Analogue Computation Converter for Nonhomogeneous Second-Order Linear Ordinary Differential Equation
Abstract
:1. Introduction
2. Mathematical Model
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- If > 1 y(t) has the roots (8) (real and distinct roots), and y(t) has an underdamped response;
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- If = 1 x(t) has the roots (real equal roots), and y(t) has a critical underdamped response;
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- If < 1 x(t) has the roots (complex conjugate roots), and y(t) has a critical overdamped response with damped oscillation.
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- If = 0, x(t) has the roots (imaginary conjugate roots), and the response will be oscillation (without damped oscillation). In a real oscillator, the first root is useful for making oscillations: . This variant is the basis of the realization of the analogue computation converter.
3. Simulations of an Analogue Computation Converter with Variable Frequency and Amplitude
4. Experiments with Discussions
5. Applications of the Analogue Computation Converter Used with Sensors
5.1. Remote Transmission of a Measured Quantity via Electrical Wires
5.2. Temperature Measured with Thermistors
5.3. Temperature Measured with Resistance Temperature Detector
5.4. Temperature Measured with Thermocouples
6. Conclusions
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- An analogue computer was developed using the nonhomogeneous second-order linear ordinary differential equation to adjust the frequency and amplitude of the sinusoidal signal at the output using two DC voltages;
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- The output signal for ui and uf is sinusoidal and stable over time over a variety of DC voltages (non-damped operation mode);
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- The analogue converter has a straightforward design with two DC voltage inputs and one (sinusoidal voltage) output;
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- The response time is relatively short because the sinusoidal converter is only realised with analogue components;
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- The output signal has a frequency in the kHz range, and the operating range might be in the tens of kHz range;
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- The uf input of the sinusoidal converter can be used on analogue sensors that have a DC voltage at the output to convert the voltage into a sinusoidal signal.
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- The precise determination of the R-C component limit values for the I1 and I2 integrated circuits, for which the sinusoidal signal at the oscillator’s output has a linear dependence (amplitude and frequency) on the DC voltages at the input;
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- Connecting resistive (for linear, angular displacements, and so on) and capacitive transducers (liquid-level gauges, pressure metres, accelerometers, precision positioners, and so on) to integration circuits to convert the signals into a sinusoidal output signal proportional to the input size of the sensors;
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- Studies on signals with noise at the input of the converter to study the influence on the output of the converter.
7. Patents
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Types of Undamped Sinusoidal Oscillators | Characteristics | Advantages | Disadvantages |
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Tuned Circuit Oscillators | These oscillators use a tuned circuit consisting of inductors and capacitors and are used to generate high-frequency (radio frequency) signals. Such oscillators are Hartley, Colpitts, and Clapp oscillators, etc. |
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RC Oscillators | These oscillators use resistors and capacitors and are used to generate low- or audio-frequency signals. Thus, they are also known as audio-frequency oscillators. Such oscillators are Phase-shift and Wein-bridge oscillators. |
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Crystal Oscillators | These oscillators use quartz crystals to generate highly stabilized output signal with frequencies up to 10 MHz. The Piezo oscillator is an example of a crystal oscillator. |
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Negative-resistance Oscillator | These oscillators use the negative-resistance characteristic of the devices such as tunnel devices. A tuned diode oscillator is an example of a negative-resistance oscillator. |
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Analogue computation converter | Using analogue electronic circuits with two DC inputs and one output (sinusoidal voltage with controlled frequency and amplitude). It is an analogue computer that solves a nonhomogeneous second-order linear ordinary differential equation. |
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Popa, G.N.; Diniș, C.M. Analogue Computation Converter for Nonhomogeneous Second-Order Linear Ordinary Differential Equation. Computation 2024, 12, 169. https://doi.org/10.3390/computation12080169
Popa GN, Diniș CM. Analogue Computation Converter for Nonhomogeneous Second-Order Linear Ordinary Differential Equation. Computation. 2024; 12(8):169. https://doi.org/10.3390/computation12080169
Chicago/Turabian StylePopa, Gabriel Nicolae, and Corina Maria Diniș. 2024. "Analogue Computation Converter for Nonhomogeneous Second-Order Linear Ordinary Differential Equation" Computation 12, no. 8: 169. https://doi.org/10.3390/computation12080169