# ec¶

## engineering calculator¶

- Author
Ken Kundert <ec@nurdletech.com>

- Date
2020-08-14

- Version
1.6.1

- Manual section
1

### SYNOPSIS¶

**ec** [*options*] [*scripts* …]

### OPTIONS¶

`-i, --interactive`Open an interactive session.

`-s``<file>`, --startup`<file>`Run commands from file to initialize calculator before any script or interactive session is run, stack is cleared after it is run.

`-c, --nocolor`Do not use colors in the output.

`-v, --verbose`Narrate the execution of any scripts.

`-V, --version`Print the ec version information.

`-h, --help`Print the usage and exit.

### DESCRIPTION¶

**ec** is a stack-based (RPN) engineering calculator with a text-based user
interface that is intended to be used interactively.

If run with no arguments, an interactive session is started. If arguments are present, they are tested to see if they are filenames, and if so, the files are opened and the contents are executed as a script. If they are not file names, then the arguments themselves are treated as scripts and executed directly. The scripts are run in the order they are specified. In this case an interactive session would not normally be started, but if the interactive option is specified, it would be started after all scripts have been run.

The contents of *~/.ecrc*, *./.ecrc*, and the start up file will be run upon
start up if they exist, and then the stack is cleared.

### STACK¶

As you enter numbers they are pushed onto a stack. The most recent member
of the stack is referred to as the *x* register and the second most recent
is the *y* register. All other members of the stack are unnamed. Operators
consume numbers off the stack to use as operands and then they push the
results back on the stack. The operations are performed immediately and
there is no use of parentheses to group calculations. Any intermediate
results are stored on the stack until needed. For example,

46+

In this case 4 gets pushed on to the stack first to become *x*. Then 6 gets
pushed on to the stack to become *x*, which makes 4 *y*. Finally, + pulls
both off the stack, sums them, and then pushes the result of 10 back onto
the stack. The stack is left with only one number on it, 10.

After each line **ec** responds by printing the value of the *x* register.
Thus the above example would actually look like this:

0: 44: 66: +10:

The benefit of the stack is that it allows you to easily store temporary results while you perform your calculation. For example, to evaluate (34 - 61)*(23 - 56) you would use:

0: 3434: 6161: --27: 2323: 5656: --33: *891:

Notice that you entered the numbers as you saw them in the formula you were evaluating, and there was no need to enter parentheses, however the operators were rearranged in order to express the precedence of the operations.

It is not necessary to type enter after each number or operator. You can combine them onto one line and just type enter when you would like to see the result:

0: 34 61 - 23 56 - *891:

Furthermore, it is not necessary to type a space between a number and most operators. For example, the above could be entered as:

0: 34 61- 23 56- *891:

You can print the entire stack using *stack*, and clear it using *clstack*.
For example,

0: 1 2 3 stack3y: 2x: 13: clstack0: stack0:

### REAL NUMBERS¶

Numbers can be entered using normal integer, floating point, and scientific notations. For example,

423.1415925,439,749.972.998e813.80651e-24

In addition, you can also use the normal SI scale factors to represent either large or small numbers without using scientific notation.

- Y
1e24 (yotta)

- Z
1e21 (zetta)

- E
1e18 (exa)

- P
1e15 (peta)

- T
1e12 (terra)

- G
1e9 (giga)

- M
1e6 (mega)

- k, K
1e3 (kilo)

- _
unity (1)

- m
1e-3 (milli)

- u
1e-6 (micro)

- n
1e-9 (nano)

- p
1e-12 (pico)

- f
1e-15 (fempto)

- a
1e-18 (atto)

- z
1e-21 (zepto)

- y
1e-24 (yocto)

For example, 10M represents 1e7 and 8.8p represents 8.8e-12.

Optionally, numbers can be combined with simple units. For example,

10KHz3.16pF2.5_V4.7e-10F

Both units and scale factors are optional, which causes a natural ambiguity as to whether the first letter of a suffix is a scale factor or not. If the first letter is a valid scale factor, then it is assume to be a scale factor. In this way, ‘300K is treated as 300e3 rather than 300 Kelvin. If you intend the units without a scale factor, add the unit scale factor: ‘_’. Thus, use 300_K to enter 300 Kelvin.

In this case the units must be simple identifiers (must not contain special
characters, though use of particular units symbols, °ÅΩƱ. are allowed). For
complex units, such as “rads/s”, or for numbers that do not have scale
factors, it is possible to attach units to a number in the *x* register by
entering a quoted string.

0: 6.626e-34662.6e-36: “J-s”662.6e-36 J-s: 50k “V/V”50 KV/V:

The dollar sign ($) is a special unit that is given before the number.

$100K

Numbers my also contain commas as digit separators, which are ignored.

