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Power System Fundamentals
Published in Stephen W. Fardo, Dale R. Patrick, Electrical Power Systems Technology, 2020
Stephen W. Fardo, Dale R. Patrick
The opposition to change of current is evident in the diagram of Figure 2-11B. In an inductive circuit, we can say that voltage leads current or that current lags voltage. If the circuit were purely inductive (containing no resistance), the voltage would lead the current by 90° (Figure 2-11B), and no actual power would be converted in the circuit. However, since all actual circuits have resistance, the inductive characteristic of a circuit typically causes the condition shown in Figure 2-12 to exist. Here, the voltage is leading the current by 30°. The angular separation between voltage and current is called the “phase angle.” The phase angle increases as the inductance of the circuit increases. This type of circuit is called a “resistive-inductive (RL) circuit.”
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
A comparison of overdamped, critically damped, and underdamped responses of the capacitor voltage is given in Figure 107.6 for a unit step input, with the circuit initially relaxed. Additional insight into the behavior of RL, RC, and RLC circuits can be obtained by examining the response of the current in the series RL, RC, and RLC circuits for corresponding component values. For example, Figure 107.7 shows the waveforms of the step response of i(t) for the following component values: R=4Ω,L=1H, and C=1F. The RL circuit has a time constant of 0.25 sec, the RC circuit has a time constant of 2.00 sec, and the overdamped RLC circuit has time constants of 0.29 and 1.69 sec. The inductor in the RL circuit blocks the initial flow of current, the capacitor in the RC circuit blocks the steady-state flow of current, and the RLC circuit exhibits a combination of both behaviors. Note that the time constants of the RLC circuit are bounded by those of the RL and RC circuits.
Transient Analysis
Published in John Okyere Attia, Circuits and Electronics, 2017
For an RL circuit, the time constant is given as τ = L/R. The time constant determines the rate of charging or discharging of a capacitor. After τ seconds, the current will have decreased to e-1 (about 0.368) of its initial value. After 2τ seconds, it will have decreased to e-2 (0.135) of its initial value, and after 5τ seconds, the current will have decreased to 0.0067 of the initial value. Example 3.2 shows how to use the Analog Discovery board to explore the behavior of an RL circuit.
Low-profile electronic beam-scanning metasurface antenna for Ka-band applications
Published in Waves in Random and Complex Media, 2023
Aqeel Hussain Naqvi, Sungjoon Lim
We selected a Gallium Arsenide (GaAs) flip-chip PIN-diode MA4GP907 (MACOM, Lowell, MA, United States) as the active tunable device due to its low insertion losses and small size. The diode is modeled as a series RL-circuit for forward bias (ON state), i.e. RON = 5.2-Ω, LON = 0.05-nH; and as a shunt RC-circuit, i.e. (ROFF = 40-kΩ, COFF = 0.025-pF) with reverse-bias for the OFF state. Figure 2(b and c) show equivalent circuits for a PIN-diode in ON and OFF states. To validate the meta-cell performance, we simulated the meta-cell periodic boundary conditions using the ANSYS high-frequency structure simulator (HFSS). Figure 2(d) shows meta-cell reflection properties for OFF and ON-states, with reflection magnitudes = 1.64 and 0.29 dB, respectively. Phase difference between OFF and ON states = 29° at 28 GHz, with lagging phase in ON state. We represent PIN diode OFF or ON states as binary, i.e. 0 or 1, respectively, to digitize the EBSMA system.
Assessing experimental apparatus for sheet metal electromagnetic forming process analysis
Published in Materials and Manufacturing Processes, 2022
E. Paese, M. Geier, R. P. Homrich, Rodrigo Rossi, Pedro Rosa
where ieq,Leq, and Req are the equivalent discharge current, equivalent inductance, and resistance as viewed from the primary series RLC circuit, respectively. Further, the Leq and Req are both dependent on the internal inductance and resistance from the pulse unit, the self-parameters of the tool coil, the high-current bus connections, and the inductance and resistance transmitted by the magnetically coupled RL circuit (workpiece) to the pulse unit RLC circuit. It is of importance to know that the transmitted electrical parameters are the result of the existence of mutual inductances between the metallic part and the coil. These equivalent parameters may be determined through experiments with and without a coupled workpiece. The characteristic of the discharge current on the EMF pulse units has an underdamped natural response of a series-connected RLC, where Eq. (6) is the solution for differential Eq. (5)[25]:
Algorithm for solving problems related to the natural vibrations of electro-viscoelastic structures with shunt circuits using ANSYS data
Published in International Journal of Smart and Nano Materials, 2019
Nataliia Iurlova, Natalia Sevodina, Dmitrii Oshmarin, Maksim Iurlov
As one of the options for assessing the reliability of the results obtained, a convergence analysis was performed on the object under study (Figure 4). For these tests, it was assumed that the material of the plate had no viscoelastic properties (was purely elastic). The piezoelectric element was connected to the external electric circuit comprising a series RL-circuit consisting of a series-connected resistor having resistance and an inductance coil having inductance (Figure 4(b)). The following values of resistance and inductance were chosen for the numerical calculations: H, Ohm.