For every problem show all your work

For every problem show all your work. i.c. loops/ assumed loop currents or nodes/ node
Voltages, RVL/ KCL equations, element currents/ voltages (if appropriate), element equations,
choice of state variables, ete. and final results,
Problem 1 20) pts
Use the appropriate method to derive the governing equations for the shown below passive
circuit. Inputs into the circuit is the supplied voltage e;,(€) and current é, (0). and the outputs
[ | = Err 5
are the voltage drop eg on current source and the current ¢, through the inductor L.
Ky
R,
' )
;
@ "
Ca) ¥
- Y O
4
Problem 2 2() pts
For the circuit shown below do the following:
(ay Use Loop Method to derive the governing equauions for the circuit, shown below,
considering that system inputs are e,(¢) and e2(¢), und the output is the voltage drop
across the capacitor C LO pts
(b) Construct the modular block diagram of this circuit using the clement equations and AVE
cquations, derived in part (a); consider that system inputs are e@, (0) and es (0), and the !
output is the voltage drop across the capacitor 10 pts

Problem 3 30 pts
For the circuit shown below do the following:
(a) Derive the state-space model for the shown below passive circuit. Input into the circuit is
the supplied current i,(¢). and the output is the voltage drop egy, as Shown on the circuit
diagram. 20 pts
b) Deriv + 7} ae] Eoue(s) . .
(b) Derive the transfer function /1 (s) 10 pts
s
il
C
i (t)
. Court)
0 O-4)/
+ -
R>
Hint: consider shown nodes A, B, and D in your derivations
Problem 4 20) pts
Derive the governing equation expressing the relationship between the input voltage e,,, and the
Output voltage @,y, for the inverting op-amp circuit, shown below,
0 Cut
O
R,
O + C
Cin KR,
Lp honed ~ Ls Lo