$200,000.00

The dollar sign ($) is a special unit that is given before the number.
**ec** takes a conservative approach to units. You can enter them and it
remembers them, but they do not survive any operation where the resulting
units would be in doubt. In this way it displays units when it can, but
should never display incorrect or misleading units. For example:

0: 100MHz100 MHz: 2pi*628.32M:

You can display real numbers using one of three available formats, *fix*,
*sci*, or *eng*. These display numbers using fixed point notation (a fixed
number of digits to the right of the decimal point), scientific notation (a
mantissa and an exponent), and engineering notation (a mantissa and an SI
scale factor). You can optionally give an integer immediately after the
display mode to indicate the desired precision. For example,

0: 10001K: fix21000.00: sci31.000e+03: eng41K: 2pi*6.2832K:

Notice that scientific notation always displays the specified number of digits whereas engineering notation suppresses zeros at the end of the number.

When displaying numbers using engineering notation, **ec** does not use the
full range of available scale factors under the assumption that the largest
and smallest would be unfamiliar to most people. For this reason, **ec**
only uses the most common scale factors when outputting numbers (T, G, M, K,
m, u, n, p, f, a).

### INTEGERS¶

You can enter integers in either hexadecimal (base 16), decimal (base 10), octal (base 8), or binary (base 2). You can use either programmers notation (leading 0) or Verilog notation (leading ‘) as shown in the examples below:

- 0xFF
hexadecimal

- 99
decimal

- 0o77
octal

- 0b1101
binary

- ‘hFF
Verilog hexadecimal

- ‘d99
Verilog decimal

- ‘o77
Verilog octal

- ‘b1101
Verilog binary

Internally, **ec** represents all numbers as double-precision real numbers.
To display them as decimal integers, use *fix0*. However, you can display
the numbers in either base 16 (hexadecimal), base 10 (decimal), base 8
(octal) or base 2 (binary) by setting the display mode. Use either *hex*,
*fix0*, *oct*, *bin*, *vhex*, *vdec*, *voct*, or *vbin*. In each of
these cases the number is rounded to the closest integer before it is
displayed. Add an integer after the display mode to control the number of
digits. For example:

0: 10001K: hex0x3b8: hex80x000003b8: hex00x3b8: voct‘o1750:

### COMPLEX NUMBERS¶

**ec** provides limited support for complex numbers. Two imaginary constants
are available that can be used to construct complex numbers, *j* and
*j2pi*. In addition, two functions are available for converting complex
numbers to real, *mag* returns the magnitude and *ph* returns the phase.
They are unusual in that they do not replace the value in the *x* register
with the result, instead they simply push either the magnitude of phase into
the *x* register, which pushes the original complex number into the *y*
register. For example,

0: 1 j +1 + j: mag1.4142: pop1 + j: ph45 degs: stacky: 1 + jx: 45 degs45 degs:

You can also add the imaginary unit to real number constants. For example,

0: j10Mj10M: -j1u *10:

Only a small number of functions actually support complex numbers; currently
only *exp* and *sqrt*. However, most of the basic arithmetic operators
support complex numbers.

### CONSTANTS¶

**ec** provides several useful mathematical and physical constants that are
accessed by specifying them by name. Several of the constants have both MKS
and CGS forms (ec uses ESU-CGS). You can set which version you want by
setting the desired unit system as follows:

0: mks0: h662.61e-36 J-s: k13.806e-24 J/K: cgs13.806e-24 J/K: h6.6261e-27 erg-s: k138.06 aerg/K:

Notice that the unit-system is sticky, meaning that it remains in force until explicitly changed. ‘mks’ is the default unit system.

The physical constants are given in base units (meters, grams, seconds). For example, the mass of an electron is given in grams rather than kilograms as would be expected for MKS units. Similarly, the speed of light is given in meters per second rather than centimeters per second as would be expected of CGS units. This is necessary so that numbers are not displayed with two scale factors (ex. 1 mkg). Thus, it may be necessary for you to explicitly convert to kg (MKS) or cm (CGS) before using values in formulas that are tailored for one specific unit system.

The 2014 NIST values are used. The available constants include:

- pi
the ratio of a circle’s circumference to its diameter

- 2pi
the ratio of a circle’s circumference to its radius

- rt2
square root of two

- 0C
0 Celsius in Kelvin

- j
imaginary unit (square root of -1)

- j2pi
j*2*pi

- k
Boltzmann constant

- h
Planck constant

- q
elementary charge (the charge of an electron)

- c
speed of light in a vacuum

- eps0
permittivity of free space

- mu0
permeability of free space

- Z0
Characteristic impedance of free space

- hbar
Reduced Planck constant

- me
rest mass of an electron

- mp
mass of a proton

- mn
mass of a neutron

- mh
mass of a hydrogen atom

- amu
unified atomic mass unit

- G
universal gravitational constant

- g
earth gravity

- Rinf
Rydberg constant

- sigma
Stefan-Boltzmann constant

- alpha
Fine structure constant

- R
molar gas constant

- NA
Avogadro Number

- rand
random number between 0 and 1

As an example of using the predefined constants, consider computing the thermal voltage, kT/q.

