SP 2005 CH 3 DT Systems 2

SP 2005 CH 3 DT Systems 2 - EE 3120 Chapter 3 Time Domain...

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EE 3120 Chapter 3 Time Domain Analysis of Discrete-Time Systems
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2 V 1 V 0 V n V 1 n V 1 m V 1 n V + Resistive Ladder Circuit, we can derive a difference to express voltage as a function of node position . 0 From the circuit: , 0 m VE V = = 12 3 11 KCL at node : 3 0, for 1,2,. .. 1 nn n n n n n n n ni i i VV V V V RR R V V V V n m −+ = + −− =+ −=+− = = 1 i 2 i 3 i For example: If m=4. find all node voltages:
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0 01 2 21 12 3 32 1 1 1 31 1: 3 0 3 2: 3 0 3 3(3 ) 8 3 E nV V V VV E V V V V E V VVE = =− + = + = = 2 V 1 V 0 V n V 1 n V 1 m V 1 n V + 1 i 2 i 3 i 23 4 43 2 1 1 41 3: 3 0 3 3(8 3 ) 3 8 V V V V EV E E + = = 8 0, E == 22 88 3 7 7 E VE E E E V  = −= =   33 8 83 E E V = −==
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Variation of the Bank Account Debt reduction or Loan Amortization: [ ] is the debt owed on a loan in month . yn n [0] is the initial loan amount y Loan must be reduced to 0 after years, y[N 12], for a total of N 12 EQUAL payments, [ ] N xn p × ×= Annual interest rate . Interest /12 applied to balance each month. rr [] [ 1 ] ] [] ] ( 1 ) ryn r p =− + + [1] [0](1 ) yy r p =+ 2 32 [2] [1](1 ) ) (1 ) [3] [2](1 ) ) [(1 ) ) 1] r p y r p r p r p y r p r r = + + + + + + 12 [ ] ) ) ) ... (1 ) 1] NN N yN y r p r r r −− + + + + + + + 1 2 : 1 1. . . 1 n n recall a aa a a + ++ + + = 1( [] [ 0 ] ( N N r y r p r −+ * * * * Solve for p.
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SP 2005 CH 3 DT Systems 2 - EE 3120 Chapter 3 Time Domain...

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