A Configuration for Realizing Voltage Controlled Floating Inductance and Its Application

A configuration using current feedback amplifiers AD844 and multiplier AD534 has been presented, which is capable of realizing Voltage Controlled Floating Inductance (proportional and inverse proportional). The application of band pass filter in Figure 4(a), notch filter in Figure 5(a) and Hartley oscillator in Figure 6(a) and simulation result in Figures 4(b)-(d), Figures 5(b)-(d), Figures 6(b)-(d) shows the workability of proposed configuration.


Introduction
Simulation of inductor has been popular area of analog circuit research.Due to the well known difficulties of realizing on chip inductors of moderate to high values and high quality factors, simulated inductors have been the alternative choice for realizing inductor-based integrated circuit.Simulated inductors are also useful in discrete designs in which case they can replace bulky Passive inductors and after the advantages of reduced size, reduced cost and complete elimination of undesirable mutual coupling when several inductors are being used in a circuit.
Electronically controlled inductor such as voltage controlled floating inductance finds application in automatic gain controller, filter and oscillator circuit.A number of configuration using a variety of active elements such as op-amps, operational-mirrored amplifier, current controlled conveyors, OTA and Combination have so far been presented in the literature for realizing such elements in Floating Form [1]- [16].
Recently, the current feedback op-amps (CFOAs) such as AD844 have attracted considerable attention in literature as alternative building blocks for analog circuit design due to the following advantages i) Widen bandwidth that is relatively independent closed loop gain.
ii) Very high slew rate (2000 V/us).iii) Ease of realizing various functions with least number of external passive components.The main objective of paper is therefore to present a new configuration which is capable of realizing voltage controlled Floating inductance both in proportional and inversely proportional form and its application.
The paper is organized as follow:   Terminal Equations of CFA: 1(a).The x and y terminal of CFA are denoted by (−) sign and (+) sign respectively.A CFA is equivalent to a plus type conveyor with a voltage buffer and is very suitable building block for realization of active circuit.

MPY534 as MULTIPLIER Description
The MPY534 is a highly accurate, general purpose four-quadrant analog multiplier.Its accurately laser trimmed transfer characteristics make it easy to use in a wide variety of applications with a minimum of external parts and trimming circuitry.Its differential X, Y and Z inputs allow configuration as multiplier, squarer, divider, square-rooter and other functions while maintaining high accuracy.

Case 1
Implementation of voltage controlled floating inductance which is directly proportional to control voltage (V c ).
The proposed configuration shown in the Figure 2(a) where each CFOAs is characterized by 0 = and multiplier with two resistance and capacitance is used for realizing the voltage controlled floating inductance.

Y Y SL I I − = −
Putting the value of (V 1 − V 2 ) and (I 1 − I 2 ) from Equation ( 3) and ( 6) After simplification we get, ( ) = and multiplier with two resistance and capacitance is used for realizing the floating voltage controlled inductance.

Mathematical Analysis
Output of the multiplier ( ) ) Now from CFOA (2)

( )(
) Applying KCL across capacitor we get ( ) Again applying KCL at input node ( ) rearranging the equation we get, Now from standard floating inductor: ( )

V V sL I I − = −
Putting the value of (V 1 − V 2 ) and (I 1 − I 2 ) from Equation ( 3) and ( 4) Thus inductance is inversely proportional to control voltage (V c ). 2(a) and Figure 3(a)

Band Pass Filter
In Figure 4(a), we realized a Band pass filter using voltage controlled floating inductance and resistance, capacitance.

Result
In the above simulation result, we show the frequency response of band pass filter made from voltage controlled floating inductance, a resistance and a capacitor.The band pass filter was designed for frequency f 0 = 5 kHz, 7.1 kHz and 10 kHz with different value of inductance as given in Table 1.The center frequency of filter was found to be electronically tunable from 5 kHz to 10 kHz with V c varying from 1 to 4. Thus from the above result it can be seen that by varying the control voltage (V c ) center frequency (F c ) of the band pass filter can be changed .Thus we can control the center frequency by varying V c .

Notch Filter
In Figure 5(a), we realized a RLC notch filter using voltage controlled floating inductance and resistance, capacitance.

Result
In the above simulation result, we show the frequency response of notch filter made from voltage controlled floating inductance, a resistance and a capacitor.The notch filter was designed for frequency f 0 = 5 kHz, 7.1 kHz and 10 kHz with different value of inductance as given in Table 2.The center frequency of filter was found to be electronically tunable from 5 kHz to 10 kHz with V c varying from 1 to 4.
Thus from the above result it can be seen that by varying the control voltage (V c ) center frequency (F c ) of the notch pass filter can be changed .Thus we can control the center frequency by varying V c .

Hartley Oscillator
In Figure 6(a), we realized an op-amp Hartley oscillator using voltage controlled floating inductance and, capacitance.

Result
In the above simulation results, we show the frequency response of Hartley oscillator made from voltage controlled   floating inductance, an op-amp and a capacitor.The Hartley oscillator was designed for frequency f 0 = 1.125 kHz, 1.59 kHz and 2.25 kHz with different value of inductance as given in Table 3.The center frequency of oscillator was found to be electronically tunable from 1.125 kHz to 2.25 kHz with V c varying from 1 to 4.
From the above result, it can be seen that by varying the control voltage (V c ) center frequency of oscillation of Hartley oscillator can be changed .Thus we can control the frequency of oscillation by varying V c .

Conclusion
The proposed circuit in Figure 2(a) and Figure 3(a) realized and compared with reference [17].In Table 4, we have used less number of CFOAs and less number of passive components.The use of multiplier nullifies the effect of non linearity of FET.The application of BPF, notch filter a Hartley oscillator have been discussed.

Figure 1 (
a) is the basic terminal equation of CFOA.Figure 1(b) is the basic structure of multiplier.Figure 2(a) is the first case of the floating voltage controlled inductance.Figure 3(a) is the another case of floating voltage controlled inductance Figure 4(a) explained the application of voltage controlled inductance as BPF.

Figure 5 (
a) explained the application of voltage controlled inductance as notch filter.

Figure 6 (
a) explained the application of voltage controlled inductance as an oscillator.

Figure 2 .
Figure 2. (a) Proposed floating voltage controlled inductance configuration; (b) Realized floating inductor.Thus inductance (L) is directly proportional to control voltage (V c ) 2.2.Case 2 Implementation of voltage controlled floating impedance with inversely proportional to control voltage.The proposed configuration shown in the Figure 3(a).where each CFOAs is characterized by 0

Table 1 .
Effect of variation in control voltage (V c ) on center frequency (f c ) of band pass filter.

Table 2 .
Effect of variation in control voltage (V c ) on center frequency (f c ) of notch filter.

Table 3 .
Effect of variation in control voltage (V c ) on center frequency (f c ) of Hartley oscillator.