Transadmittance Mode First Order LP/HP/AP Filter and its Application as an Oscillator

In this paper new transadmittance mode first order low pass, high pass and all pass filter topologies using operational floating current conveyor (OFCC) is proposed and its application as an oscillator is also put forward. This proposal offers all filter functions at high impedance. Only two OFCCs, two resistors and one grounded capacitor are employed for realization. Workability is verified through SPICE simulations and results conform to the theoretical predictions very well. The proposed circuit is prototyped and tested experimentally for its application as an oscillator.


1.INTRODUCTION
First order filters specially low pass, high pass and all pass filters are very basic blocks for realization of higher order filter topologies. The first order low pass and high pass filters finds their applications in communication systems while all pass filter is most commonly used analog filter offering capability to modify phase of the input signal with unity magnitude for all frequencies. Over the desired frequency range, phase varies from 0˚to 180˚for a one pole filter, due to this frequency dependent time displacement property first order all pass filters may be used in radio systems, communication subsystems such as reconstruction filters and signal generation using multiphase sinusoidal oscillators and quadrature oscillators [1]. As a result a number of such first order filters have been reported earlier [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], out of which some are realized in voltage mode (VM) [1][2][3][4][5][6][13][14][15] and in current mode (CM) [5, 7-9, 15, 16] (as well as references cited therein). First order filters with low pass, high pass and all pass functions are reported in VM [4,5] and CM [5] only.
Keeping in view the above facts, a new proposal for TA mode first order filter based on current mode active block operational floating current conveyor (OFCC) offering low pass, high pass and all pass responses, is put forward. The aim of this paper is to contribute towards TA mode first order filters by providing solution for proper input and output impedances to improve cascadability, low passive component count, more than one response simultaneously without any changes in configuration and to introduce an application as a sinusoidal oscillator. The OFCC combines the feature of current conveyor and current feedback opamp (CFOA) and also provides proper inputs with additional current outputs at proper impedances make it suitable for TA mode applications. Significant research efforts has introduced many applications using OFCC such as current mode filter [16,17], voltage mode filter [18][19][20], TA mode filter [21], instrumentation amplifier [22], wheat stone bridge [23], variable gain amplifier [24], readout circuit [25] and current conveyor realizations [26][27][28]. To the best knowledge of authors, none of the literature is reported for TA mode first order LP/HP/AP filter to overcome all or some of the above mentioned problems. To bridge this gap, a TA mode first order LP/HP/AP filter is proposed in this paper. An application namely sinusoidal oscillator is also included. It uses two OFCCs and three passive components.SPICE simulations are carried out using 0.5 µm CMOS process model by MOSIS (AGILENT) and prototyped using commercially available IC AD844. Followings are the key points of proposalproper input and output impedances that makes it suitable for V-I converter application; availability of two responses at a time, either LP and HP or AP and HP on high output impedance ports; suitable for higher order filter applications. including implementation and verification responses are reported in Section 3 and further concluded in Section 4.

OFCC Port Relationship
The symbolic representation of OFCC [26][27][28] is shown in Fig. 1. The port relationship is given in (1) and describes that I Y = 0, V X = V Y , V W = I X Z t , I Z+ = I W , I Z-= -I W . On input ports voltage tracking property exists so voltage at port X follows the voltage at port Y. Similarly current tracking exists at output ports and port W current copied to ports Z+ in phase and Z-out of phase.

Fig. 1 OFCC Circuit symbol
Where Z t is transimpedance gain of OFCC and in practice has a frequency dependent finite value. Port X is low impedance current input and port Y is high impedance voltage input. Port W is low impedance voltage output while Z+ and Z-are high impedance current outputs.

Proposed Filter
In this subsection proposed OFCC based TA mode first order LP/HP/AP filter is described. It emloys two OFCCs, two resistors (one floating and one grounded) and one grounded capacitor is shown in Fig. 2. By applying nodal analysis following filter transfer functions are derived: (2) will provide low pass response, will enable all pass function and (2) becomes, (4) and high pass function is independent of above conditions so will be available along with low pass or all pass, but one response at a time.
The pole frequency is given as

Filter application
A Sinusoidal Oscillator is implemented using all pass section as shown in Fig. 3. The routine analysis gives the following characteristic equation: The condition of oscillation and frequency of oscillation is derived respectively as:

PERFORMANCE ANALYSIS
The proposed filter topology is verified through PSPICE simulation program using MOSIS (AGILENT) 0.5 µm CMOS process parameters. The circuit schematic of OFCC is given in Fig.  4 [24] and W/L parameters for MOS transistors used in simulation are reported in Table II [24]. The supply voltages (V DD and V SS ) are taken as ±1.5V and bias voltages (V B1 and V B2 ) of ±0.8V are applied.  The pole frequency of 159 KHz is selected for proposed first order filters and corresponding component values found are C 1 = 100pF, R 1 = R 2 = 10 kΩ for low pass function while R 1 = 10 kΩ , R 2 = 2R 1 = 20 kΩ to obtain all pass response. High pass response is independent of R 2 thus will be available in both conditions. Thus high pass along with either low pass or all pass will be available simultaneously.
The frequency responses of proposed first order low pass and high pass filter are shown in Fig.  5(a) and selecting another component values will facilitate high pass and all pass responses as shown in Fig. 5(b). Fig. 6 showing phase response of all pass filter and is complied with theoretical predictions. Time domain behavior is also verified to confirm the functionality of all the proposed filter topologies by applying sinusoidal signal of amplitude 1 mV, f o = 159 kHz and corresponding transient responses for low pass, high pass and all pass filter are plotted in Fig. 7 (a), Fig. 7 (b) and Fig. 8 (a). For all pass filter topology Lissagous pattern through simulation is also plotted in Fig. 8 (b). The sinusoidal oscillator as an application of proposed all pass filter section is prototyped using commercially available IC AD844 [29] as shown in Fig. 9 and simulated using CMOS schematic Fig. 4 [24].

CONCLUSION
In this paper new TA mode first order LP/HP/AP filter using OFCC and its application as an oscillator is proposed. This proposal offers total three filter functions LP/HP/AP in transadmittance mode at high impedance. Only two OFCCs, two resistors and one grounded capacitor are employed for realization. Workability is verified through PSPICE program and found that simulated results conform the theoretical predictions very well. The proposed circuit is prototyped and tested experimentally for its application as an oscillator.