VOLTAGE MODE OTRA MOS-C SINGLE INPUT MULTI OUTPUT BIQUADRATIC UNIVERSAL FILTER

In this paper, an Operational transresistance amplifier (OTRA) based MOS-C voltage mode single input multi output (SIMO) biquadratic universal filter configuration is proposed. The configuration is made fully integrated by implementing the resistors using matched transistors operating in the linear region. It exhibits the feature of orthogonal controllability of angular frequency and quality factor through gate bias voltage. The non-ideality analysis of the circuit is also given. Workability of the universal filter is demonstrated through PSPICE simulations using 0,5 μm CMOS process parameters provided by MOSIS (AGILENT).


Introduction
Recently the OTRA has emerged as an alternate analog building block since it inherits all the advantages offered by current mode techniques.The OTRA is a high gain current input voltage output device.The input terminals of OTRA are internally grounded, thereby eliminating response limitations due to parasitic capacitances and resistances at the input.Several high performance CMOS OTRA topologies have been proposed in literature [1], [2], [3], [4], [5] leading to growing interest in OTRA based analog signal processing circuits.In the recent past, OTRA has been extensively used as an analog building block for realizing a number of analog signal processing and generation circuits such as immittance simulators [6], [7], [8], [9], oscillators [10], [11] multivibrators [12], [13] and filters [1], [14], [15], [16], [17], [18], [19], [20], [21], [22].Many voltage-mode biquadratic filters using OTRA were proposed in the literature that can be classified as single input and single output (SISO) [1], [13], [14], [15], [16] multi-input single output (MISO) [17], [18], [19], and single input multi output (SIMO) [1], [20].However, only one standard filter function can be obtained at a time in each filter realization of SISO and MISO category.In SIMO configuration with only one input, multiple filter functions may be obtained simultaneously.A detailed comparison of these structures is given in Tab. 1 which reveals that no OTRA based SIMO structure is available in the literature that provides all five standard responses simultaneously.In this paper, a voltage-mode OTRA MOS-C universal biquadratic SIMO filter based on ref. [1] is presented which realizes all the standard filter functions; namely lowpass, highpass, bandpass, notch and allpass, simultaneously.The proposed structure puts no restriction on the input signal in contrast to the structures reported in [18], [19], [20].Additionally the earlier reported structures require either change of component type [14], [17]or removal of components [1], [22] for realizing various filter responses.However, the proposed circuit does not require a change in component type/ removal of components.It simply poses matching condition on component values for notch and all pass responses.The proposed OTRA MOS-C universal biquadratic SIMO filter employs five OTRAs, twelve resistors and two capacitors.It also enjoys the feature of orthogonal controllability of angular frequency, quality factor and filter gain.All resistors are implemented using MOS transistors operating in the linear region.This not only makes filter electronically tunable but also consumes less chip area.The function of proposed filter has been confirmed by SPICE simulations.

Circuit Description
OTRA is a three terminal device, shown symbolically in Fig. 1  For ideal operations, the transresistance gain R m of OTRA approaches infinity and forces the input currents to be equal.Thus, OTRA must be used in a negative feedback configuration.The proposed filter is shown in Fig. 2. Routine analysis of the circuit of Fig. 2 results in the following transfer functions: ) ( ) ) ( 2)-( 4) clearly indicate that high pass, band pass, low pass responses are available at V 01 , V 02 , and V 03 respectively.Band reject response is available at V 04 as given in (5), with BR gain An allpass response is available at V 05 , as expressed in (6) with allpass gain (G AP ) = G 1 /G 3 , if The high pass gain (G HP ), band pass gain (G BP ) and the low pass gain (G LP ) are respectively given by The resonant angular frequency (ω 0 ) and the quality factor (Q 0 ) are given by: © 2012 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 339 This suggests that the Q 0 can be independently controlled by varying R 5 without affecting the ω 0 .It can be noted from ( 10) that simultaneous adjustment of R 2 and R 4 results in orthogonal tuning of ω 0. Also, the filter gain can be controlled through R 1 without affecting ω 0 and Q 0 .
The sensitivities of ω 0 and Q 0 with respect to each passive component are low and obtained as 2 1 , 2 , 2 1 , 1 It is well known that the linear passive resistor consumes a large chip area as compared to the linear resistor implementation using transistors operating in the linear region.The differential input of OTRA allows the resistors connected to the input terminals of OTRA to be implemented using MOS transistors with complete nonlinearity cancellation [1]. Figure 3 shows a typical MOS implementation of resistance connected between negative input and output terminals of OTRA.The resistance value may be adjusted by appropriate choice of gate voltages thereby making filter parameters electronically tunable.The value of resistance so obtained is expressed as where μ n , C ox , W and L are electron mobility, oxide capacitance per unit gate area, effective channel width, and effective channel length of MOS respectively which may be expressed as V a and V b are the gate voltages and other symbols have their usual meaning.Figure 4 shows the MOS-C implementation of the circuit of Fig. 2.

