set01new - ECE3050 Homework Set 1 1. For V = 18 V, R1 = 39...

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ECE3050 Homework Set 1 1. For V =18V , R 1 =39k , R 2 =43k ,and R 3 =11k ,useOhm ’sLaw ,vo ltaged iv is ion , and current division to solve for V 1 , V 2 , I 1 , I 2 I 3 . V 1 =18 39k 39 k +43k k 11k =14 . 7V V 2 43k k k =3 . 30V I 1 = 18 k = 376 . 8 µ A I 2 = 43 k +11k I 1 =76 . 8 µ A I 3 = I 1 = 300 µ A 2. For I = 250 µ A , R 1 = 100k , R 2 =68k R 3 =82k , use Ohm’s Law, voltage division, and current division to solve for I 1 , I 2 V 3 . I 1 = 250 µ A 68k +82k 100k +68k = 150 µ A I 2 = 250 µ A 100 k = 100 µ A V 3 = 100 µ A × 82k =8 . 2V 3. It is given that R 1 =1k , A v =10 4 , A i =50 R 2 =40k . (a) With i o =0 , use superposition to write the equations for i 1 and v o ( oc ) . Solve the equations for v o ( oc ) as a function of v s . i 1 = v s A v v o R 1 v o ( oc ) = A i i 1 R 2 1
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v o ( oc ) = A i R 2 R 1 1 A i A v R 2 R 1 v s = 2500 v s (b) With v o =0 , use superposition to write the equations for i 1 and i o ( sc ) . Solve the equations for i o ( sc ) as a function of v s . i o ( sc ) = A i v s R 1 = 0 . 05 v s (c) Use the solutions for v o ( oc ) and i o ( sc ) to show that r out =50k . (d) Show that the Thévenin equivalent circuit seen looking into the output is a voltage source v o ( oc ) = 2500 v s in series with a resistance r out . (e) Show that the Norton equivalent circuit seen looking into the output is a current source i o ( sc ) = 0 . 05 v s in parallel with a resistance r out . (f) If a load resistor R L =20k is connected from the output node to ground, use both the Thévenin and the Norton equivalent circuits to show that v o = 714 . 3 v s for both. 4. It is given that R 1 =10 , G m . 5S , R 2 =5 , R 3 =50 ,and A v =4 . (a) With i o , use superposition to solve for v o ( oc ) as a function of v s . v o ( oc ) = R 3 R 2 + R 3 v s + A v v s R 2 R 2 + R 3 = R 3 + A v R 2 R 2 + R 3 v s =1 . 273 v s (b) With v o , use superposition to solve for i o ( sc ) as a function of v s . i o ( sc ) = v s R 2 + A v v s R 3 = v s μ 1 R 2 + A v R 3 . 28 v s (c) Solve for r out . r out = v o ( oc ) i o ( sc ) . 545 (d) Show that the Thévenin equivalent circuit seen looking into the output is a voltage source v o ( oc ) . 273 v s in series with a resistance r out . 545 . (e) Show that the Norton equivalent circuit seen looking into the output is a current source i o ( sc ) . 28 v s in parallel with a resistance r out . 545 . (f) If a load resistor R L is connected from the output node to ground, show v o . 667 v s .
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set01new - ECE3050 Homework Set 1 1. For V = 18 V, R1 = 39...

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