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Topics: Electrical impedance, Complex number, Alternating current Pages: 80 (11194 words) Published: May 13, 2013
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 • 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

1 0 -1 0 1 0 -1 0 5 t 10 15 5 t 10 15

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

same shape but with a time shift.

v(t) = sin t ⇒

dv dt

= cos t

1 0 -1 0 1 0 -1 0 5 t 10 15 5 t 10 15

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

same shape but with a time shift.

v(t) = sin t ⇒

dv dt

= cos t

1 0 -1 0 1 0 -1 0 5 t 10 15 5 t 10 15

sin t completes one full period every time t increases by 2π .

E1.1 Analysis of Circuits...
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