Signals and Waveforms: Common electrical signals and their waveform characteristics

Signals and Waveforms: Common electrical signals and their waveform characteristics

1. What a Signal / Waveform Is

Signal = time-varying voltage $v(t)$ or current $i(t)$ that carries information or power. Waveform = graph of signal vs time $y(t)$. Characteristics: amplitude ($V_m, I_m$), period $T$, frequency $f=1/T$, angular frequency $ω=2πf$, phase $φ$, offset (DC).

2. Common Electrical Signals (exam list)

Signal	Expression $v(t)$ / $i(t)$	Waveform Sketch	Periodic?	Use
DC (constant)

(e.g., 5V battery) | horizontal line | no (or infinite period) | Supply |
| Sinusoidal AC |

or

| smooth sine | yes ($T=2π/ω$) | mains $230V/50Hz$, most AC |
| Square wave |

| rectangular | yes, 50% duty | Digital clock, switching |
| Triangular / Sawtooth | Linear ramp up/down | triangle / sawtooth | yes | Sweep, PWM |
| Pulse train | Short rectangular pulses, duty $D=τ/T$ | spikes | yes if regular | Digital data, radar |
| Exponential / Step |

| decaying | no (transient) | RC charging, transients |

Mains: $v(t)=325 sin(314t)$ V peak (230V RMS) at $50$ Hz ⇒ $T=20$ ms, $ω=314$ rad/s.

3. Waveform Characteristics (what exam asks to describe)

• Peak amplitude $V_m$ (maximum).
• Peak-to-peak $V_{p-p}=2V_m$ for symmetric sine.
• Average $V_{avg}$ over cycle (sine 0, half-wave $V_m/π$, full-wave $2V_m/π$).
• RMS $V_{rms}=√(1/T ∫ v² dt)$ (heating equivalent; sine $V_m/√2$).
• Duty cycle for pulse: $D=τ/T$.
• Frequency $f$ and period $T$.

4. Worked Illustration

(a) Square wave 5V, 1kHz, 50% duty: V_m=5V, T=1ms, RMS=5V (since V² always 25) ⇒ RMS = peak! ✓

(b) Sine V_m=10V: V_rms=7.07V, V_avg (full cycle 0), half-cycle avg =6.37V ✓

(c) Identify: 230V RMS mains ⇒ V_m=325V, V_p-p=650V.

(d) Triangular wave amplitude 10V: RMS= V_m/√3≈5.77V

5. Exam Points

• Sketch and define sinusoidal, square, triangular, DC waveforms with $V_m, T, f$ — 5 marks, very frequent.
• Give $v(t)=V_m sin(ωt+φ)$ and define $ω=2πf$, $T=1/f$ — 3-5 marks, frequent.
• Mention mains $325 sin(314t)$ — 3 marks, frequent.
• Distinguish periodic vs transient — 3 marks.