Impedance
the measure of opposition a circuit offers to alternating current (AC), combining both resistance and reactance.
Thevenin Equivalent Circuit (AC)
is a simplified version consisting of a single voltage source (Vth) in series with an impedance (Zth). It makes analyzing power delivery to a load easier by reducing a complex network to just two components, using phasors and impedance in the AC case.
Maximum Power Transfer (AC)
a load occurs when the load impedance is the complex conjugate of the source’s Thevenin impedance: Z_load=Z*th
Low Pass Filter (LPF)
Allows low-frequency signals to pass while attenuating high frequencies.
High Pass Filter (HPF)
Passes high frequencies and blocks low ones.
Band Pass Filter (BPF)
Passes a range of frequencies (band) and blocks those outside
Root Mean Square (RMS)
values represent the effective value of a time-varying voltage or current.
Power Triangle
visually represents the relationship between:
Real Power (P): power actually consumed (in watts),
Reactive Power (Q): power stored and released (in VAR),
Apparent Power (S): total power supplied (in VA).
time constant (τ)
defines how quickly voltage or current in RC or RL circuits changes over time during transient conditions:
τ=RC for RC circuits
τ=L/R for RL circuits
It determines the exponential rate at which a circuit responds to a step input.
Underdamped RLC Response
when resistance is low, allowing oscillations to occur while gradually decreasing in amplitude. The response is sinusoidal but multiplied by an exponentially decaying envelope.
It occurs when: R^2 < 4L/C or something < 1
Overdamped RLC Response
resistance is high enough that the circuit does not oscillate. The transient response consists of two distinct decaying exponentials. The system returns to steady-state slowly and without overshoot.
It occurs when: R^2 > 4L/C or something > 1
Critically Damped RLC Response
is the boundary between underdamping and overdamping. It is the fastest non-oscillatory response a system can have. The system returns to equilibrium in the shortest possible time without oscillating.
It occurs when: R^2 = 4L/C or something = 1