0: k 27 0C + * q/ “V”25.865 mV:

### VARIABLES¶

You can store the contents of the *x* register to a variable by using an
equal sign followed immediately by the name of the variable. To recall it,
simply use the name. For example,

0: 100MHz =freq100 MHz: 2pi* “rads/s” =omega628.32 Mrads/s: 1pF =cin1 pF: 1 omega cin* /1.5915K:

You can display all known variables using *vars*. If you did so immediately
after entering the lines above, you would see:

1.5915K: varsRref: 50 Ohmscin: 1 pFfreq: 100 MHzomega: 628.32 Mrads/s

Choosing a variable name that is the same as a one of a built-in command or constant causes the built-in name to be overridden. Be careful when doing this as once a built-in name is overridden it can no longer be accessed.

Notice that a variable *Rref* exists that you did not create. This is a
predefined variable that is used in dBm calculations. You are free to change
its value if you like.

### USER-DEFINED FUNCTIONS¶

You can define functions in the following way:

```
( ... )name
```

Here ‘(‘ starts the function definition and ‘)name’ ends it. The name must be immediately adjacent to the name. The ‘…’ represents a sequence of calculator actions. For example:

0: (2pi * “rads/s”)to_omega0: (2pi / “Hz”)to_freq0: 100MHz100 MHz: to_omega628.32 Mrads/s: to_freq100 MHz:

The actions entered while defining the function are not evaluated until the function itself is evaluated.

Once defined, you can review your function with the *vars* command. It shows
both the variable and the function definitions:

Rref: 50 Ohmsto_freq: (2pi / “Hz”)to_omega: (2pi * “rads/s”)

The value of the functions are delimited with parentheses.

### OPERATORS, FUNCTIONS, NUMBERS and COMMANDS¶

In the following descriptions, optional values are given in brackets ([])
and values given in angle brackets (<>) are not to be taken literally (you
are expected to choose a suitable value). For example “fix[<*N*>]” can
represent “fix” or “fix4”, but not “fixN”.

For each action that changes the stack a synopsis of those changes is given
in the form of two lists separated by `=>`

. The list on the left
represents the stack before the action is applied, and the list on the right
represents the stack after the action was applied. In both of these lists,
the *x* register is given first (on the left). Those registers that are
involved in the action are listed explicitly, and the rest are represented
by `...`

. In the before picture, the names of the registers involved in
the action are simply named. In the after picture, the new values of the
registers are described. Those values represented by `...`

on the right
side of `=>`

are the same as represented by `...`

on the left, though
they may have moved. For example:

```
x, y, ... => x+y, ...
```

This represents addition. In this case the values in the *x* and *y*
registers are summed and placed into the *x* register. All other values move
to the left one place.

#### Arithmetic Operators¶

`+`

: addition

The values in the

xandyregisters are popped from the stack and the sum is placed back on the stack into thexregister.x, y, ... => x+y, ...

`-`

: subtraction

The values in the

xandyregisters are popped from the stack and the difference is placed back on the stack into thexregister.x, y, ... => x-y, ...

`*`

: multiplication

The values in the

xandyregisters are popped from the stack and the product is placed back on the stack into thexregister.x, y, ... => x*y, ...

`/`

: true division

The values in the

xandyregisters are popped from the stack and the quotient is placed back on the stack into thexregister. Both values are treated as real numbers and the result is a real number. So0: 1 2/500m:x, y, ... => y/x, ...

`//`

: floor division

The values in the

xandyregisters are popped from the stack, the quotient is computed and then converted to an integer using the floor operation (it is replaced by the largest integer that is smaller than the quotient), and that is placed back on the stack into thexregister. So0: 1 2//0:x, y, ... => y//x, ...

`%`

: modulus

The values in the

xandyregisters are popped from the stack, the quotient is computed and the remainder is placed back on the stack into thexregister. So0: 14 3%2:In this case 2 is the remainder because 3 goes evenly into 14 three times, which leaves a remainder of 2.

x, y, ... => y%x, ...

`chs`

: change sign

The value in the

xregister is replaced with its negative.x, ... => -x, ...

`recip`

: reciprocal

The value in the

xregister is replaced with its reciprocal.x, ... => 1/x, ...

`ceil`

: round towards positive infinity

The value in the

xregister is replaced with its value rounded towards infinity (replaced with the smallest integer greater than its value).x, ... => ceil(x), ...

`floor`

: round towards negative infinity

The value in the

xregister is replaced with its value rounded towards negative infinity (replaced with the largest integer smaller than its value).x, ... => floor(x), ...

`!`

: factorial

The value in the

xregister is replaced with its factorial.x, ... => x!, ...

`%chg`

: percent change

The values in the

xandyregisters are popped from the stack and the percent difference betweenxandyrelative toyis pushed back into thexregister.x, y, ... => 100*(x-y)/y, ...

`||`

: parallel combination

The values in the

xandyregisters are popped from the stack and replaced with the reciprocal of the sum of their reciprocals. If the values in thexandyregisters are both resistances, both elastances, or both inductances, then the result is the resistance, elastance or inductance of the two in parallel. If the values are conductances, capacitances or susceptances, then the result is the conductance, capacitance or susceptance of the two in series.x, y, ... => 1/(1/x+1/y), ...

