Interactive Workbenches in Electrical & Electronic Systems
Core Fundamentals
Fundamentals
Sweeps an alternating source through a series R-L-C network. Visualize voltage across the inductor and capacitor exchanging energy, the collapse of phase lag at resonance, and transient decaying step responses.
Equation: \omega_0 = \frac{1}{\sqrt{LC}}, \quad \zeta = \frac{R}{2}\sqrt{\frac{C}{L}}
Standard: IEEE Std 1459-2010 / IEC 60076 (Power Factor, Resonance & Damping Dynamics)
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Industrial Grid
Intermediate
Visualizes the spatial summation of magnetic fields produced by coils displaced by 120° in space energized by currents displaced 120° in time. Inspect rotor torque angle, slip velocity, and lagging/leading power factor.
Equation: \vec{B}_{net}(t) = \frac{3}{2} B_m \left[ \cos(\omega t)\hat{i} + \sin(\omega t)\hat{j} \right]
Standard: IEC 60034-1 / IEEE 141 / IS 3043 (Standard R-Y-B-N 4-Wire Sequence)
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Switching Dynamics
Intermediate
Adjust duty cycle and load resistance in real time to observe the magnetic flux accumulation during MOSFET switch-on, and rapid diode freewheeling energy dump to output capacitor during switch-off.
Equation: V_{out} = -V_{in}\frac{D}{1 - D}, \quad \Delta I_L = \frac{V_{in} D}{L f_{sw}}
Standard: IEEE Std 1573 / IEC 62040 (Switching Mode Power Regulators)
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Op-Amp Filter Design
Fundamentals
Demonstrates active op-amp filtering with -40 dB/decade roll-off. Watch how damping factor controls frequency peaking at the cutoff boundary and phase transition from 0° to -180°.
Equation: H(s) = \frac{K \omega_c^2}{s^2 + \frac{\omega_c}{Q} s + \omega_c^2}, \quad f_c = \frac{1}{2\pi \sqrt{R_1 R_2 C_1 C_2}}
Standard: IEEE Std 1057 / Butterworth-Chebyshev Biquad Filter Realization
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Wave Mechanics
Advanced
Solve the Telegrapher equations along a coaxial line. When the load impedance fails to match characteristic impedance Z₀, reflections create constructive/destructive interference along the spatial length.
Equation: \Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}, \quad \text{VSWR} = \frac{1 + |\Gamma|}{1 - |\Gamma|}
Standard: IEEE Std 399 / Pozar Microwave Engineering (Telegrapher Equations)
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Spectral Analysis
Fundamentals
Direct mathematical demonstration of Fourier analysis. Adjust the count of odd harmonics, inspect Gibbs phenomenon overshoot at step discontinuities, and calculate real-time Total Harmonic Distortion (THD).
Equation: f(t) = \frac{4}{\pi} \sum_{n=1,3,5,\dots}^{N} \frac{1}{n} \sin(n \omega_0 t)
Standard: IEEE 519 (Recommended Practice for Harmonic Control in Electric Power)
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