^{1}

^{*}

^{2}

^{3}

^{4}

Although a variety of applications of the OTRAs have been reported in literature, the pole of the transresistance gain Rm of the OTRA has been usually considered to affect the performance of the circuits due to being parasitic. In this paper, the pole of the OTRA has been used to evolve some simple OTRA-based active-R circuits for realizing a synthetic inductor, single resistance controlled oscillator and low-pass/band-pass filter. The workability of all the proposed circuits has been verified by SPICE simulations and all the new circuits have been found to work as predicted by theory. The exemplary propositions suggest that it is worthwhile to further investigate new circuit designs using OTRA-pole.

Operational Transresistance Amplifier (OTRA) has received a lot of attention over the past decades. Due to being a differential current controlled voltage source, it has a virtual ground at both the input terminals, which provides the significant advantages of eliminating parasitics at the input ports. Thus, motivated by these advantages, several CMOS OTRA [

Although the non-ideal one pole and two pole models [_{m}) have been employed by several authors in performing a non-ideal analysis of their propositions but to the best of the knowledge of the authors, any explicit use of OTRA-pole in evolving external capacitor-less, active-R circuits using OTRAs has not been reported so far. The main purpose of this paper is, therefore, to report three OTRA-based active-R circuits which realize an inductor, an oscillator and a low-pas/band-pass filter respectively in which the pole of the OTRA has been exploited advantageously to result in circuits which have the interesting feature of employing a low number of total components. The workability of the proposed circuits has been demonstrated by SPICE simulation results based upon CMOS-OTRA implementation using 0.5 µm CMOS technology.

The OTRA can be symbolically shown as in

The two-pole model of the transresistance [

The above expression for R_{m}(s) can be further modified and written as-

For frequencies lying in the range:

R_{o} is the dc resistance of the OTRA.

Consider now the following:

1) For the circuit of

From Equation (5), we observe that the circuit of _{p}) in parallel with an inductance (L_{p}), where

The quality factor of the simulated inductor is found using the expression

2) In

The straight forward analysis of the proposed circuit using Equation (4) gives the characteristic equation (CE) of the circuit as

It can be easily verified from the CE given by Equation (7) that the condition of oscillation (C.O.) and the frequency of oscillation (F.O.) are respectively given by

It may be noted that the circuit offers fully uncoupled CO and FO, the former is adjusted by R_{1} and/or R_{2} and the latter may be varied by R_{3} and/or R_{4}. It may be mentioned that any fully uncoupled oscillator using only four resistors along with only two active elements, that too without using any external capacitors, has not been reported in the literature earlier.

3) The last proposition is of an active-R OTRA-based low-pass/band pass filter which has been obtained from the circuit of

where the filter parameters are given by

A novel feature of the proposed band-pass filter is that all the three filter parameters can be found to be electronically tunable [_{o} by R_{3} while the

bandwidth (BW) by R_{1} and finally, the gain by R_{2}.

1) For the circuit of

Thus, from Equation (15) the circuit of _{p}) in parallel with a series combination of a frequency dependent negative capacitance (FDNC), an inductor

and a resistance (R_{s}) such that

equivalent circuit of which is shown in

The quality factor of the simulated inductor considering all the parasitics is found to be using the expression

2) By a straight forward analysis, using Equation (3) we obtain the characteristic equation (CE) of the circuit shown in

Neglecting the term s^{4} and the coefficients involving the term

simplified and rewritten as

Comparing the above equation with the standard form given as

we obtain the following values for the coefficients of the Equation (19) as

For the CE of the form given by (19) the expression for the frequency of oscillation (F.O.) and the condition of oscillation (C.O.) are given respectively as

F.O.:

Thus, for the CE given by (13), the expressions for F.O. and C.O. are found to be

F.O.:

where f_{o} is as given by Equation (9).

C.O.:

The percentage error in the frequency of oscillation can be found using the expression for percentage error =

3) A straight forward analysis of the circuit shown in

Equations (25) and (26) on neglecting the terms containing s^{4} and s^{3} can be simplified and the modified transfer functions are thus obtained as follows

From Equations (27) and (28) we obtain the expressions for the filter parameters as

where f_{o}, BW, H_{oBP} and H_{oLP} are given respectively by Equations (12), (13) and (14).

All the three proposed circuits have been verified through SPICE version 16.0 simulations using CMOS OTRA of [

_{p} and L_{p} respectively as compared to their theoretical plots. The proposed inductor was simulated using the component values as R_{1} = 2.2 KΩ, R_{2} = 3.3 KΩ and C_{p} = 1.2 pF resulting in the theoretical value of R_{p} = 1.32 KΩ and L_{p} = 8.71 µH which are in close agreement with the simulated values of R_{p} = 1.34 KΩ and L_{p} = 8 µH.

