OTRA Based Second Order Universal Filter and its optimization like Butterworth, Chebyshev and Bessel

This research work brings operational transresistance amplifier (OTRA) based second order universal filter, with three main filter optimizations like Butterworth, Chebyshev and Bessel. The universal filter offers all five sections of filter responses likes: Low-Pass, High-Pass, Band-Pass, BandRejection and All-Pass. Design is based on the RC-RC decomposition technique. Finally, simulation results are performed to verify the theoretical results using ORCAD 10.5 circuit simulator.


I. INTRODUCTION
A number of voltage-mode (VM) and current-mode (CM) filtering circuits have been designed using different active elements such as operational amplifiers [1], operational transconductance amplifiers [2], current conveyors [3], current differencing buffered amplifier [4] etc, which have the low power consumption, high slew rate, wide bandwidth etc.Now days the operational transresistance amplifier (OTRA) has acts as an substitutional analog building block [5] that posses all the advantages of current mode techniques.OTRA eliminate parasitic capacitances throw input grounded terminals [6][7][8].Presently OTRA manufactured commercially as norton amplifiers or differencing amplifiers for several integrated circuit.Manufactures observed that CMOS OTRA is more simpler and more efficient than the commercially available another building blocks.Other useful applications of OTRA have been reported in literature [9][10][11].These reports include, designing of universal filter [9], single-resistancecontrolled oscillators [10], and all-pass filters [11].On the other hand, a literature study enhance our knowledge that both Kerwin-Huelsman-Newcomb (KHN) and Tow-Thomas (TT) biquads designed by using current conveyors, operational amplifier or OTAs [12][13][14][15].On the basis of literature study we found that although Fleischer-Tow biquad, is an improved version of the Tow-Thomas configuration, offers the realization of all five different second-order filtering functions, namely low-pass, high-pass, band-pass, notch, and all-pass.But as per the author knowledge not a single paper that includes all filter optimization like Butterworth, Chebyshev and Bessel are reported in a single paper.The purpose of this work is to analyse second order universal filter structure with its all optimizations like Butterworth, Chebyshev and Bessel, that exhibits all responses of filter like Band-Pass (BP), Band-Reject (BR), Low-Pass (LP), High-Pass (HP) and All-Pass (AP) functions from the same configuration.Also, a comparative study for the second order universal filter is reported in this paper.II.CIRCUIT DESCRIPTION A 0.5 m Complementary metal oxide semiconductor technology based internal circuit of operational transresistance amplifier is shown in Figure 1 [5], and the schematic circuit symbol of OTRA is shown in Figure 2. Corresponding input/ output -relationship is characterized as: (1) and is the input voltage respectively at terminal p and n, with the transresistance gain which approaches infinity for ideal one. where Y and 8 Y are positive admittance terms.The generalized structure can be used for design different type of filter optimization like Butterworth, Chebyshev and Bessel filter.The general transfer function of second order low-pass filter can be expressed as: Here the design part is done with unity gain (A 0 =1) and the filter coefficients 1 A and 1 B must be different for different types of filter transfer function, which is given in Table 1.

Types of Filter
Filter Coefficients

4142
The transfer function is decomposing by RC-RC decomposition technique [14] as below: The general transfer function of second order low pass filter is Rearrange the equation as [14]: (5) There after second order low pass Butterworth filter having numerator and denominator must be decomposed as [14]       Similarly for second order low pass chebyshev having numerator and denominator must be decomposed as [14]       Again for second order low pass Bessel filter having numerator and denominator must be decomposed as [14]       Finally, all other filter response like high pass, band pass, band reject and all pass response like Butterworth, Chebyshev and Bessel filters are summarized with their transfer function and decomposed as per the above discussion which is summarized in Table 2.
The obtained transfer function for Butterworth, Chebyshev and Bessel are nothing but simply the combination of R and C or simply R and C. Normalized value of passive components of different optimization computed by above analysis and actual value of passive component scaled by using impedance scaling factor (ZSF) =80×10 3 and frequency scaling factor (FSF) =2π ×100× 10 3 (100KHz desired cut off frequency), which is given in Table 3.This analysis is made with the help of paper [16].From above discussion we may modify the generalized equation ( 2) to equation ( 12).Here the proposed second order filter structure which is shown in Figure 3 is modified as Figure 4 and the corresponding transfer function can be written as equation ( 12) for Butterworth, Chebyshev and Bessel second order universal filter.
Finally to obtain the various filter response, a proper input selection is required, Table 4 shown the corresponding selection of 1 V , 2 V , 3 V , 4 V and 5 V to achieve different filter response.

