An expression is an algebraic combination of already defined vectors, scalars (a scalar is a vector of length 1), constants, operators and functions. Some examples of expressions are:
cos(time) + db(v(3))
TIME*rnd(v(9)) - 15*cos(vin#branch)^7.9e5
not ((ac3.freq & tran1.time) gt 3)
One should note that there are two math subsystems in WRspice, the vector system described here, and a second system for processing equations found in device descriptions during simulation (see 2.15.1). Although the expressions are syntactically similar, there are important differences that must be taken into account, and one should refer to the appropriate documentation for the type of expression.
Vector expressions can also contain calls to the built-in ``tran'' functions ordinarily used in voltage/current source specifications in transient analysis. These are the pulse, pwl, etc. functions described in 2.15.3. If assigned to a vector, the vector will have a length equal to the current scale (e.g., the time values of the last transient analysis plot), and be filled in with values just as if the analysis was run with the given source specification. For example
(run transient analysis: tran .1n 10n)Vector a will have length 101 and contain the pulse values.
let a = pulse(0 1 1n 1n)
There are three such functions, sin, exp, and gauss, that have the same names as math functions. The math functions always return data of the same length as the argument(s), and take 1 argument for sin, exp and 2 for gauss. When one of these names is encountered in an expression, WRspice counts the arguments. If the number of arguments is 1 for sin/exp or 1 or 2 for gauss, the math function is called, otherwise the tran function is called. It may be necessary to give the gauss function a phony additional argument to force calling the tran function.
Vectors can be evaluated by the shell parser by adding the prefix $& to the vector's name. This is useful, for example, when the value of a vector needs to be passed to the shell's echo command, or in circuit description files where vectors are to be evaluated by the shell as the file is read. Similar to the shell constructs, $?&word expands to 1 if word is a defined vector, 0 otherwise. Also $#&word expands to the length of word if word is a defined vector, or 0 if not found. Additionally, the notation $&(vector expression) is replaced by the value of the vector expression. A range specification can be added, for example echo $&(a+1) prints the third entry in a+1, or 0 if out of range. If white space exists in the $&(...) construct, it probably should be quoted. Finally, the shell recognizes the construct $&v($something) as a reference to a SPICE node voltage, so that one can index node voltages as echo $&v($&i), for example. A range specification can be added, which can contain shell variables. This is true for both vectors ($& prefix) and variables.
There is a special case when $& is used with a special vector (see 3.16.5) that is referencing a string-type parameter. Since one can have
.param foo="hello there"$&@foo will expand to ``hello there'' in this case. Other references to @foo will return 0.0.