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EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001 Lecture 12 1 Ideal Transformer For an ideal transformer (which is coupled with good magnetic material so that the core permeability and winding conductivities are assumed infinite, and it is therefore lossless) the time domain relations are N1 v1 v2 N1 i1 N 2 i2 0 N2 where both currents are entering the dots on the positive terminal. Lecture 12 2 Ideal Transformer • Note that the two equations above can be combined to show that the power into the ideal transformer is zero, and it is therefore lossless v1 i1 + v2 i2 = 0 = p1 + p2 • An ideal transformer is very tightly coupled (k1) N2 n N1 L2 M L2 L2 L1 M Lecture 12 3 Ideal Transformer • Defining the turns ratio, n=N2/N1, provides the frequency domain equations for an ideal xformer V2 V1 n I1 n I 2 • NOTE: these equations require I2 in the reverse direction (see Fig. 11.13)---against dot convention • Each change of voltage or current with respect to the dot introduces a negative sign in the corresponding equation Lecture 12 4 Ideal Transformer I1 1:n + V1 – I2 + V2 – V2 V1 n ZL I1 n I 2 V2 * n I 2 V2 I*2 S 2 S1 V1 I n * 1 Z input Z 1 V1 V2 / n Z L 2 I1 n I2 n Lecture 12 5 Class Examples • Extension Exercise E11.6 • Extension Exercise E11.7 Lecture 12 6 Thevenin Equivalent Circuit Thevenin's theorem may be used to derive equivalent circuits for the transformer and either its primary or secondary circuit Equivalent Circuit Voltage Source Impedance Current Replace transformer and primary circuit Primary voltage multiplied by n Primary impedance multiplied by n² Primary current divided by n Replace transformer and secondary circuit Secondary voltage divided by n Secondary impedance divided by n² Secondary current multiplied by n Lecture 12 7 Class Examples • Extension Exercise E11.9 Lecture 12 8