Non-Ideality Analysis
The response of the filter may deviate due to non-ideality of OTRA in practice.Ideally the trans-resistance gain R m is assumed to approach infinity.However, practically R m is a frequency dependent finite value.Considering a single pole model for the trans-resistance gain, R m can be expressed as where R 0 is low frequency transresistance gain.For high frequency applications, the transresistance gain, R m (s) reduces to Taking this effect into account the transfer functions of the circuit of Fig. 3

modify to
where The effect of C p can be eliminated by preadjusting the value of capacitors C 1 and C 2 and thus achieving self-compensation.The sC p term appearing in parallel to G i for i = 3, 9, 12 will result in the introduction of another pole having radian frequency as ω = 1/R i C p .The smallest frequency of this newly introduced pole would occur for the largest value of R i .The effect of this additional pole can be ignored by selecting the operating frequency range of the SIMO biquadratic universal filter much lower than pole frequency.

Simulation Results
The proposed SIMO biquadratic universal filter is verified through simulations using the CMOS implementation of the OTRA [3] as given in Fig. 5.The SPICE simulation was performed using 0,5 μm CMOS process parameters provided by MOSIS (AGILENT).Supply voltages taken are ±1,5 V. Aspect ratios for different transistors used in OTRA are given in Tab. 2. For simulations L drawn and W drawn are taken as 5 µm for all transistors used for resistance realization.The proposed SIMO biquadratic universal filter as given in Fig. 4 is designed for the resonant frequency (f 0 ) of 120 kHz and Q 0 =1 with component values C 1 =C 2 =100 pF and R i ≈ 10,5 kΩ for i = 1, 2, . . .12. The value of R i was set by taking the gate voltages as V ai = 1,4 V and V bi = 0,75 V for all i = 1, 2,. . ., 12. Figure 6 shows the simultaneously available frequency responses for low-pass, high-pass, band-pass, notch and allpass.The simulated resonant frequency is found to be in close agreement to the theoretical value.The orthogonal tunability of Q 0 with R 5 at f 0 = 11,5 kHz is shown in Fig. 7.This is obtained by selecting   To check the quality of the output of BP filter, the percentage total harmonic distortion (%THD) with the sinusoidal input signal is obtained as shown in Fig. 10.It is observed that the %THD remains considerably low [23] for input signal values till 70 mV.Simulated power consumption for the proposed universal filter is 4,04 mW.

Conclusion
A new voltage-mode OTRA MOS-C universal biquadratic filter is presented which realizes all the standard filter functions simultaneously.The proposed circuit employs five OTRAs, two capacitors and twelve resistors.The filter possesses orthogonal and electronic tunability of filter parameters through MOS implemented resistors.The theoretical proposition is verified using PSPICE simulations.

Fig. 3 :
Fig. 3: MOS implementation of a linear resistance connected between negative terminal and the output.

Fig. 6 :
Fig. 6: Simulated frequency responses of the proposed circuit (a) lowpass and high-pass, (b) band-pass and notch, (c) all pass.

C 1 =
C 2 = 50 pF, and R i = 272 kΩ for i = 1,…, 4, 6,…,12 for different values of R 5 .The values of Q 0 as obtained and gate bias voltages used for tuning of R 5 are listed in Tab. 3.
. Its port relations are characterized by the One One LP,HP,BP,NF,AP No Yes Three Two/Eight Proposed work One Five LP,HP,BP,NF,AP No Yes Five Two/Twelve following matrix.