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Signals & Waveforms

Understand different types of electrical signals and their characteristics

Types of Signals

1. DC (Direct Current):

Constant voltage or current over time. Example: Battery output

2. AC (Alternating Current):

Voltage/current that varies sinusoidally with time

$$V(t) = V_p \sin(2\pi ft)$$

3. Square Wave:

Alternates between two voltage levels (used in digital circuits)

4. Triangle/Sawtooth:

Linear rise and fall patterns

Signal Parameters
  • Amplitude: Maximum value of the signal (peak voltage/current)
  • Frequency (f): Number of cycles per second (measured in Hertz)
  • Period (T): Time for one complete cycle: T = 1/f
  • Phase: Timing offset between signals
  • RMS Value: Root Mean Square, effective AC value

RMS Voltage (for sine wave):

$$V_{RMS} = \frac{V_p}{sqrt{2}} \approx 0.707 \times V_p$$

Fourier Analysis

Any periodic signal can be decomposed into a sum of sine waves at different frequencies (harmonics). This is the basis of frequency domain analysis.

Fourier Series:

$$f(t) = a_0 + \sum_{n=1}^infty [a_n \cos(n\omega t) + b_n \sin(n\omega t)]$$

Filters
  • Low-pass: Allows low frequencies, blocks high frequencies
  • High-pass: Allows high frequencies, blocks low frequencies
  • Band-pass: Allows frequencies within a specific range
  • Band-stop (Notch): Blocks frequencies within a specific range
Applications
  • Audio: Processing sound signals (20Hz - 20kHz)
  • Radio: RF signals for wireless communication
  • Power: 50Hz/60Hz AC power distribution
  • Sensors: Converting physical quantities to electrical signals
  • Communications: Modulation techniques (AM, FM, digital)