Network Theory (Electronics)

Two-Port Networks:

Four parameters describe the network:

• Z-parameters (impedance): V = Z·I.
• Y-parameters (admittance): I = Y·V.
• h-parameters (hybrid): common for transistors.
• ABCD-parameters (transmission): used in cascading.

Network functions:

• Driving point: same port.
• Transfer: between ports.
• Examples: voltage gain, current gain, transimpedance.

Laplace Transform:

• Time domain → s-domain.
• F(s) = ∫₀^∞ f(t) e^(−st) dt.
• Used for solving differential equations of circuits.

Common Laplace transforms:

• u(t) → 1/s.
• e^(−at) → 1/(s+a).
• sin(ωt) → ω/(s²+ω²).
• cos(ωt) → s/(s²+ω²).

Frequency Response:

• How circuit responds to different frequencies.
• Bode plot: magnitude (dB) and phase (degrees) vs log frequency.
• Cutoff frequency (-3dB point).

Resonance:

• Series RLC: at f_r, X_L = X_C; current max.
• Parallel RLC: at f_r, current min.
• Quality factor (Q): high Q = sharp resonance.

Filters (RC/RL/RLC):

• Low-pass, high-pass, band-pass, band-stop.
• Pass-band, stop-band, transition.

Fourier Series:

• Any periodic function = sum of sinusoids.
• Fundamental frequency + harmonics.

Transient Response:

• RC circuit time constant: τ = RC.
• RL circuit time constant: τ = L/R.
• 99% of final value reached in ~5τ.

Filters Design:

• Butterworth (max flat).
• Chebyshev (sharp cut-off, ripple).
• Bessel (linear phase).

RRB JE focus: Laplace basics, simple resonance frequency, RC time constant.