#### Powers, Roots, Exponentials and Logarithms¶

`**`

: raise y to the power of x

The values in the

xandyregisters are popped from the stack and replaced with the value ofyraised to the power ofx.x, y, ... => y**x, ...aliases: pow, ytox

`exp`

: natural exponential

The value in the

xregister is replaced with its exponential. Supports a complex argument.x, ... => exp(x), ...alias: powe

`ln`

: natural logarithm

The value in the

xregister is replaced with its natural logarithm. Supports a complex argument.x, ... => ln(x), ...alias: loge

`pow10`

: raise 10 to the power of x

The value in the

xregister is replaced with 10 raised tox.x, ... => 10**x, ...alias: 10tox

`log`

: base 10 logarithm

The value in the

xregister is replaced with its common logarithm.x, ... => log(x), ...aliases: log10, lg

`pow2`

: raise 2 to the power of x

The value in the

xregister is replaced with 2 raised tox.x, ... => 2**x, ...alias: 2tox

`log2`

: base 2 logarithm

The value in the

xregister is replaced with its base 2 logarithm.x, ... => log2(x), ...alias: lb

`sqr`

: square

The value in the

xregister is replaced with its square.x, ... => x**2, ...

`sqrt`

: square root

The value in the

xregister is replaced with its square root.x, ... => sqrt(x), ...alias: rt

`cbrt`

: cube root

The value in the

xregister is replaced with its cube root.x, ... => cbrt(x), ...

#### Trigonometric Functions¶

`sin`

: trigonometric sine

The value in the

xregister is replaced with its sine.x, ... => sin(x), ...

`cos`

: trigonometric cosine

The value in the

xregister is replaced with its cosine.x, ... => cos(x), ...

`tan`

: trigonometric tangent

The value in the

xregister is replaced with its tangent.x, ... => tan(x), ...

`asin`

: trigonometric arc sine

The value in the

xregister is replaced with its arc sine.x, ... => asin(x), ...

`acos`

: trigonometric arc cosine

The value in the

xregister is replaced with its arc cosine.x, ... => acos(x), ...

`atan`

: trigonometric arc tangent

The value in the

xregister is replaced with its arc tangent.x, ... => atan(x), ...

`rads`

: use radians

Switch the trigonometric mode to radians (functions such as

sin,cos,tan, andptorexpect angles to be given in radians; functions such asarg,asin,acos,atan,atan2, andrtopshould produce angles in radians).

`degs`

: use degrees

Switch the trigonometric mode to degrees (functions such as

sin,cos,tan, andptorexpect angles to be given in degrees; functions such asarg,asin,acos,atan,atan2, andrtopshould produce angles in degrees).

#### Complex and Vector Functions¶

`abs`

: magnitude of complex number

The absolute value of the number in the

xregister is pushed onto the stack if it is real. If the value is complex, the magnitude is pushed onto the stack.x, ... => abs(x), x, ...alias: mag

`arg`

: phase of complex number

The argument of the number in the

xregister is pushed onto the stack if it is complex. If the value is real, zero is pushed onto the stack.x, ... => arg(x), x, ...alias: ph

`hypot`

: hypotenuse

The values in the

xandyregisters are popped from the stack and replaced with the length of the vector from the origin to the point (x,y).x, y, ... => sqrt(x**2+y**2), ...alias: len

`atan2`

: two-argument arc tangent

The values in the

xandyregisters are popped from the stack and replaced with the angle of the vector from the origin to the point.x, y, ... => atan2(y,x), ...alias: angle

`rtop`

: convert rectangular to polar coordinates

The values in the

xandyregisters are popped from the stack and replaced with the length of the vector from the origin to the point (x,y) and with the angle of the vector from the origin to the point (x,y).x, y, ... => sqrt(x**2+y**2), atan2(y,x), ...

`ptor`

: convert polar to rectangular coordinates

The values in the

xandyregisters are popped from the stack and interpreted as the length and angle of a vector and are replaced with the coordinates of the end-point of that vector.x, y, ... => x*cos(y), x*sin(y), ...

#### Hyperbolic Functions¶

`sinh`

: hyperbolic sine

The value in the

xregister is replaced with its hyperbolic sine.x, ... => sinh(x), ...

`cosh`

: hyperbolic cosine

The value in the

xregister is replaced with its hyperbolic cosine.x, ... => cosh(x), ...

`tanh`

: hyperbolic tangent

The value in the

xregister is replaced with its hyperbolic tangent.x, ... => tanh(x), ...

`asinh`

: hyperbolic arc sine

The value in the

xregister is replaced with its hyperbolic arc sine.x, ... => asinh(x), ...

`acosh`

: hyperbolic arc cosine

The value in the

xregister is replaced with its hyperbolic arc cosine.x, ... => acosh(x), ...

`atanh`

: hyperbolic arc tangent

The value in the

xregister is replaced with its hyperbolic arc tangent.x, ... => atanh(x), ...

