VERSATILE ACTIVE BIQUAD USING FTFNs

A universal active biquad using the four-terminal floating nullors 
(FTFNs) is presented. The propsed circuit uses two FTFNs, 
three capacitors and two resistors. The proposed circuit has three 
input voltages and can simultaneously provide a high-impedance 
output current and/or an output voltage. Without changing the 
circuit topology, the output voltage can realise lowpass, 
highpass, bandpass, notch and allpass transfer functions and the 
output current can realise bandpass and highpass transfer 
functions. The proposed circuit enjoys low active and passive 
sensitivities and independent control of the parameters ωo and ω0/Q0.


INTRODUCTION
The four-terminal floating nullor (FTFN) is a more flexible and versatile building block than the operational amplifier and the current- conveyor [1][2][3][4].This explains the growing interest in using the FTFN in designing current-amplifiers, voltage-to-current converters, gyra- tors, floating immittances [1] and [5-7], and more recently in designing current-mode active-RC filters [3,4] and [8][9][10] and sinusoidal oscillators [11][12][13].Higashimura  [3] described a procedure for transforming voltage-mode circuits with operational amplifiers to current-mode circuits with FTFNs.Using this procedure, a current- *Corresponding author.242 M.T. ABUELMA'ATTI AND H. A. AL-ZAHER mode lowpass transfer function is obtained from a Sallen-Key voltage-mode lowpass circuit.A stable grounded-capacitor first-order allpass filter using an FTFN was proposed by Higashimura [4].Liu  [8] proposed a cascadable current-mode configuration using single FTFN.This configuration can realise second-order lowpass, highpass, band- pass, notch and allpass filters.However, its active sensitivities are large and it requires a floating capacitor.Moreover, these five filters cannot be realised without changing the circuit topology to achieve a specific filter function.A current-mode configuration using two FTFNs was presented by Liu and Lee [9].This configuration enjoys low active and passive sensitivities and can simultaneously realise lowpass/bandpass, or highpass/bandpass or bandpass/notch filters using two grounded capacitors.It can also realise an allpass filter.However, it requires a floating resistor and more importantly, its parameters Wo and wo/Qo are interdependent.Thus it is impossible to adjust any of these two parameters without disturbing the other parameter.Abuelma'atti [10] proposed a cascadable current-mode configuration using single FTFN enjoying low active and passive sensitivities.This configuration can realise second-order lowpass, highpass, bandpass, allpass and notch filters using six passive elements at most.These five filters, however, cannot be realised without changing the circuit topology to achieve a specific filter function.Moreover, the parameters Wo and wo/Qo are interdependent.
We present a new universal active biquad structure using two FTFNs, three capacitors and two resistors.The circuit has three input voltages and can simultaneously provide a high-impedance output current and/or an output voltage.Without changing the circuit topology, the output voltage can realise lowpass, highpass, bandpass, notch and allpass transfer functions and the output current can realise bandpass and highpass transfer functions.The proposed circuit enjoys low active and passive sensitivities and independent control of the parameters Oo and wo/Qo.

PROPOSED CIRCUIT
The proposed circuit is shown in Figure 1.Assuming that the port relations of the ideal FTFN, shown in Figure 2a, can be expressed as I1 12 0, V2 V1 and Io2 Iol routine analysis of the circuit shown in D(s) G3G5 + s(Gs(C2 + C1)) -I-$2C4C1 From (3) the parameters Wo and wo/Qo can be expressed as and (3) From ( 1) and (2) it can be seen that: (i) if V2 V3 0, then a lowpass response is obtained from Vo and a bandpass response is obtained from Io, (ii) if V V2 0, then a bandpass response is obtained from Vo and a highpass response is obtained from Io, (iii) if V1 V3 =0, then a highpass response is obtained from Vo and no standard response is obtained from Io, (iv) if V V2 and V3 0, then a notch response is obtained from Vo and a highpass response is obtained from Io, (v) if V1 V2 -V3 and Ca 0, then an allpass response is obtained from Vo and a highpass response is obtained from Io.
From (4) and ( 5) it can be seen that the parameter Wo can be adjusted by controlling the resistor R3 l/G3 without disturbing the parameter wo/Qo.Moreover, the parameter wo/Qo can be adjusted by controlling the capacitor C2 without disturbing the parameter wo/Qo.
Thus the proposed circuit enjoys independent control of the parameters Wo and wo/Qo.
Taking into consideration the nonidealities of the FTFNs, assuming that the port relations of the FTFN, shown in Figure 2a, can be expressed as I1 12 0, V2 V1 and lo2 alo where /3 1-e, (l e I<< 1), denote the voltage tracking error of the FTFN and a -6, (16[<< 1), dinotes the current-tracking error, reanalysis of the circuit shown in Figure shows that (3) can be expressed as (6) where 3i, ai, 2, are the voltage-and current-tracking errors of the th FTFN.Thus, the parameters Wo and wo/Qo can be expressed W2 a2G3G5 o o1/2C1C4 (7) and o 6(:c:.+ /:c) (8) Qo a132C1 C4 From ( 7) and ( 8) it is easy to show that the active and passive sensitivities of the parameters Wo and Qo are s o, s _so

SIMULATION RESULTS
To verify the theoretical analysis, the proposed circuit was used to realise lowpass, highpass, bandpass, notch and allpass filters.
QN2907 PNP and QN2222 NPN transistors.The simulation results obtained are shown in Figure 3 which agrees very well with the presented theory.A universal active biquad circuit has been presented.The circuit has three input voltages, one output voltage and one high-impedance output current, and can realise lowpass, highpass, bandpass, notch and allpass transfer functions without any changes in the circuit topology.The proposed realisations enjoy the following advantages:

FIGURE 3
FIGURE 3 Simulation results obtained from the curcuit of Figure with (a) Notch: