test2sp01_sols

# test2sp01_sols - V1 = Vs V2 − V1 V At node V2 − αV X 2...

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Unformatted text preview: V1 = Vs V2 − V1 V At node V2 : − αV X + 2 = 0 * / R R R Controllin g variable : V x = V1 − V2 At node V1 : V1 V2 Solving for the node voltages 2V2 − Vs − αR(Vs − V2 ) = 0 V1 = Vs , V2 = ( 2 + αR)V2 = (1 + αR)Vs 1 + αR Vs 2 + αR Power at dependent source R[kOhm] Vs[V] a[mA/V] V1[V] V2[V] Vx[V] P_D[mW] 4 24 0.5 24 18 6 -54 5 20 0.4 20 15 5 -30 10 20 0.2 20 15 5 -15 4 24 0.25 24 16 8 -32 PD = V2 (−αV x ) = −αV2 (Vs − V2 ) I1 = bV x Mesh 1 : Vs + RI2 + R( I 2 − I1) = 0 Mesh 2 : Controllin g variable : V x = R( I1 − I 2 ) Computing the mesh currents I1 I1 = bR ( I1 − I 2 ) I2 (1 − bR) I1 + bRI 2 = 0 * / 2 − RI1 + 2 RI 2 = −Vs * /( −b) (2 − 2bR + bR) I1 = bVs R[kOhm] Vs[V] b[mA/V] I1[mA] I2[mA] Vx[V] 10 60 0.05 2 -2 40 5 45 0.1 3 -3 30 4 36 0.125 3 -3 24 2 60 0.25 10 -10 40 I2 = − Vx = I1 = 1 − bR I1 bR I1 Vs = = R( I1 − I 2 ) b 2 − bR b Vs (2 − bR) V3 = RI s V1 Super node V2 I1 (Ohm' s Law) Using node analysis Constraint Eq : V1 − V2 = Vs VV KCL @ super node : − I s + 2 + 1 = 0 RR Solving V1 + V2 = RI s V1 − V2 = Vs I2 2V1 = Vs + RI s (adding eqs) 2V2 = −Vs + RI s (substracting eqs) Using mesh analysis I1 = I s − Vs + RI 2 + R( I 2 − I1 ) = 0 V1 = RI 2 V2 = R( I1 − I 2 ) I2 = Vs + RI s 2R R[kOhm] Vs[V] Is[mA] V1 V2 V3 6 24 10 42 18 60 8 12 6 30 18 48 6 20 8 34 14 48 10 12 6 36 24 60 v− vo Ri vs + - R Ro v+ + - A(v+ − v− ) Loop analysis − v s + ( R + Ri + R0 ) I + A(v+ − v− ) = 0 Ro[kOhm] Ri[kOhm] A R[kOhm] Vs/I[kOhm] G 2 1 1 2 100 50 50 100 40 25 20 30 10 10 10 10 4112 1311 1061 3112 0.9732 0.9542 0.9434 0.9647 v+ − v− = Ri I vs vo = Ro I + A(v+ − v − ) I= R + Ro + (1 + A) Ri vs = R + Ro + (1 + A) Ri I v Ro + ARi G= o = v s R + Ro + (1 + A) Ri Rin = ...
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