uA/V.From the frequency response of the simulated grounded inductor (Figure 9) it has been observed that the inductance value remains constant up to 1 MHz.From the frequency response of the simulated floating inductor (Figure 10) it has been observed that the inductance value remains constant up to 1 MHz.
To verify the theoretical analysis, the application circuits shown in Figures 6 and 7 15 shows the step response of the filter of Figure 6 which confirms the stability of the implemented filter.Figure 16 shows the simulated spectrum of the output signal Vo in Figure 6, where the total harmonic distortion (THD) is found to be 2.98%.The comparison of performance characteristics of VD-DIBA with OTA (CA3080) and CMOS OTA (as shown in Figure 17) has been given in Table 1.These results, thus, confirm the validity of the application of the proposed grounded/floating simulated inductance circuits.

Concluding Remarks
Among various modern active building blocks, VD-DIBA is emerging as quite flexible and versatile building block for analog circuit design.However, the use of VD-DIBA in the realization of grounded/ floating inductor had not been known earlier.This paper has filled this void by introducing new VD-DIBA-based grounded and floating inductor configurations.This paper, thus, has added a new application circuits to the existing repertoire of VD-DIBA-based application circuits.The workability of new propositions has been confirmed by SPICE simulations.

Figure 5 :
Figure 5: Non-ideal equivalent circuit of floating inductor of Figure 3.

Figure 16 :
Figure 16: Simulated spectrum of the output signal Vo in Figure 6.
have been simulated using CMOS-based OTA as shown in Figure 17 and CFOA SPICE macromodel of AD844 to realise VD-DIBAs as per the schematic of Figure 8.The component values used were for Figure 6, C 1 = 16.65 pF, C 2 = 16.65 pF, R 1 = 5.479 kΩ, and for Figure 7, C 1 = 16.65 pF, C 2 = 16.65 pF and R 1 = 10.959kΩ, the VD-DIBA was biased with ±1 volts D.C. power supplies with I B1 = I B2 = I B3 = 32 μA.I B1 , I B2 , and I B3 are the biasing currents for transconductances.