Universal second order Low Pass Filter
From equation ( 12) transfer function of Low Pass filter is obtained by selecting input V 1 and V 4 .

Universal second order High Pass Filter
From equation ( 12) transfer function of High Pass filter is obtained by selecting input V 2 and V 4 .

Universal second order Band Pass Filter
From equation ( 12) transfer function of Band Pass filter is obtained by selecting input V 1 , V 3 and V 5 .

Universal second order Band Reject Filter
From equation ( 12) transfer function of Band Reject filter is obtained by selecting input V 1 , V 2 and V 4 .

Universal second order All Pass Filter
From equation ( 12) transfer function of All Pass filter is obtained by selecting input V 1 , V 2 and V 4 .
(28) All filter realization must have some condition.The condition for realization of low pass, high pass, band pass, band reject and all pass filters are summarised in Table 5.The natural frequency and quality factor of the designed circuit for low pass, high pass, band pass, band reject and all pass filter can be obtained as and the sensitivity of 0  and 0 Q with respect to passive elements may be expressed as It proclaims that the designed circuit gives low sensitivity.

Condition
III. NON-IDEALITY ANALYSIS OF OTRA Normally the trans-resistance gain is assumed to infinity for filter designing.However, practically trans-resistance gain ( m R ) is a frequency dependent finite value.Considering a single pole model for the trans-resistance gain can be approximately given in terms of high frequencies as If the denominator of equation( 2) modifies as equation( 33) or in other words admittances Y 6 Y 7 and Y 8 contain a parallel capacitor, this result a complete self compensation [10].In our designed circuits, Y 7 contains a parallel capacitor branch , hence the designed filters taking the magnitude of Cp into consideration.In this way, the effect of Cp can be absorbed in capacitance Y 7 without using additional elements and achieving complete self compensation [10].
IV. SIMULATION RESULT The designed 0.5 m Complementary metal oxide semiconductor technology based internal circuit of operational trans-resistance amplifier as shown in Figure 1[5], with dc power supply voltages  DD = − SS = 1.5volt and bias voltage  B = −0.5volt.The simulations are performed using ORCAD 10.5 circuit simulator based on 0.5 m Complementary metal oxide semiconductor technology.The filter is designed for a natural frequency (3dB frequency) of f 0 = 100 kHz.Comparative simulated and theoretical result of the Butterworth, Chebyshev and Bessel filters, followed by five sections describing the most common filter response: low pass, high pass, band pass, band reject and all pass filters are shown in Figure 5.The Butterworth gives flat frequency response in the pass band and its stop band attenuates with -40 dB/decade as given in Figure 5.The Chebyshev gives a sharper roll off with comparison to Butterworth and Bessel filters, but allowing distortion in form of ripple in the frequency response shown in Figure 5.As the roll-off more sharper, the ripple become increases, so trade-off between these two parameters observed in the Chebyshev response.The Bessel filters gives constant group delay for wide frequency range because it shows a linear phase response over a wide frequency range with comparison to Butterworth and Chebyshev filters.Figure 6 shown the comparison result of phase response of Butterworth, Chebyshev and Bessel all pass filter.To verify the output quality, total harmonic distortion is obtained for low pass Butterworth, Chebyshev and Bessel filters as shown in Figure 7.It is found that the output distortion is very small and it is 5 % up to 4 volt [1].It proclaim that the output of filters are very good quality and dynamic range is high.The simulated results verify with the theoretical results, shown in Figure 5.A comparative study for the second order universal filter is shown in Table 6.

TABLE 3 :
ACTUAL VALUE OF PASSIVE ELEMENTS.

Table 4 ,
results the transfer function of Low-Pass (LP), High-Pass (HP) Band-Pass (BP), Band-Reject (BR) and All-Pass (AP) functions.From equation (12) we can realize a different filtering function which is summarized as.

TABLE 5 :
CONDITION OF REALIZATION OF EACH FILTER.

TABLE 6 .
COMPARISION OF AVAILABLE SECOND ORDER UNIVERSAL FILTERS