eldo_user

Optimization
Designing a Low Noise Amplifier (LNA)
Our problem with pseudodiscrete variables can be solved by utilizing the solution of the
continuous problem. The results of the optimization are summarized in the .otm file, and the
information shown in Table 13-7 can be extracted:
Table 13-7. Extracted Information from .otm File
Name Initial Value Final Value Discretized value Increment
LS 2.5x10 −10 1.5352x10 −9 3.0x10 −9 1.5x10 −9
CPIN1 1.0x10 −13 0.0 0.0 0.0
CPIN2 1.0x10 −13 8.7506x10 −14 2.234x10 −13 0.0
CSIN 1.0x10 −12 1.0x10 −12 1.0x10 −12 0.0
LSIN 1.0x10 −10 1.3651x10 −8 1.3651x10 −8 0.0
N1 30 18.453 20 5
The optimal N1 value when handled as a continuous variable is 18.453, and the optimal discrete
value is unlikely to be very different. This will be confirmed by the next two experiments. The
first experiment represents a general approach for handling optimization problems with
pseudodiscrete variables, while the second illustrates a “well-defined” problem.
N1 was defined as the variable that must assume one of the integer values {10, 15, 20, ..., 50}.
Let N1 C denote the value of N1 at the solution of the continuous problem, which is supposed to
be unique. Suppose that N1 C satisfies: ns < N1 C < ns+1
The value of the merit function Fmerit at the continuous solution is a lower bound on the value
of Fmerit at any solution to the discrete problem. If the variable N1 is a value other than N1 C ,
the merit function will be larger than Fmerit at the continuous solution, irrespective of the other
variables (LS, CPIN1, CPIN2, ...).
The next stage is to fix the pseudodiscrete variables at either n s or n s+1 by combining the values
in Table 13-8:
Table 13-8. Combinations of N1 and LS Values
Name s s+1
N1 15 20
LS 1.5x10 −9 1.75x10 −9
The problem is then solved again, minimizing with respect to the remaining continuous
variables, and using the old optimal values as the initial estimate of the new solution.
Eldo® User's Manual, 15.3 669