# muParser Functions

muParser is a wonderful program. It is what allows Mason to process text equations. More information can be found on sourceforge. Also see the muParser license.## Run-time variables

Name |
Explanation |

frequency |
Changes as the simulation runs, this is the simulation frequency |

## Built-in variables

For convenience, some constants are built into the library. Please note that the underscore must be used as shown in the table.Name |
Explanation |

_e |
e (2.71828...) |

_pi |
pi (3.1415...) |

_j |
sqrt(-1) |

_c |
speed of light in a vacuum |

_eps0 |
permittivity of a vacuum |

_mu0 |
permeability of a vacuum |

## Built-in constants (v 4.4.9)

For convenience, some unit constants are built into the library. Please note that the underscore must be used as shown in the table. These are used for making conversions in calculations: "width = 10 * _mil * length"Name |
Explanation |

_mil, _mils |
2.54e-5 |

_in |
0.0254 |

_ft |
0.3028 |

_mi |
1609.34 |

_m |
1 |

_cm |
1e-2 |

_mm, _mH, _mF |
1e-3 |

_um, _uF, _uH |
1e-6 |

_nm, _nF, _nH |
1e-9 |

_pm, _pF, _pH |
1e-12 |

_deg |
_pi / 180 |

_rad |
180 / _pi |

## Built-in functions

The following table gives an overview of the functions supported by the default implementation. It lists the function names, the number of arguments and a brief description.Name |
Argument Count |
Explanation |
Uses the... |

sin |
1 |
sine function (radians) |
complex argument |

cos |
1 |
cosine function (radians) | complex argument |

tan |
1 |
tangent function (radians) | complex argument |

asin |
1 |
arc sine function (radians) | real part |

acos |
1 |
arc cosine function (radians) | real part |

atan |
1 |
arc tangent function (radians) | real part |

sinh |
1 |
hyperbolic sine function | complex argument |

cosh |
1 |
hyperbolic cosine function | complex argument |

tanh |
1 |
hyperbolic tangent function |
complex argument |

asinh |
1 |
hyperbolic arc sine function |
complex argument |

acosh |
1 |
hyperbolic arc cosine function |
complex argument |

atanh |
1 |
hyperbolic arc tangent function |
complex argument |

Ci | 1 | Cosine integral function |
complex argument |

Si |
1 | Sine Integral function |
complex argument |

K |
1 | First order elliptic integral |
complex argument |

Ji(x,i) | 2 | First order Bessel function of order i | complex argument |

Y0(x) | 1 | Second order Bessel function of order 0 | real part |

Y1(x) | 1 | Second order Bessel function of order 1 | real part |

log2 |
1 |
logarithm to the base 2 |
complex argument |

log10 |
1 |
logarithm to the base 10 |
complex argument |

log |
1 |
natural log (base e) |
complex argument |

ln |
1 |
logarithm to the base e (2.71828...) |
complex argument |

exp |
1 |
e raised to the power of x |
complex argument |

sqrt |
1 |
square root of a value |
complex argument |

sign |
1 |
sign function: -1 if x<0; 1 if x> 0 |
real part |

rint |
1 |
round to the nearest integer |
real part |

abs |
1 |
absolute value |
complex argument |

arg |
1 |
argument- angle in degrees |
complex argument |

real |
1 |
returns the real part |
complex argument |

imag |
1 |
returns the imaginary part |
complex argument |

if |
3 |
if(condition,then,else) example if statement: Y1 = if(B>0, m*X+B, m*X-B) [same as: Y1 = m*X+abs(B)] |
complex argument |

pow |
2 |
power: pow(x,y) == x^y |
complex argument |

min |
variable |
minimum of all arguments |
real part |

max |
variable |
maximum of all arguments |
real part |

sum |
variable |
sum of all arguments |
complex argument |

avg |
variable |
mean value of all arguments |
complex argument |

lor |
variable |
logical or of all arguments |
list of arguments, e.g. lor(A==B,C==D,E>F) |

land |
variable |
logical and of all arguments |
list of arguments, e.g. land(A==B,C==D,E>F) |

## Built-in binary operators

The following table lists the default binary operators supported by the parser.Operator |
Meaning |
Priority |

= |
assignment* |
-1 |

<= |
less or equal |
2 |

>= |
greater or equal |
2 |

!= |
not equal |
2 |

== |
equality |
2 |

> |
greater than |
2 |

< |
less than |
2 |

+ |
addition |
3 |

- |
subtraction |
3 |

* |
multiplication |
4 |

/ |
division |
4 |

^ |
raise x to the power of y |
5 |

*The assignment operator is special since it changes one of its arguments and can only be applied to variables.

MOR Code (Method of Relaxation- 2D Finite Difference)

The MOR code is accessed through muParser calls. Several "dummy" functions are called to set up the problem- dummy in the sense that they do not return any useful value, the only set up the geometry.

MORSetStrip(X, Y, Width, Thickness, Value):

Set up the a line of voltage "Value" whose left most point is at coordinates (X, Y), goes Width to the right, and is Thickness tall. The impedance and the permittivity will be calculated for the line associated with the first call to MORSetStrip.

A value of 1 is consistent with a "positive" side of a coupled line.

A value of -1 is consistent with a "negative' side of a coupled line.

A value of 0 is consistent with a ground line. Balanced structures like CPS should use +/-1; unbalanced structures like CPW should use 0/1.

Use Thickness = 0 for infinitely thin PEC.

The current loop is 2 cells from the first strip... try to keep gaps between lines at least four cells.

The current loop is 2 cells from the first strip... try to keep gaps between lines at least four cells.

MORSetStrip1(X, Y, Width, Thickness): [deprecated for MORSetStrip]

MORSetStrip2(X, Y, Width, Thickness): [deprecated for MORSetStrip]

MORSetStrip3(X, Y, Width, Thickness): [deprecated for MORSetStrip]

MORSetDielectric(EpsR, DYmin, DYMax):

MORSetBounds(XMax, YMax)

MORImpedance(dummy_variable)

MORPermittivity(dummy_variable)

Set up the "positive" line whose left most point is at coordinates (X, Y), goes Width to the right, and is Thickness tall.

Use Thickness = 0 for infinitely thin PEC. The impedance and the permittivity will be calculated for the line associated with this call.

MORSetStrip2(X, Y, Width, Thickness): [deprecated for MORSetStrip]

Set up the "negative" (-1) line whose left most point is at coordinates (X, Y), goes Width to the right, and is Thickness tall.

Use Thickness = 0 for infinitely thin PEC.

MORSetStrip3(X, Y, Width, Thickness): [deprecated for MORSetStrip]

Optional "negative" (-1) line whose left most point is at coordinates (X, Y), goes Width to the right, and is Thickness tall.

Use Thickness = 0 for infinitely thin PEC.

MORSetStrip2 MUST be called before MORSetStrip3

MORSetDielectric(EpsR, DYmin, DYMax):

Set up a dielectric slab of EpsR relative permittivity, from DYmin to DYMax.

MORSetBounds(XMax, YMax)

Set the boundary conditions, bottom left of grid is (0,0), upper right of grid is (XMax, YMax).

MORImpedance(dummy_variable)

Run the MOR code, returns a complex number whose real part is the even impedance, the imaginary is the odd.

MORPermittivity(dummy_variable)

Run the MOR code, returns a complex number whose real part is the even mode EpsR, the imaginary is the odd.