#### Decibel Functions¶

`db`

: convert voltage or current to dB

The value in the

xregister is replaced with its value in decibels. It is appropriate to apply this form when converting voltage or current to decibels.x, ... => 20*log(x), ...aliases: db20, v2db, i2db

`adb`

: convert dB to voltage or current

The value in the

xregister is converted from decibels and that value is placed back into thexregister. It is appropriate to apply this form when converting decibels to voltage or current.x, ... => 10**(x/20), ...aliases: db2v, db2i

`db10`

: convert power to dB

The value in the

xregister is converted from decibels and that value is placed back into thexregister. It is appropriate to apply this form when converting power to decibels.x, ... => 10*log(x), ...alias: p2db

`adb10`

: convert dB to power

The value in the

xregister is converted from decibels and that value is placed back into thexregister. It is appropriate to apply this form when converting decibels to voltage or current.x, ... => 10**(x/10), ...alias: db2p

`vdbm`

: convert peak voltage to dBm

The value in the

xregister is expected to be the peak voltage of a sinusoid that is driving a load resistor equal toRref(a predefined variable). It is replaced with the power delivered to the resistor in decibels relative to 1 milliwatt.x, ... => 30+10*log10((x**2)/(2*Rref)), ...alias: v2dbm

`dbmv`

: dBm to peak voltage

The value in the

xregister is expected to be a power in decibels relative to one milliwatt. It is replaced with the peak voltage of a sinusoid that would be needed to deliver the same power to a load resistor equal toRref(a predefined variable).x, ... => sqrt(2*10**(x - 30)/10)*Rref), ...alias: dbm2v

`idbm`

: peak current to dBm

The value in the

xregister is expected to be the peak current of a sinusoid that is driving a load resistor equal toRref(a predefined variable). It is replaced with the power delivered to the resistor in decibels relative to 1 milliwatt.x, ... => 30+10*log10(((x**2)*Rref/2), ...alias: i2dbm

`dbmi`

: dBm to peak current

The value in the

xregister is expected to be a power in decibels relative to one milliwatt. It is replaced with the peak current of a sinusoid that would be needed to deliver the same power to a load resistor equal toRref(a predefined variable).x, ... => sqrt(2*10**(x - 30)/10)/Rref), ...alias: dbm2i

#### Constants¶

`pi`

: the ratio of a circle’s circumference to its diameter

The value of pi (3.141592…) is pushed on the stack into the

xregister.... => pi, ...

`2pi`

: the ratio of a circle’s circumference to its radius

Two times the value of pi (6.283185…) is pushed on the stack into the

xregister.... => 2*pi, ...

`rt2`

: square root of two

The square root of two (1.4142…) is pushed on the stack into the

xregister.... => sqrt(2), ...

`0C`

: 0 Celsius in Kelvin

Zero celsius in kelvin (273.15 K) is pushed on the stack into the

xregister.... => 0C, ...

`j`

: imaginary unit (square root of -1)

The imaginary unit (square root of -1) is pushed on the stack into the

xregister.... => j, ...

`j2pi`

: j*2*pi

2 pi times the imaginary unit (j6.283185…) is pushed on the stack into the

xregister.... => j*2*pi, ...

`k`

: Boltzmann constant

The Boltzmann constant (R/NA or 1.38064852e-23 J/K [mks] or 1.38064852e-16 erg/K [cgs]) is pushed on the stack into the

xregister.... => k, ...

`h`

: Planck constant

The Planck constant (6.626070e-34 J-s [mks] or 6.626070e-27 erg-s [cgs]) is pushed on the stack into the

xregister.... => h, ...

`q`

: elementary charge (the charge of an electron)

The elementary charge (the charge of an electron or 1.6021766208e-19 C [mks] or 4.80320425e-10 statC [cgs]) is pushed on the stack into the

xregister.... => q, ...

`c`

: speed of light in a vacuum

The speed of light in a vacuum (2.99792458e8 m/s) is pushed on the stack into the

xregister.... => c, ...

`eps0`

: permittivity of free space

The permittivity of free space (8.854187817e-12 F/m [mks] or 1/4π [cgs]) is pushed on the stack into the

xregister.... => eps0, ...

`mu0`

: permeability of free space

The permeability of free space (4e-7*pi H/m [mks] or 4π/c² s^2/m^2 [cgs]) is pushed on the stack into the

xregister.... => mu0, ...

`Z0`

: Characteristic impedance of free space

The characteristic impedance of free space (376.730313461 Ω) is pushed on the stack into the

xregister.... => Z0, ...

`hbar`

: Reduced Planck constant

The reduced Planck constant (1.054571800e-34 J-s) is pushed on the stack into the

xregister.... => h/(2*pi), ...

`me`

: rest mass of an electron

The rest mass of an electron (9.10938356e-28 g) is pushed on the stack into the

xregister.... => me, ...

`mp`

: mass of a proton

The mass of a proton (1.672621898e-24 g) is pushed on the stack into the

xregister.... => mp, ...

`mn`

: mass of a neutron

The mass of a neutron (1.674927471e-24 g) is pushed on the stack into the

xregister.... => mn, ...

`mh`

: mass of a hydrogen atom

The mass of a hydrogen atom (1.6735328115e-24 g) is pushed on the stack into the

xregister.... => mh, ...

`amu`

: unified atomic mass unit

The unified atomic mass unit (1.660539040e-24 g) is pushed on the stack into the

xregister.... => amu, ...

`G`

: universal gravitational constant

The universal gravitational constant (6.6746e-14 m^3/(g-s^2)) is pushed on the stack into the

xregister.... => G, ...

`g`

: earth gravity

The standard acceleration at sea level due to gravity on earth (9.80665 m/s^2)) is pushed on the stack into the

xregister.... => g, ...

`Rinf`

: Rydberg constant

The Rydberg constant (10973731 m^-1) is pushed on the stack into the

xregister.... => Ry, ...

`sigma`

: Stefan-Boltzmann constant

The Stefan-Boltzmann constant (5.670367e-8 W m^-2 K^-4) is pushed on the stack into the

xregister.... => sigma, ...

`alpha`

: Fine structure constant

The fine structure constant (7.2973525664e-3) is pushed on the stack into the

xregister.... => alpha, ...

`R`

: molar gas constant

The molar gas constant (8.3144598 J/(mol-K) [mks] or 83.145 Merg/deg-mol [cgs]) is pushed on the stack into the

xregister.... => R, ...

`NA`

: Avogadro Number

Avogadro constant (6.022140857e23 mol^-1) is pushed on the stack into the

xregister.... => NA, ...

`mks`

: use MKS units for constants

Switch the unit system for constants to MKS or SI.

`cgs`

: use ESU CGS units for constants

Switch the unit system for constants to ESU CGS.

#### Numbers¶

`<N[.M][S[U]]>`

: a real number

The number is pushed on the stack into the

xregister.Nis the integer portion of the mantissa andMis an optional fractional part.Sis a letter that represents an SI scale factor.Uthe optional units (must not contain special characters). For example, 10MHz represents 1e7 Hz.... => num, ...

`<N[.M]>e<E[U]>`

: a real number in scientific notation

The number is pushed on the stack into the

xregister.Nis the integer portion of the mantissa andMis an optional fractional part.Eis an integer exponent.Uthe optional units (must not contain special characters). For example, 2.2e-8F represents 22nF.... => num, ...

`0x<N>`

: a hexadecimal number

The number is pushed on the stack into the

xregister.Nis an integer in base 16 (use a-f to represent digits greater than 9). For example, 0xFF represents the hexadecimal number FF or the decimal number 255.... => num, ...

`0o<N>`

: a number in octal

The number is pushed on the stack into the

xregister.Nis an integer in base 8 (it must not contain the digits 8 or 9). For example, 0o77 represents the octal number 77 or the decimal number 63.... => num, ...

`0b<N>`

: a number in binary

The number is pushed on the stack into the

xregister.Nis an integer in base 2 (it may contain only the digits 0 or 1). For example, 0b1111 represents the octal number 1111 or the decimal number 15.... => num, ...

`'h<N>`

: a number in Verilog hexadecimal notation

The number is pushed on the stack into the

xregister.Nis an integer in base 16 (use a-f to represent digits greater than 9). For example, ‘hFF represents the hexadecimal number FF or the decimal number 255.... => num, ...

`'d<N>`

: a number in Verilog decimal

The number is pushed on the stack into the

xregister.Nis an integer in base 10. For example, ‘d99 represents the decimal number 99.... => num, ...

`'o<N>`

: a number in Verilog octal

The number is pushed on the stack into the

xregister.Nis an integer in base 8 (it must not contain the digits 8 or 9). For example, ‘o77 represents the octal number 77 or the decimal number 63.... => num, ...

`'b<N>`

: a number in Verilog binary

The number is pushed on the stack into the

xregister.Nis an integer in base 2 (it may contain only the digits 0 or 1). For example, ‘b1111 represents the binary number 1111 or the decimal number 15.... => num, ...

#### Number Formats¶

`eng[<N>]`

: use engineering notation

Numbers are displayed with a fixed number of digits of precision and the SI scale factors are used to convey the exponent when possible. If an optional whole number

Nimmediately followseng, the precision is set toNdigits.

`sci[<N>]`

: use scientific notation

Numbers are displayed with a fixed number of digits of precision and the exponent is given explicitly as an integer. If an optional whole number

Nimmediately followssci, the precision is set toNdigits.

`fix[<N>]`

: use fixed notation

Numbers are displayed with a fixed number of digits to the right of the decimal point. If an optional whole number

Nimmediately followsfix, the number of digits to the right of the decimal point is set toN.

`hex[<N>]`

: use hexadecimal notation

Numbers are displayed in base 16 (a-f are used to represent digits greater than 9) with a fixed number of digits. If an optional whole number

Nimmediately followshex, the number of digits displayed is set toN.

`oct[<N>]`

: use octal notation

Numbers are displayed in base 8 with a fixed number of digits. If an optional whole number

Nimmediately followsoct, the number of digits displayed is set toN.

`bin[<N>]`

: use binary notation

Numbers are displayed in base 2 with a fixed number of digits. If an optional whole number

Nimmediately followsbin, the number of digits displayed is set toN.

