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exp(j f ) = cos( f ) + j sen( f )

FASORES. Identidad de Euler. exp(j f ) = cos( f ) + j sen( f ). sen( f ) = Im[exp(j f )]. cos( f ) = Re[exp(j f )]. v(t) = Vm cos( w t + f ) = Re[Vm exp(j( w t+ f )]. v(t) = Re[Vm exp(j f ) exp(j w t) ]. v(t) = Re[ V exp(j w t) ]. V = Vm exp(j f ) = Vm ang( f ). V = Fasor Voltaje.

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exp(j f ) = cos( f ) + j sen( f )

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  1. FASORES Identidad de Euler exp(jf) = cos(f) + j sen(f) sen(f) = Im[exp(jf)] cos(f) = Re[exp(jf)] v(t) = Vm cos(wt + f) = Re[Vm exp(j(wt+f)] v(t) = Re[Vm exp(jf) exp(jwt) ] v(t) = Re[V exp(jwt) ] V = Vm exp(jf) = Vm ang(f) V = Fasor Voltaje

  2. Representación de señales senoidales utilizando fasores dv/dt => jwV Integral (v dt) => V/jw

  3. Ejemplo de operaciones con fasores

  4. 1 = = = V I v ( t ) R i ( t ) R Z R = Y R 1 di ( t ) = w = = w V I j L Y Z j L = v ( t ) L w j L dt 1 1 1 ò = = = w V I Z Y j C = v ( t ) i ( t ) dt w w j C j C C 1 = + + Z Z Z Z L = Z = + + Y Y Y Y L eq 1 2 N 1 1 1 eq eq 1 2 N + + L Z Z Z 1 2 N Relación voltaje-corriente en elementos pasivos Element Time domain frequency domain Impedance Admitance R L C Z1 Z2 Zeq Zeq L Z1 Z2 ZN ZN ZN .

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