The simulated lossy inductor of

Transistor | W(µm)/L(µm) |
---|---|

M_{1}-M_{3 } | 100/2.5 |

M_{4} | 10/2.5 |

M_{5}, M_{6 } | 30/2.5 |

M_{7} | 10/2.5 |

M_{8}-M_{11} | 50/2.5 |

M_{12}, M_{13} | 100/2.5 |

M_{14} | 50/2.5 |

Device Type | Model Parameters |
---|---|

NMOS | LEVEL = 3 UO = 460.5 TOX = 1.0E−8 TPG = 1 VTO = 0.62 JS = 1.08E−6 XJ = 0.15E−6 RS = 417 RSH = 2.73 LD = 4E−8 VMAX = 130E3 NSUB = 1.71E17 PB = 0.761 ETA = 0.00 THETA = 0.129 PHI = 0.905 GAMMA = 0.69 KAPPA = 0.10 CJ = 76.4E−5 MJ = 0.357 CJSW = 5.68E−10 MJSW = 0.302 CGSO = 1.38E−10 CGDO = 1.38E−10 CGBO = 3.45E−10 KF = 3.07E−28 AF = 1 WD = 1.1E−7 DELTA = 0.42 NFS = 1.2E11 |

PMOS | LEVEL = 3 UO = 100 TOX = 1.0E−8 TPG = 1 VTO = −0.58 JS = 0.38E−6 XJ = 0.10E−6 RS = 886 RSH = 1.81 LD = 3E−8 VMAX = 113E3 NSUB = 2.08E17 PB = 0.911 ETA = 0.00 THETA = 0.120 PHI = 0.905 GAMMA = 0.76 KAPPA = 2 CJ = 85E−5 MJ = 0.429 CJSW = 4.67E−10 MJSW = 0.631 CGSO = 1.38E−10 CGDO = 1.38E−10 CGBO = 3.45E−10 KF = 1.08E−28 AF = 1 WD = 1.4E−7 DELTA = 0.81 NFS = 0.52E11 |

For the band pass filter shown in

Considering the equivalent circuit of

The above equation can be simplified and written as

From Equation (33) we obtain the modified filter parameters as

where, H_{o}, _{o} are respectively given by Equation (31).

_{o} = R_{p} = 1.32 KΩ, L_{p} = 8.712 µH, C_{o} = 4.65 pF resulting in theoretical value of filter parameters as-H_{o} = 0.5, BW = 326 MHz and f_{o} = 25 MHz as compared to the simulated values H_{o} = 0.499, BW = 325.7 MHz and f_{o} = 25.16 MHz.

_{1} = 25.01 KΩ, R_{2} = 25 KΩ, R_{3} = R_{4} = 30 KΩ and C_{p} = 1.2 pF resulting in theoretical value of oscillation frequency f_{o} = 4.42 MHz which agrees with the simulated result of f_{o} = 4.45 MHz.

_{3} and R_{4} when the values of the resistances R_{3} and R_{4} are respectively varied from 5 KΩ to 40 KΩ.

For the component values chosen as R_{1} = 25.01 KΩ, R_{2} = 25 KΩ, R_{3} = R_{4} = 30 KΩ, C_{p} = 1.2 pF, R_{o} = 126 MΩ and_{o} = 4.42 MHz using one-pole model and f_{o} = 4.485 MHz using two-pole model resulting in the percentage error of 1.47%.

_{2} = R_{3} = R_{4} = 47 KΩ, R_{1} = 300 KΩ and C_{p} = 1.2 pF resulting in theoretical values of f_{o} = 2.82 MHz and BW = 2.78 MHZ which is in accordance with the simulated values of f_{o} = 2.8363 MHz, BW = 2.7554 MHz.

_{2} when its value is varied from 280 Ω to 320 KΩ and _{3} when its value is varied from 40 KΩ to 80 KΩ. Thus, _{2} and R_{4}.

It can be seen that the results obtained from SPICE simulations demonstrate good correspondence with the theoretical values, which confirms the workability of the proposed circuits.

Three simple circuits using OTRA-pole were proposed: a simulated inductance, a fully uncoupled SRCO and a low-pass/band-pass filter. In these circuits the pole of the OTRA has been exploited advantageously to result in circuits which have the interesting feature of employing a low number of total components. The theory has been validated by SPICE simulation results. The workability of the proposed circuits, thus, demonstrates that the design of active-R circuits using OTRA-pole warrants further investigations.

This work was performed partly at Analog Signal Processing Research Lab., Division of ECE, NSIT, New Delhi and partly at Advanced Analog Signal Processing Lab., Department of ECE, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi.

RajSenani,Abdhesh KumarSingh,AshishGupta,Data RamBhaskar, (2016) Simple Simulated Inductor, Low-Pass/Band-Pass Filter and Sinusoidal Oscillator Using OTRA. Circuits and Systems,07,83-99. doi: 10.4236/cs.2016.73009