`vhex[<N>]`

: use Verilog hexadecimal notation

Numbers are displayed in base 16 in Verilog format (a-f are used to represent digits greater than 9) with a fixed number of digits. If an optional whole number

Nimmediately followsvhex, the number of digits displayed is set toN.

`vdec[<N>]`

: use Verilog decimal notation

Numbers are displayed in base 10 in Verilog format with a fixed number of digits. If an optional whole number

Nimmediately followsvdec, the number of digits displayed is set toN.

`voct[<N>]`

: use Verilog octal notation

Numbers are displayed in base 8 in Verilog format with a fixed number of digits. If an optional whole number

Nimmediately followsvoct, the number of digits displayed is set toN.

`vbin[<N>]`

: use Verilog binary notation

Numbers are displayed in base 2 in Verilog format with a fixed number of digits. If an optional whole number

Nimmediately followsvbin, the number of digits displayed is set toN.

#### Variable Commands¶

`=<name>`

: store value into a variable

Store the value in the

xregister into a variable with the given name.... => ...

`<name>`

: recall value of a variable

Place the value of the variable with the given name into the

xregister.... => name, ...

`vars`

: print variables

List all defined variables and their values.

#### Stack Commands¶

`swap`

: swap x and y

The values in the

xandyregisters are swapped.x, y, ... => y, x, ...

`dup`

: duplicate *x*

The value in the

xregister is pushed onto the stack again.x, ... => x, x, ...alias: enter

`pop`

: discard x

The value in the

xregister is pulled from the stack and discarded.x, ... => ...alias: clrx

`lastx`

: recall previous value of x

The previous value of the

xregister is pushed onto the stack.... => lastx, ...

`stack`

: print stack

Print all the values stored on the stack.

`clstack`

: clear stack

Remove all values from the stack.

... =>

#### Miscellaneous Commands¶

`rand`

: random number between 0 and 1

A number between 0 and 1 is chosen at random and its value is pushed on the stack into

xregister.... => rand, ...

``<text>``

: print text

Print “text” (the contents of the back-quotes) to the terminal. Generally used in scripts to report and annotate results. Any instances of $N or ${N} are replaced by the value of register N, where 0 represents the

xregister, 1 represents theyregister, etc. Any instances of $Var or ${Var} are replaced by the value of the variableVar.

`"<units>"`

: set the units of the x register

The units given are applied to the value in the

xregister. The actual value is unchanged.x, ... => x "units", ...

`functions`

: describes how to define and use functions.

`quit`

: quit (:q or ^D also works)

alias: :q

`help`

: print a summary of the available features

`?[<topic>]`

: detailed help on a particular topic

A topic, in the form of a symbol or name, may follow the question mark, in which case a detailed description will be printed for that topic. If no topic is given, a list of available topics is listed.

`about`

: print information about this calculator

### COMMENTS¶

Any text that follows a # is ignored. In this way you can add documentation to initialization files and scripts, as shown in the next few sections.

### HELP¶

You can use help to get a summary of the various features available in EC
along with a short summary of each feature. For more detailed information,
you can use ‘?’. If you use ‘?’ you will get a list of all available help
topics. If you use ‘?<*topic*>’ where *topic* us either a symbol or a
name, you will get a detailed description of that topic.

### INITIALIZATION¶

At start up **ec** reads and executes commands from files. It first tries
‘~/.ecrc’ and runs any commands it contains if it exists. It then tries
‘./.ecrc’ if it exists. Finally it runs the startup file specified on the
command line (with the **-s** or **–startup** option). It is common to put
your generic preferences in ‘~/.exrc’. For example, if your are an astronomer
with a desire for high precision results, you might use:

eng66.626070e-27 “erg-s” =h # Planck’s constant in CGS units1.054571800e-27 “erg-s” =hbar # Reduced Planck’s constant in CGS units1.38064852e-16 “erg/K” =k # Boltzmann’s constant in CGS units

This tells **ec** to use 6 digits of resolution and redefines *h* and *hbar*
so that they are given in CGS units. The redefining of the names *h*,
*hbar*, and *k* would normally cause **ec** to print a warning, but such
warnings are suppressed when reading initialization files and scripts.

After all of the startup files have been processed, the stack is cleared.

A typical initialization script (~/.ecrc) for a circuit designer might be:

# Initialize Engineering Calculator27 “C” =T # ambient temperature(k T 0C + * q/ “V”)vt # thermal voltage(2pi* “rads/s”)tw # to omega - converts Hertz to rads/s(2pi/ “Hz”)tf # to freq - converts rads/s to Hertz

### SCRIPTING¶

Command line arguments are evaluated as if they were typed into an interactive session with the exception of filename arguments. If an argument corresponds to an existing file, the file treated as a script, meaning it is is opened its contents are evaluated. Otherwise, the argument itself is evaluate (often it needs to be quoted to protect its contents from being interpreted by the shell). When arguments are given the calculator by default does not start an interactive session. For example: to compute an RC time constant you could use:

$ ec 22k 1pF*22n

Notice that the * in the above command is interpreted as glob character, which is generally not what you want, so it is often best to quote the script:

$ ec ‘22k 1pF*’22n

Only the calculator commands would be quoted in this manner. If you included
a file name on the command line to run a script, it would have to be given
alone. For example, assume that the file ‘bw’ exists and contains ‘* 2pi*
recip “Hz”’. This is a script that assumes that the value of R and C are
present in the *x* and *y* resisters, and then computes the 3dB bandwith of
the corresponding RC filter. You could run the script with:

$ ec ‘22k 1pF’ bw7.2343 MHz

Normally *ec* only prints the value of the *x* register and only as it
exits. It is possible to get more control of the output using back-quoted
strings. For example:

$ ec ‘`Hello world!`’Hello world!0

Whatever is found within back-quotes is printed to the output. Notice that
the value of the *x* register is also output, which may not be desired when
you are generating your own output. You can stop the value of the *x*
register from being printed by finishing with the *quit* command, which
tells *ec* to exit immediately:

$ ec ‘`Hello world!` quit’Hello world!

You can add the values of registers and variables to your print statements.
*$N* prints out the value of register *N*, where 0 is the *x* register,
1 is the *y* register, etc. *$name* will print the value of a variable
with the given name. Alternatively, you can use *${N*} and *${name*} to
disambiguate the name or number. To print a dollar sign, use *$$*. To
print a newline or a tab, use *\n* and *\t*. For example,

0: 100MHz =freq100 MHz: 2pi* “rads/s”628.32 Mrads/s: `$freq corresponds to $0.`100 MHz corresponds to 628.32 Mrads/s.628.32 Mrads/s:

To illustrate its use in a script, assume that a file named *lg* exists and
contains a calculation for the loop gain of a PLL,

# computes and displays loop gain of a frequency synthesizer# x register is taken to be frequency=freq88.3u “V/per” =Kdet # gain of phase detector9.07G “Hz/V” =Kvco # gain of voltage controlled oscillator2 =M # divide ratio of divider at output of VCO8 =N # divide ratio of main divider2 =F # divide ratio of prescalarfreq 2pi* “rads/s” =omegaKdet Kvco* omega/ M/ =aN F* =fa f* =T`Open loop gain = $a\nFeedback factor = $f\nLoop gain = $T`quit

When reading scripts from a file, the ‘#’ character introduces a comment. It and anything that follows is ignored until the end of the line.

Notice that the script starts by saving the value in the *x* register to the
variable *freq*. This script would be run as:

$ ec 1KHz lgOpen loop gain = 63.732Feedback factor = 16Loop gain = 1.0197K

The first argument does not correspond to a file, so it is executed as a script. It simply pushes 1KHz onto the stack. The second argument does correspond to a file, so its contents are executed. The script ends with a print command, so the results are printed to standard output as the script terminates.

One issue with command line scripting that you need to be careful of is that
if an argument is a number with a leading minus sign it will be mistaken to
be a command line option. To avoid this issue, specify the number without
the minus sign and follow it with *chs*. Alternatively, you can embed the
number in quotes but add a leading space. For example,

$ ec -30 dbmvec: -30 dbmv: unknown option.$ ec 30 chs dbmv10 mV$ ec ‘ -30’ dbmv10 mV

### INITIALIZATION SCRIPTS¶

You can use scripts to preload in a set of useful constants and function
that can then be used in interactive calculations. To do so, use the **-i**
or *–interactive* command line option. For example, replace the earlier
‘lg’ script with the following:

88.3u “V/per” =Kdet9.07G “Hz/V” =Kvco2 =M8 =N2 =F(N F* recip)f(2pi * Kdet * Kvco* M*)a(a f*)Tclstack

Now run:

$ ec -i lg0: 1kHz T629.01M:

Doing so runs lg, which loads values into the various variables, and then they can be accessed in further calculations.

Notice that the script ends with *clstack* so that you start fresh in your
interactive session. It simply clears the stack so that the only effect of
the script is to initialize the variables. Using **-s** or **–startup**
does this for you automatically.

Alternatively, you can put the constants you wish to predeclare in
*./.ecrc*, in which case they are automatically loaded whenever you invoke
*ec* in the directory that contains the file. Similarly, placing constants
in *~/.ecrc* causes them to be declared for every invocation of *ec*.

### DIAGNOSTICS¶

If an error occurs on a line, an error message is printed and the stack is restored to the values it had before the line was entered. So it is almost as if you never typed the line in at all. The exception being that any variables or modes that are set on the line before the error occurred are retained. For example,

0: 1KOhms =r1 KOhms: 100MHz =freq 1pF = c=: unrecognized1 KOhms: stackx: 1 KOhms1 KOhms: varsRref: 50 Ohmsfreq: 100MHzr: 1 KOhms

The error occurred when trying to assign a value to *c* because a space was
accidentally left between the equal sign and the variable name. Notice that
100MHz was saved to the variable *freq*, but the stack was restored to the
state it had before the offending line was entered.

### SEE ALSO¶

bc, dc