PHYS 241 Signal Processing
RC Circuit
Network theorems
Fourier Analysis
Basics
I. Kirchhoff's Laws
II. Thevenin's Theorem
II. Norton's Theorem
Fourier Series
Bandwidth Theorem (Uncertainty)
Fourier Theory
System Frequency Response
Alternating Current(AC)
Square/Triangular wave
Properties of Capacitor: V=Q/C
Charging RC circuit with direct current (Use ODE to solve for current, voltage curve)
Real/Ideal battery
Power dissipated by resistor
Linearity and Superposition
Circuit Theory beyond electrics
- Linear relation between current and driving potential
- System effectively 1D or has a network topology
Discharging RC circuit
Capacitor Charging energy
RL circuit
Properties of inductor V=L* dI/dt
Energy stored in inductor: U(t)=L/2×I2
Inductor networks
Sine Wave
RLC circuit
Time constant R*C
Capacitor networks
Low Frequency: differentiator
High Frequency: integrator
RC circuit and LR circuit analogy
Use traditional ODE way to solve RC circuit
Convert input signal to complex form to calculate
Power dissipation in AC circuit (C, L dissipates 0 power, only R do)
Impedance
Impedance Divider and Phasor Diagram method
RC circuit as low-pass / high-pass (dB plot)
transient response
Driven RLC circuit
Analogy to spring-mass oscillator
Overdamped
Underdamped
Critically damped
In pure LC circuit, resonance goes forever
Capacitor Voltage
Quality Factor
Frequency domain analysis (current, phase offset)
Power input into RLC circuit
s-domain analysis
Poles and Zeros
Time constant: L/R