NEW CURRENT-MODE NOTCH AND ALLPASS FILTERS WITH SINGLE CURRENT DIFFERENCE AMPLIFIER

At present, there is a growing interest in designing current-mode signal processing circuits. In these circuits, the current rather than the voltage is used as the active variable either throughout the whole circuit or only in certain critical areas. The use of current as the active parameter can result in circuits operating with higher signal bandwidths, greater linearity, and larger dynamic range than voltage-mode circuits [1]. The current conveyor, a powerful analog building block with current-mode capability, is therefore a strong potential candidate for implementing current-mode circuits, and recently a number of realizations have been presented using firstand second-generation current conveyors [see, for example, [2] and the references cited therein]. However, in many industrial electronic control systems, circuits are designed to operate off only a single power supply voltage. The current conveyor is typically designed for split power supplies and, therefore, current-mode active filters employing conventional current conveyors cannot be used in many industrial control applications. The current difference amplifier, designed to operate from a single power supply, is therefore, a strong candidate for such applications. A literature survey, [see, for example, [3]-[5] and the references cited therein] reveals that while the current-difference amplifier has been extensively used in designing voltage-mode biquadratic transfer functions, no attempt has been reported yet for its use in designing current-mode biquadratic filter circuits. It is the purpose of this paper to present current-mode biquadratic notch and allpass filter realizations using the current-difference amplifier.


INTRODUCTION
At present, there is a growing interest in designing current-mode signal processing circuits. In these circuits, the current rather than the voltage is used as the active variable either throughout the whole circuit or only in certain critical areas. The use of current as the active parameter can result in circuits operating with higher signal bandwidths, greater linearity, and larger dynamic range than voltage-mode circuits [1]. The current conveyor, a powerful analog building block with current-mode capability, is therefore a strong potential candidate for implementing current-mode circuits, and recently a number of realizations have been presented using first-and second-generation current conveyors [see, for example, [2] and the references cited therein]. However, in many industrial electronic control systems, circuits are designed to operate off only a single power supply voltage. The current conveyor is typically designed for split power supplies and, therefore, current-mode active filters employing conventional current conveyors cannot be used in many industrial control applications. The current difference amplifier, designed to operate from a single power supply, is therefore, a strong candidate for such applications. A literature survey, [see, for example, [3]- [5] and the references cited therein] reveals that while the current-difference amplifier has been extensively used in designing voltage-mode biquadratic transfer functions, no attempt has been reported yet for its use in designing current-mode biquadratic filter circuits.
It is the purpose of this paper to present current-mode biquadratic notch and allpass filter realizations using the current-difference amplifier.

PROPOSED CIRCUITS
Consider the general circuit shown in Fig. 1. Assuming an ideal current difference amplifier defined by i+ i_, v+ _ 0, routine analysis of the circuit of Note that the ratio between the output and input currents of this notch filter is R 4 R L. Such ratio can be made larger than one and, therefore, this notch realization is not suffering from a constant loss. Note also that this realization requires only six passive elements, including the load resistor Rt, plus one active element.
Now if a parallel RC combination is used for Y3, that is Y3 1/R 3 + sC 3 while Y1 and Yz remain as before, shown in Fig. 2(b), then (1) reduces to Note that the ratio between the output and input currents of this allpass filter is R4/Rt.. Such ratio can be made larger than one. Note also that this realization requires only four passive elements, including the load resistor, RL, plus one active element.  (14) and their values are given in Table I. From Table I, one can easily see that all the passive o tOo-Sensitivities and -sensitivities of the second-order notch filters are -< 1. One can also see that while the passive t%-sensitivities of the second-order allpass filter o are <-1, the -sensitivities may be appreciably high due to the presence of the  (17) The transfer function of (17) can be decomposed into two cascaded transfer functions T(s) and T2(s). The first transfer function, T(s), is expressed by

SENSITIVITY
This transfer function corresponds to a lowpass filter with high-frequency gain R determined by the ratio -7"2-7. Both the pole top 1/C(R + R4/(1 + A)) and the zero to z IlCIR in this transfer function are adjustable through C, but the ratio is held constant. The second transfer function, T2(s), is expressed by R4 1 + s(CIRI+ C2R2 C1R2) + s2C1C2R1R2 Tz(s) RL(I /"I/A) 1 + $(CIR + C2R2 + CIR2) +$2CIC2RIR 2 (19) This transfer function is the same as the transfer function of (2) with the gain slightly modified to R4/Rz(1 + I/A) rather than R4/Rt,. The notch filter parameters to o and Oo/Q o will remain the same inspite of the finite gain of the amplifier. Thus, R4 by selecting + llA << R1 the notch characteristics of the circuit of Fig. 2(a) will preserve its shape.
In a similar way, if we take into consideration the effect of the finite gain of the amplifier, the transfer function of the allpass circuit of Fig. 2(b) (5) Fig. 3. From Fig. 3, it is easy to see that the notch occurs at 49 KHz while the predicted value using eqn (5)

CONCLUSION
A new circuit for realizing current-mode, second-order notch and allpass filters has been presented. The proposed circuit uses a single current difference (Norton) amplifier and at most eight passive RC one-port elements, including the load resistor. The circuit can also realize a first-order allpass filter using a single current difference amplifier and four passive elements only including the load resistor. The current-difference amplifier requires a single dc power supply and, therefore, the proposed realizations are very useful for many industrial electronic control systems designed to operate off only a single power supply voltage. The proposed realizations enjoy low active and passive sensitivities.