New Method of Solving Complicated Operational Amplifier Systems and Application to Online Electrocardiograph

Abstract

We propose a new systematic matrix approach, which is an alternative to the disordered virtual ground technique, the Kirchhoff's law， and traditional Thevenin approaches, of designing the desired performance and simultaneously finding two Thevenin equivalent parameters for general complicated operational amplifier systems. One cannot apply the virtual ground method to non-ideal and partially ideal operational amplifier systems including instrumentation and frequency sensors. There has been no matrix method for efficiently solving a complicated operational amplifier circuit for conventional tedious approaches that apply Kirchhoff's law. We also propose a new method of finding Thevenin equivalent circuits for general complicated operational amplifier systems that has significant merits over traditional approaches including the open-circuit voltage and short-circuit current methods, the matrix node voltage (mesh current) method, the modified nodal (mesh) analysis, the reference node r model, the reflected impedance method, and the virtual ground method. To compare the proposed and traditional approaches, one demonstrated example and one comparative example are chosen. Moreover, we report a Bessel low-pass filter that is mainly made up of an AD8618 quad op-amp. Its transfer function for existing methods is incorrect in the non-ideal case, and thus the important amplitude-frequency and phase-frequency characteristic curves will not be exact. An online electrocardiograph (ECG) device is an important tool for many industrial medicine applications and is investigated in this study to demonstrate the practical value of the proposed results.

Correction of traditional incorrect oscillation formula for the Wien‐Bridge Oscillator

“…An important particularity of CEUA is the utilisation of R CCC = ∞ ( R CCC = 0) to effectively reduce the solving load. The invented equivalent circuits of significant electronic devices including Figures 4–13 are shown as follows. Ideal transformer device [21]: Mutual inductance device [21]: Quiescent DC BJT transistor device [9]: First‐order delay device [20]: Complex operational amplifier device [23]: …”

“…A new necessary and sufficient oscillation formula of the Wien-Bridge oscillator via our series approach CEUA [18][19][20][21][22][23][24] will be investigated in this section. CEUA is an effective approach of addressing a complex circuit via the invented equivalent circuits of significant electronic devices and reducing matrix operations.…”

“…To derive the oscillation condition and frequency of the Wien-Bridge oscillator in this study, we will apply our series research CEUA [18][19][20][21][22][23][24] to overcome the serious shortcomings of the traditional Barkhausen method. Moreover, another important feature of our method is that the oscillation condition is effective for a range, not a single value, and it can solve the impact caused by the change in environmental factors.…”

New Method of Designing Controller for Uncertain Differential-Difference Systems and Application to Time-Delay Operational Amplifier System

“…Operational amplifiers are very common in most electrical equipment [7]. Operational amplifiers have important applications in analog computers, where they are used to perform mathematical operations in many industrial circuits, including Internet monitoring systems for electrocardiograms [6,28]. In order to show its practicability, this study first designed the adder and the delay circuit based on the recent research of Chen electrical unifying approach (C.E.U.A.)…”

“…; The study applies C.E.U.A. to take the place of using the disorganized virtual ground technique and the Kirchhoff's law for those traditional approaches [6]. The significant advantage of the invented time-delay circuit is that it can be utilized as a time-delay unit for industrial applications; (3) the research firstly constructs the easyimplementation adder based on C.E.U.A.…”