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10: Sine waves and phasors
• Sine Waves • Rotating Rod • Phasors • Phasor Examples • Phasor arithmetic • Complex Impedances • Phasor Analysis • CIVIL • Impedance and
Admittance • Summary (Irwin/Nelms Ch 8)
10: Sine waves and phasors
E1.1 Analysis of Circuits (2012-2517)
Phasors: 10 – 1 / 11
Sine Waves
10: Sine waves and phasors
• Sine Waves • Rotating Rod • Phasors • Phasor Examples • Phasor arithmetic • Complex Impedances • Phasor Analysis • CIVIL • Impedance and
Admittance • Summary (Irwin/Nelms Ch 8)
di For inductors and capacitors i = C dv and v = L dt so we need to dt differentiate i(t) and v(t) when analysing circuits containing them.
E1.1 Analysis of Circuits (2012-2517)
Phasors: 10 – 2 / 11
Sine Waves
10: Sine waves and phasors
• Sine Waves • Rotating Rod • Phasors • Phasor Examples • Phasor arithmetic • Complex Impedances • Phasor Analysis • CIVIL • Impedance and
Admittance • Summary (Irwin/Nelms Ch 8)
di For inductors and capacitors i = C dv and v = L dt so we need to dt differentiate i(t) and v(t) when analysing circuits containing them.
Usually differentiation changes the shape of a waveform.
1 0 -1 0 5 0 -5 0 1 2 t 3 4 1 2 t 3 4
E1.1 Analysis of Circuits (2012-2517)
Phasors: 10 – 2 / 11
Sine Waves
10: Sine waves and phasors
• Sine Waves • Rotating Rod • Phasors • Phasor Examples • Phasor arithmetic • Complex Impedances • Phasor Analysis • CIVIL • Impedance and
Admittance • Summary (Irwin/Nelms Ch 8)
di For inductors and capacitors i = C dv and v = L dt so we need to dt differentiate i(t) and v(t) when analysing circuits containing them.
Usually differentiation changes the shape of a waveform. For bounded waveforms there is only one exception:
1 0 -1 0 5 0 -5 0 1 2 t 3 4 1 2 t 3 4
v(t) = sin t ⇒
dv dt
= cos t
E1.1 Analysis of Circuits (2012-2517)
Phasors: 10 – 2 / 11
Sine Waves
10: Sine waves and phasors
• Sine Waves • Rotating Rod • Phasors • Phasor Examples
• Sine Waves • Rotating Rod • Phasors • Phasor Examples • Phasor arithmetic • Complex Impedances • Phasor Analysis • CIVIL • Impedance and
Admittance • Summary (Irwin/Nelms Ch 8)
10: Sine waves and phasors
E1.1 Analysis of Circuits (2012-2517)
Phasors: 10 – 1 / 11
Sine Waves
10: Sine waves and phasors
• Sine Waves • Rotating Rod • Phasors • Phasor Examples • Phasor arithmetic • Complex Impedances • Phasor Analysis • CIVIL • Impedance and
Admittance • Summary (Irwin/Nelms Ch 8)
di For inductors and capacitors i = C dv and v = L dt so we need to dt differentiate i(t) and v(t) when analysing circuits containing them.
E1.1 Analysis of Circuits (2012-2517)
Phasors: 10 – 2 / 11
Sine Waves
10: Sine waves and phasors
• Sine Waves • Rotating Rod • Phasors • Phasor Examples • Phasor arithmetic • Complex Impedances • Phasor Analysis • CIVIL • Impedance and
Admittance • Summary (Irwin/Nelms Ch 8)
di For inductors and capacitors i = C dv and v = L dt so we need to dt differentiate i(t) and v(t) when analysing circuits containing them.
Usually differentiation changes the shape of a waveform.
1 0 -1 0 5 0 -5 0 1 2 t 3 4 1 2 t 3 4
E1.1 Analysis of Circuits (2012-2517)
Phasors: 10 – 2 / 11
Sine Waves
10: Sine waves and phasors
• Sine Waves • Rotating Rod • Phasors • Phasor Examples • Phasor arithmetic • Complex Impedances • Phasor Analysis • CIVIL • Impedance and
Admittance • Summary (Irwin/Nelms Ch 8)
di For inductors and capacitors i = C dv and v = L dt so we need to dt differentiate i(t) and v(t) when analysing circuits containing them.
Usually differentiation changes the shape of a waveform. For bounded waveforms there is only one exception:
1 0 -1 0 5 0 -5 0 1 2 t 3 4 1 2 t 3 4
v(t) = sin t ⇒
dv dt
= cos t
E1.1 Analysis of Circuits (2012-2517)
Phasors: 10 – 2 / 11
Sine Waves
10: Sine waves and phasors
• Sine Waves • Rotating Rod • Phasors • Phasor Examples