Browsing by Author "Varonov A.M."
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Item CallenāWelton fluctuation dissipation theorem and Nyquist theorem as a consequence of detailed balance principle applied to an oscillator(2019-09-15) Mishonov T.M.; Dimitrova I.M.; Varonov A.M.We rederive the Nyquist theorem and CallenāWelton fluctuation dissipation theorem as a consequence of detailed balance principle applied to a harmonic oscillator. The usage of electrical notions in the beginning makes the consideration understandable for every physicists. Perhaps it is the simplest derivation of these well-known theorems in statistical physics. The classical limit is understandable as a consequence of WaterstonāHerapath equipartition theorem.Item Determination of the Boltzmann constant by the equipartition theorem for capacitors(2019-04-08) Mishonov T.M.; Gourev V.N.; Dimitrova I.M.; Serafimov N.S.; Stefanov A.A.; Petkov E.G.; Varonov A.M.A new experimental set-up for measurement of the Boltzmann constant is described. The statistically averaged square of voltage U2 is measured for different capacitances C. The Boltzmann constant is determined by the equipartition theorem C U2 k T = . For fixed capacitance, voltages could be measured for different temperatures. The set-up consists of low-noise, highfrequency operational amplifiers ADA4898-2. An instrumental amplifier is followed by an inverting amplifier, the square of the voltage is created by an analog multiplier AD633, and finally, the averaged signal is measured by a multimeter. More than ten high-school students were able to measure the Boltzmann constant with the experimental set-up in the 5th Experimental Physics Olympiad with excellent accuracy compared to the price, conditions and available time for the experiment. A new derivation of the important statistical physics theorems by Nyquist and Callen-Welton is given in an appendix at the level of introductory courses in physics studied by future teachers. To understand the work of the experimental set-up, it is only necessary to know the equipartition theorem.Item Master equation for operational amplifiers: Stability of negative differential converters, crossover frequency and pass-bandwidth(2019-02-26) Mishonov T.M.; Stefanov A.A.; Petkov E.G.; Dimitrova I.M.; Danchev V.I.; Varonov A.M.The well forgotten master equation from the seminal article by Ragazzini, Randall and Russell [J. R. Ragazzini, R. H. Randall and F. A. Russell, ``Analysis of Problems in Dynamics by Electronic Circuits``, Proc. of the I.R.E., 35, pp. 11-19, (1947)] is recovered as indispensable tool for the analysis of contemporary circuits with operational amplifiers. This equation gives the relation between time dependent the output voltage U 0 (t) and the difference between the input voltages (U + (t) and U - (t)). The crossover frequency f 0 parameterizes the time constant Ļ 0 of this equation. The work of the master equation is illustrated by two typical examples: a) the stability criterion of the devices with negative impedance converters, which we consider as a new result b) the frequency dependence of the amplifiers with operational amplifiers given in the technical specifications. A simple circuit for determination of f 0 is suggested and the method is illustrated by determination of crossover frequency for the low-noise and high speed ADA4898 operational amplifier. It is concluded that for an exact calculation of the pass bandwidth of amplifiers with active filters the 70 years old master equation is indispensable.Item Master equation for operational amplifiers: Stability of negative differential converters, crossover frequency and pass-bandwidth(2019-03-01) Mishonov T.M.; Danchev V.I.; Petkov E.G.; Gourev V.N.; Dimitrova I.M.; Serafimov N.S.; Stefanov A.A.; Varonov A.M.The time dependent master equation from the seminal article by Ragazzini, Randall and Russell (Ragazzini et al 1947 Proc. of the I.R.E. 35, 444ā452) is recovered as a necessary tool for the analysis of contemporary circuits with operational amplifiers. This equation gives the relation between time dependent the output voltage U0(t) and the difference between the input voltages (U+(t ) and U-(t )). The crossover frequency f0 is represented with the time constant Ļ in this equation. The work of the 0 master equation is illustrated by two typical examples: a) the stability criterion of the devices with negative impedance converters, which we consider as a new result b) the frequency dependence of the amplifiers with operational amplifiers given in the technical specifications without citations of the time dependent equation. A simple circuit for determination of f0 is suggested and the method is illustrated by determination of crossover frequency for the low-noise and high speed ADA4898 operational amplifier. It is concluded that for an exact calculation of the pass bandwidth of amplifiers with active filters the 70 years old master equation is a useful technique implicitly included in the contemporary software. The frequency dependent formulae for the amplification coefficient of inverting and non-inverting amplifiers are given for the case of