New Electronically-Controllable Lossless Synthetic Floating Inductance Circuit Using Single VDCC

A new electronically-controllable lossless floating inductance (FI) circuit (without any matching condition) has been presented, which employs only one Voltage Differencing Current Conveyor (VDCC), one grounded capacitor and one grounded resistor. The main aim of the paper is to present a new floating inductance simulator using single active device with minimum passive components. The proposed floating inductance simulator can be electronically controllable by changing the bias current. The workability of the new presented FI circuit has been verified using SPICE simulation with TSMC CMOS 0.18 μm process parameters.

Therefore, the main objective of this paper is to propose a new circuit which employs one VDCC, one grounded capacitor and one grounded resistor to realize electronically-controllable lossless matchless FI circuit.The presented circuit has also the features like only two passive components (i.e. one grounded capacitor (as desired for IC implementation) and one grounded resistor) and low active and passive sensitivities.The validity of the presented new circuit has been verified using SPICE simulation with TSMC CMOS 0.18 μm process parameters.

The Proposed New Configuration
The symbolic notation of recently proposed active building block, VDCC is shown in Figure 1, where P and N are input terminals and Z, X, W P and W N are output terminals.All of the terminals exhibit high impedance, except the X terminals [27].The VDCC is characterized by the Equation (1).
The proposed FI circuit is shown in Figure 2.
A routine circuit analysis of the new FI circuit shown in Figure 2 yields which shows that the circuit simulates a floating lossless electronically-controllable inductance with the inducbtance value given by eq m CR L g = (3)

Non-Ideal Analysis and Sensitivity Performance
The proposed FI circuit consisting various non-ideal parasitics is shown in Figure 3.The X-terminal parasitic impedance consisting of a resistance 2 p R in series with inductance x L , the parasitic impedance at the W P -ter- minal consisting of a resistance where  ( ) The non-ideal equivalent circuit of FI of Figure 3 is derivable from Equation (4) and is shown in Figure 4.
The various sensitivities of L FI with respect to active and passive elements are: Thus, all the passive and active sensitivities of FI circuit are low.

Application Examples of New FI Circuit
The workability of the proposed FI circuits are demonstrated by realizing (i) a band pass filter (BPF) (Figure 5) and (ii) a fourth order Butterworth low pass filter with a cutoff frequency 500 kHz was designed using the normalised proto-type shown in Figure 6 [15].
The transfer function realized by the configuration shown in Figure 5 is given by From Equation ( 6), it is clear that centre frequency is tunable by R 2 .
The performance of the proposed circuit was verified by SPICE simulations.The frequency response of the FI circuit was obtained by using CMOS-based VDCC [27].The following values were used for FI circuit: C = 0.01 nF, g m = 277.833μA/V, R = 10 kΩ.From the frequency response of the simulated FI circuit (Figure 7) it has been observed that the inductance value remains constant upto 10 MHz.
The application circuits shown in  1.
Thus, the above simulation results confirm the validity of the applications of the proposed FI circuit.

Conclusions
A new electronically-controllable loss-less FI circuit without any matching condition has been proposed which employs one VDCC, one grounded capacitor and one grounded resistor.The proposed circuit offers the following advantageous features: 1) only two passive components i.e. one grounded capacitor (as desired for IC implementation) and one grounded resistor; 2) no matching condition; 3) fully electronically controllable (by changing bias currents); and 4) low active and passive sensitivities.The SPICE simulation results have con-firmed the workability of the new proposed floating inductance circuit.

1 pR in parallel with capacitance 1 pC 4 pR in parallel with capacitance 4 pC
, the parasitic impedance at the W Nterminal consisting of a resistance and the parasitic impedance at the Zterminal consisting of a resistance 3 p R .For the circuit shown in Figure3, the input-output currents and voltages relationship is given by

Figure 5 .
Figure 5. Band pass filter realized by the new FI circuit of Figure 2.