GATE EC Formula Sheet for Quick Revision
GATE Electronics and Communication formulas on one page: networks, signals, devices, analog and digital circuits, control, communications and EM waves.
The formulas that GATE Electronics and Communication numerical questions use most, subject by subject. Use this page for revision after studying each lesson.
Networks
| Formula | Meaning |
|---|---|
| τ = RC or L/R | Time constant |
| ω₀ = 1/√(LC); series Q = ω₀L/R; bandwidth = ω₀/Q | Resonance |
| Maximum power transfer: Z_L = Z_th* | Load matching |
| Two-port: V₁ = z₁₁I₁ + z₁₂I₂, V₂ = z₂₁I₁ + z₂₂I₂ | Z parameters |
See Networks.
Signals and systems
| Formula | Meaning |
|---|---|
| f_s ≥ 2 f_max | Nyquist rate |
| DFT of N points: N² multiplications directly, (N/2) log₂ N with FFT | Computation |
| Parseval: energy = ∫ x(t)² dt = (1/2π) ∫ (magnitude of X(jω))² dω | Energy in time and frequency (real x) |
See Signals and systems.
Electronic devices
| Formula | Meaning |
|---|---|
| V_T = kT/q ≈ 26 mV at 300 K | Thermal voltage |
| I = I_s(e^(V/(ηV_T)) − 1) | Diode equation |
| σ = q(nμ_n + pμ_p) | Conductivity of a semiconductor |
| n p = n_i² | Mass-action law |
See Electronic devices.
Analog circuits
| Formula | Meaning |
|---|---|
| g_m = I_C/V_T (BJT) | Transconductance |
| I_D = (k/2)(V_GS − V_T)² | MOSFET in saturation (square law) |
| Inverting gain −R_f/R₁; non-inverting 1 + R_f/R₁ | Op-amp amplifiers |
| Gain–bandwidth product = constant | Op-amp frequency response |
See Analog circuits.
Digital circuits
| Formula | Meaning |
|---|---|
| n-bit 2's complement: −2^(n−1) to 2^(n−1) − 1 | Number range |
| Mod-N counter: ⌈log₂ N⌉ flip-flops | Counters |
| 2ⁿ:1 multiplexer has n select lines | Multiplexers |
| n-bit DAC resolution = V_ref/(2ⁿ − 1) or V_ref/2ⁿ (by convention) | Data converters |
See Digital circuits.
Control systems
| Formula | Meaning |
|---|---|
| T(s) = G/(1 + GH) | Closed loop |
| M_p = e^(−πζ/√(1 − ζ²)), t_s ≈ 4/(ζω_n) | Second-order step response |
| Routh: number of sign changes in the first column = number of right-half-plane poles | Stability test |
See Control systems.
Communications
| Formula | Meaning |
|---|---|
| AM: P_t = P_c(1 + μ²/2) | Total power with modulation index μ |
| Carson's rule: B = 2(Δf + f_m) | FM bandwidth |
| C = B log₂(1 + SNR) | Shannon capacity |
| PCM bit rate = n × f_s | n bits per sample |
| H = −Σ p log₂ p | Entropy of a source |
See Communications.
Electromagnetics
| Formula | Meaning |
|---|---|
| v = 1/√(με), η₀ ≈ 377 Ω | Wave speed and free-space impedance |
| Γ = (Z_L − Z₀)/(Z_L + Z₀), VSWR = (1 + ρ)/(1 − ρ), ρ = magnitude of Γ | Transmission lines |
| δ = 1/√(πfμσ) | Skin depth |
| Rectangular waveguide TE₁₀: f_c = c/(2a) | Cutoff frequency |
See Electromagnetics.
Check yourself
A channel has bandwidth 3 kHz and SNR 15 (linear). What is its Shannon capacity in kbit/s?
Show answer and explanation
Answer: 12C = 3 × log₂ 16 = 3 × 4 = 12 kbit/s.
An FM signal has frequency deviation 75 kHz and message frequency 15 kHz. What is its bandwidth by Carson's rule in kHz?
Show answer and explanation
Answer: 180B = 2(75 + 15) = 180 kHz.
A line with Z₀ = 50 Ω is terminated in 150 Ω. What is the VSWR?
Show answer and explanation
Answer: 3Γ = 100/200 = 0.5; VSWR = 1.5/0.5 = 3.
A source emits four symbols with equal probability. What is its entropy in bits per symbol?
Show answer and explanation
Answer: 2H = log₂ 4 = 2 bits.
An AM carrier of 100 W is modulated with μ = 1. What is the total transmitted power in W?
Show answer and explanation
Answer: 150P_t = 100(1 + 0.5) = 150 W.