eldo_user

Optimization
Designing a Low Noise Amplifier (LNA)
Table 13-6. Results of Optimization for MINIMIZE Objectives
Name Initial Value Current Value
NF_DB@2.4GHZ 3.03 1.41
NF_DB@2.5GHZ 3.06 1.41
NFMIN_DB@2.4GHZ 1.01 0.97
NFMIN_DB@2.5GHZ 1.06 1.03
Solving Problems with Pseudodiscrete Variables
As with many problems in circuit design, some of the variables are restricted to being members
of a finite set of values. These variables were LS, the NMOS source inductor, and N1, the
number of fingers in the NMOS. The LNA problem illustrates the distinction between the two
types of discrete variables that may be encountered in practical problems. Some of the
techniques in this topic are freely adapted from the book of Gill, Murray and Wright [4].
First consider the LNA problem with respect to the variable LS (assuming N1 is fixed at its
initial value of 30 for now). The problem is a mixed continuous-discrete problem since the LS
inductor comes from a design kit library which restricts the values to specific sizes. Such
variables are termed pseudodiscrete, since the solution to the continuous problem (in which the
variables are not subject to discrete restrictions) is well defined.
The other category of discrete variables is represented by the variable N1 where there is no
physical meaning of a non-integer value.
In our case, the definition of the NMOS model parameters used in the design kit library makes
the LNA problem a problem with continuous variables. For example, the parameter WR, which
represents the width offset for the channel resistance (RDS) calculation, is redefined as follows:
.PARAM WR=’(C1 + C2*Lm - C3*N1)’
The symbols C1, C2 and C3 refer to some constant factors which are not specified here. The
parameter Lm is simply the length of the transistor. This definition of the WR parameter does
not use the discrete nature of the N1 parameter. During the evaluation of this expression, the
value of N1 is considered to be a floating number. The problem is implicitly reformulated as
continuous.
The situation is more difficult to handle when the integer part of N1 is used explicitly in the
previous expression:
WR=’(C1 + C2*Lm - C3*TRUNC(N1))’
Such situations should be avoided wherever possible.
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Eldo® User's Manual, 15.3