Filters, Feedback, Stability & Oscillators

Filters, Feedback, Stability & Oscillators: Passive & Active Filters: Butterworth, Chebyshev, Bessel, Sallen-Key & MFB, Negative Feedback: Topologies, Benefits & Loop Gain, Stability, Phase Margin & Frequency Compensation, Sinusoidal Oscillators: Wien, Phase-Shift, LC & Crystal, 555 Timer & Waveform Generators.

• Passive & Active Filters: Butterworth, Chebyshev, Bessel, Sallen-Key & MFB — Shaping the frequency content of signals. Learn filter types (low-pass, high-pass, band-pass, band-stop/notch, all-pass), specifications (passband, stopband, ripple, attenuation, transition band, order), passive RC/RLC filters and their loading problems, response families (Butterworth, Chebyshev, Bessel, elliptic) and their trade-offs in flatness, steepness, phase and step response, active topologies (Sallen-Key, multiple-feedback, state-variable, biquads), cascading second-order sections, component sensitivity and anti-aliasing filters — with Python computing the required order, Sallen-Key component values and comparing Butterworth and Chebyshev attenuation.
• Negative Feedback: Topologies, Benefits & Loop Gain — The principle that makes precise analog circuits possible. Learn the feedback loop (forward gain A, feedback factor β, loop gain T = Aβ), closed-loop gain A/(1 + Aβ), desensitivity, bandwidth extension, distortion and noise-in-loop reduction, the four topologies (series-shunt voltage amplifier, shunt-series current amplifier, series-series transconductance, shunt-shunt transresistance) and how each changes input and output impedance, loop-gain measurement, and positive feedback — with Python quantifying desensitivity, bandwidth, distortion and impedance changes.
• Stability, Phase Margin & Frequency Compensation — Keeping feedback loops from oscillating. Learn the Barkhausen condition and why negative feedback becomes positive at high frequency, loop-gain Bode plots, gain and phase margin, their link to overshoot and ringing, the rate-of-closure rule, dominant-pole and Miller (pole-splitting) compensation, lead/lag compensation, noise-gain shaping, capacitive-load instability and its cures (isolation resistor, in-loop compensation, snubbers), stability of regulators and TIAs, and measuring stability with step response and loop-gain injection — with Python computing phase margins for different feedback factors and with a capacitive load.
• Sinusoidal Oscillators: Wien, Phase-Shift, LC & Crystal — Circuits designed to be unstable in a controlled way. Learn the Barkhausen criterion, start-up and amplitude limiting, the Wien-bridge oscillator with amplitude stabilisation, RC phase-shift oscillators, LC oscillators (Colpitts, Hartley, Clapp), crystal equivalent circuit (motional L, C, R and shunt C₀), series and parallel resonance, Pierce oscillators and load capacitance, oscillator frequency stability, phase noise and jitter basics — with Python computing Wien, phase-shift, Colpitts and crystal frequencies and load capacitors.
• 555 Timer & Waveform Generators — Generating square, triangle, sawtooth and pulse waveforms. Learn the 555's internal comparators, flip-flop and discharge transistor, the monostable (one-shot) and astable modes with their timing equations and duty-cycle limits, 50% duty and PWM variants, CMOS 555s, the op-amp relaxation oscillator, the integrator + Schmitt triangle/square function generator, sawtooth generators with current sources, VCOs and function-generator ICs — with Python computing astable frequency and duty, monostable pulse width and triangle-generator frequency and amplitude.