Fractional Order Colpitts Oscillators for Impedimetric Analysis of Bio and Chemical Sensors

Abstract

The innovation of smart biosensors for a healthy lifestyle, starting from in-home health monitoring to food quality analysis, is one of the most emerging research trends of the twenty first century.  Fabrication of novel biosensors originates from the inherent physicochemical dynamics of target biological samples. Fractional order (FO) calculus describes the inherent dynamics of real-time biological samples far more accurately than the conventional integer-order models.  However, there is a bridge gap in the present state of the art for designing proper electronic interfaces when the biosensors are modeled in the FO domain. In this thesis, a solution to the above problem has been sought by proposing three different configurations of FO Colpitts oscillators (FOCO) for signal conditioning of FO biosensors.

The first configuration (FOCO I) is designed by simply replacing conventional capacitors with fractors. It also includes the 1st order behavioral model of practical op-amp into the analysis. Different case studies based on the different circuit parameters and non-ideal parameters of op-amp are carried out to present compact step-by-step design guidelines for the design of FOCO I. The designed FOCO has an oscillation frequency ranging from 5 kHz to 1.23 MHz as the order varies from 1.0 to 0.1. In the same line, two different configurations of FOCO are also presented, where in place of a single fractor, a lossy fractor (FOCO II) and a single Cole model (FOCO III) have been substituted.

As discussed earlier, different electrochemical and biological systems act like a fractor. In this work, applications of above designed FOCO are discussed in context of urea sensor and fruit sensor. First, a novel two-electrode paper-based disposable water urea sensor is presented. The equivalent electrical model of the urea sensor behaves like a lossy fractor (fractor with parallel resistor). As the concentration of the urea varies, the lossy fractor parameters change. In practice, the lossy fractor parameters are estimated using bio-impedance spectroscopy, followed by equivalent electrical modeling. However, for that one needs costly equipment like impedance analyzer, high-end computer and multistage human intervention and discission making. However, by using the proposed FOCO II, one can eliminate all the abovementioned processes. The urea sensor itself acts as a lossy fractor, and therefore, the oscillation frequency of the designed FOCO II becomes a function of the sensor response. In other words, it can be stated that the change in oscillation frequency is now the measurement of urea concentration. The meter shows excellent linearity in the range of 1-1000 mg/dl of urea concentration, small response time (2 min), high repeatability (standard deviation less than 6.3%), and high sensitivity (- 58 kHz/decade). 

Fruit quality analysis can also be carried out using the proposed FOCO and shown as the real time application of the FOCO III configuration. Banana behaves like a single Cole model which is used as a part of the FOCO III circuit. The exact ripe stage of the banana (green, ripe, overripe, or decay) is detected by observing the change in the frequency output. Moreover, the work also provides a smart solution by predicting the remaining ripe hour/green hour of a said sample. The accuracy of ripe stage detection and the ripe hour prediction are found 96% and 83%, respectively, based on the FOCO III output. In the same line, the ripeness of mango is also carried out using the FOCO III circuit. Two different mango species, Chausa and Banganapalleare, are tested. The detection model based on the FOCO III response achieves a precision and recall value of 0.83-0.85 for the four-stage classification.