non-zero conductivity between the inputs of the operational amplifiers.Item On the Influence of the Ionization-Recombination Processes on the Hydrogen Plasma Polytropic Index(2021-07-20) Mishonov T.M.; Dimitrova I.M.; Varonov A.M.An analytical approximation for the polytropic index of a hydrogen gas has been derived. The derived expressions can be useful for theoretical work and numerical calculations. These results open the possibility of direct computation of these thermodynamic quantities, rather than interpolating from tables. Additionally, the polytropic index is graphically represented as a function of temperature and density. It is concluded that the partially ionized hydrogen plasma cannot be exactly polytropic. The calculated deviations from the monoatomic value 5/3 are significant and measurable. The present theory supposes that hydrogen molecules are completely dissociated, and this analytical result for pure hydrogen plasma can be applied for the solar chromosphere, where He ionization is negligible and H2 dissociation is almost complete. These two conditions define the ranges of applicability of temperatures and densities. The analytical result for pure hydrogen plasma is a test example of how this approach can be extended for an arbitrary gas cocktail.Item Probability distribution function of crossover frequency of operational amplifiers(2021-07-01) Mishonov T.M.; Petkov E.G.; Dimitrova I.M.; Serafimov N.S.; Varonov A.M.For the first time the cumulative distribution function and histogram of the crossover frequency of a contemporary operational amplifier ADA4898-2 is experimentally studied. Using a USB lockāin amplifier, which allows automatic frequency sweep of the current response of a non-inverting amplifier with significant static amplification, we measure the crossover frequency of 200 samples of ADA4898-2 operational amplifiers. This new method gives a significant advantage in accuracy and speed of study of every operational amplifier. The theory we use is based on the universal relation between time dependent output and input voltages. This common relation for all operational amplifiers is applicable for frequencies much smaller than the crossover frequency and the frequencies of non-dominant poles. In other words, this approximation is adequate, when an operational amplifier is included in a circuit with significant amplification.Item Simple do-it-yourself experimental set-up for electron charge qe measurement(2018-08-29) Mishonov T.M.; Petkov E.G.; Mihailova N.Z.; Stefanov A.A.; Dimitrova I.M.; Gourev V.N.; Serafimov N.S.; Danchev V.I.; Varonov A.M.A simple experiment for the electron charge q e measurement is described. The experimental set-up contains standard electronic equipment only and can be built in every high-school lab all around the world with several days' pocket money budget. It is concluded that it is time such a practice should be included in regular high-school education. The achieved 13% accuracy is comparable to the best student university labs. The measurement is based on Schottky noise generated by a photodiode. Using a criterion of dollar-per-accuracy for the electron charge q e measurement, this is definitely the world's best educational experiment. An industrial replica can easily be sold across the globe.Item Sound absorption in partially ionized hydrogen plasma and heating mechanism of solar chromosphere(2021-02-01) Mishonov T.M.; Dimitrova I.M.; Varonov A.M.The temperature dependence of rates of electron impact ionization and two electrons recombination are calculated using Wannier cross section of electron impact ionization of neutral hydrogen atom. Entropy production and power dissipation are derived for the case when the ionization degree deviates from its equilibrium value. This is the special case of the obtained general formula for entropy production accompanying chemical reactions. Damping rate of the sound waves is calculated and the conditions when ionization processes dominate are considered. A quasi-classical approximation for the heating mechanism of solar chromosphere is proposed. Several analogous phenomena for damping rates in liquids and crystals are shortly discussed, for example, deaf sound of a glass of beer or English salt solution. An explicit expression for the second or bulk (or volume) viscosity of hydrogen plasma is calculated from firsts principles. For the first time some second viscosity is calculated from first principles.Item Tunable high-Q resonator by general impedance converter(2021-02-01) Mifune T.; Mishonov T.M.; Serafimov N.S.; Dimitrova I.M.; Popeski-Dimovski R.; Velkoska L.; Petkov E.G.; Varonov A.M.; Barone A.A tunable high-Q resonator is performed in the schematics of the General Impedance Converter (GIC). In the framework of frequency dependent open-loop gain of operational amplifiers, a general formula of the frequency dependence of the impedance of GIC is derived. The explicit formulas for the resonance frequency and Q-factor include as an immanent parameter the crossover frequency of the operational amplifier. Voltage measurements of GIC with a lock-in amplifier perfectly agree with the derived formulas.