unit 10 B

• Parameters

  Describe a sinusoidal waveform
• General equation for sinusoidal waveforms

  v = Vp sin(ωt) or v = Vp sin(2πft)
• Conversion from radian to degree and vice versa

  1. Radian to degree: θ(deg) = θ(rad) * 180/π

  2. Degree to radian: θ(rad) = θ(deg) * π/180
• Phase difference


  Of two sinusoidal waveforms
• Average value


  Of a sinusoidal waveform
• Root mean square value (rms)

  Of a sinusoidal waveform
• AC voltage and AC current are both sinusoidal waveforms
• A sinusoidal waveform has its magnitude that varies as a sine function
• Sinusoidal waveform


  Can be represented by an equation of a sine function
• Sinusoidal waveform

  • Periodic waveform
  • Repeats itself cycle after cycle
• Period (T)


  Duration to complete 1 cycle of sine wave
• Frequency (f)


  Number of complete cycles in one second, unit is Hertz (Hz)
• Sinusoidal waveform

  • Period = 20 ms
  • Frequency = 50 Hz
• Peak value (Vp)


  Maximum positive value, also called amplitude
• Peak-to-peak value (Vpp)


  Voltage measured between the two peaks
• Sinusoidal waveform

  • Peak voltage Vp = 0.5 V
  • Peak-to-peak voltage Vpp = 1 V
• Writing the sine wave equation

  v = Vp sin(ωt) or v = Vp sin(2πft)
• Radian (rad)


  Unit for measuring angles
• Degree (°)

  Unit for measuring angles
• Determining angle in radian and degree

  1. Angle in radian = ωt

  2. Angle in degree = (ωt * 180)/π
• Sine wave with 2000 Hz frequency


  • Angle at 50 μs: (a) in radian = 0.628 rad (b) in degree = 36°
• Converting angle from degree to radian

  Angle in radian = (Angle in degree * π)/180
• Sine wave with 200 Hz frequency


  • Time to reach 36° after crossing zero level = 0.05 s
• Angular position can be represented in degree (°) or radian (rad)
• Sinusoidal waveform

  • Vp = 300 V, Time for 10 cycles = 0.2 s
• Phase angle (φ)


  Angular position of a sine wave relative to a reference
• If voltage rises above zero level earlier than the reference, the phase is positive
• If voltage rises above zero level later than the reference, the phase is negative
• Phase difference


  Between two sine waves
• Phase difference between two sine waves


  • Waveform A leads Waveform B by 90°
• Average value (Vav)


  Over a full cycle of a sinusoidal waveform is zero
• Average value (Vav)

  Over a positive half cycle is (2/π) * Vp
• Average value (Vav)

  Over a negative half cycle is -(2/π) * Vp
• Root mean square (RMS) value (Vrms)


  Of a sinusoidal waveform is (1/√2) * Vp
• Vrms of a sinusoidal waveform = Vdc that produces the same amount of heating in a resistor
• You have learned parameters, equations, phase, and values associated with sinusoidal waveforms
• Next topic is AC Circuit Analysis