EE 616 COMPUTER AIDED ANALYSIS OF ELECTRONIC
NETWORKS
Dr. J.A. Starzyk
FINAL
Friday, November 19, 2004
THIS IS A CLOSED BOOK EXAM
Name:
Box #:
_________________
Note:
1) All scratch and problem papers must be turned in.
2) Estimated times required to complete problems are indicated.
Problem
1
2
3
4
5
TOTAL
Weight
(points)
Examiner' Use
10
10
10
10
40
GOOD LUCK!!!
Problem 1
Let us assume that in the circuit shown, the nominal solution vector is equal to
X0 = [VB VB' VE' VC’ VC] = [1 2 3 -1 -2],
and the inverse of the nodal admittance matrix for the nominal parameter values is as follows:
S  T01
6
2
1 
 0
10 
1
1
2 1 1 2 B
4 1 3 1 B '
0 5 2 1 E '

1 2 2 1 C '
2 1 1 3 C
and
det(T0)=599
Use the large change sensitivity approach to find the symbolic transfer function of the circuit
with respect to variation of parameter gm. For simplicity assume that the nominal value of gm
is gm0 =1[S] and that the complex frequency s = 1, so all the calculations can be limited to real
numbers.
Problem 2
An active network was analyzed with normalized nominal parameter values and the solution
vector as well as the adjoint vector was obtained as follows:
X= (1 2 –3 0 3 2 1 ) [V],
Xa= (3 -3 –2 -1 -2 2 2) [V].
1. The input current excitation (the right hand side of your system equation) is applied to
node one, and the output voltage is determined by the difference Vout=x4-x7. Use the
adjoint method to find the nominal value of the input current for which the given nominal
solution vector X was obtained.
2. Use the adjoint small change sensitivity based method to find semi-normalized sensitivity
of the output voltage to parasitic capacitance placed between nodes 2 and 3.
3. Use this semi-normalized sensitivity to predict the output voltage change if the parasitic
capacitance of 0.01 (F) is present.
Problem 3
Find symbolically (i.e. by direct derivative of the transfer function) the sensitivity of the voltage
transfer function in circuit from Fig. w.r.t. parameter G2, and evaluate it for given parameter
values (G1=1 S, G2=2 S, C1=1 F, C2=2 F, C3=1 F ,K1=1, K2=2, E= 1V, and s=1). What would
be your estimate of the change in the output voltage if G2 increases by 5%?
C3
G2
V2
C1 V1
E
G1
K1
C2
K2
Vout=K1 K2 V2
Problem 4
Find the minimum of
F ( x1 , x2 )  2 x1 x22  x12
subject to
1.
2.
3.
4.
5.
x1  x2  2  0
Use the Lagrange approach with the initial starting point x1  0, x2  0.
Use LU factorization to solve gradient minimization equations.
Check your results.
Compute function and error values at the beginning and at the end of the first iteration.
Do one iteration only.