HP 50g: Bolt Pattern, Solar Irradiance, Thermal Noise, Regular Polygons, Center of Mass (Matrix of Masses)

HP 50g:   Bolt Pattern, Solar Irradiance, Thermal Noise, Regular Polygons,

Center of Mass (Matrix of Masses)

Bolt Pattern: BOLTPAT

Link to the original blog entry:  http://edspi31415.blogspot.com/2015/03/hp-prime-ti-84-bolt-pattern.html

Input:

4:  xc:   x coordinate, center

3:  yc:   y coordinate, center

2:  n:  number of bolts

1:  d:  diameter of the circle

Program:

<< DEG OVER 1 – → xc yc n d k

<< { } 0 k FOR I 360 I * n / DUP COS d 2 / * xc +

SWAP SIN d 2 / * yc + (0,1) * + + NEXT

DUPDUP 2 GET SWAP 1 GET – ABS >> >>

Output: 

2:  list of bolts (x+yi)

1:  OC-Distance

Solar Irradiance:  IRRAD

Link to the original blog entry:  http://edspi31415.blogspot.com/2015/03/hp-prime-and-casio-prizm-solar.html

Input:

5:  es:   elevation of the sun (as decimal degrees)

4:  as:   azimuth of the sun from south going east (as decimal degrees)

3:  ep:   elevation of the panel (as decimal degrees)

2:  ap:   azimuth of the panel from south going east (as decimal degrees)

1:  ib:  the sun’s power or irradiance (usually 1,000 or 1,367 W/m^2)

Program:

<< → es as ep ap ib

<< DEG ep COS es SIN * ep SIN es COS * as ap – COS *

+ ACOS DUP COS ib * >> >>

Output:

2:  incidence angle

1:  surface radiance

Thermal Noise:  THNOISE

Link to the original blog entry:  http://edspi31415.blogspot.com/2015/02/hp-prime-ti-84-thermal-noise-johnson.html

Input:

3:  R:  resistance (Ω)

2:  T:   temperature (K)

1:  B:   noise bandwidth (Hz)

Program:

<< → R T B

<< T R * B * 4 * 1.3806488E-23 * √

T B * LOG 10 * 198.599167802 -  >> >>

Output:

2:  Voltage (Volts)

1:  Noise Power (dB)

Regular Polygon:  Internal Angle and Area:  RPOLYG

Link to the original blog entry:  http://edspi31415.blogspot.com/2015/03/regular-polygons-internal-angles-and.html

Input:

2:  s:  side length

1:  n:  number of sides

Program: 

<< DEG DUP INV 360 * NEG 180 + UNROT 4 / SWAP SQ * SWAP DUP UNROT 2 / TAN * >>

Output:

2:  Interior Angle

1:  Area

Center of Mass using Matrix:  CENTERMTX

Link to the original blog entry:  http://edspi31415.blogspot.com/2015/04/hp-prime-center-of-mass-matrix.html

Input:

1:  Matrix of Masses

Program:

<< DUP SIZE OBJ→ DROP → M R C

<< M 1  C START 1 NEXT C →ARRY * AXL ∑LIST

M 1 C FOR I I NEXT C 1 2 →LIST →ARRY * TRAN

1 R START 1 NEXT R 1 2 →LIST →ARRY * OBJ→ DROP

M TRAN 1 R FOR I I NEXT R 1 2 →LIST →ARRY * TRAN

1 C START 1 NEXT C 1 2  →LIST →ARRY * OBJ→ DROP

→ tm rw cw

<< rw tm / cw tm  / {1,2} →ARRY >> >> >>

Output:

[[ x center of mass point,  y center of mass point ]]

Special Note:  April 11 will mark the fourth anniversary of this blog.  I appreciate the readers and followers of this blog and thank you for that, and the comments.  Best always,  Eddie!

This blog is property of Edward Shore.  2015.

HP Prime & TI-84+: Thermal Noise (Johnson-Nyquist Noise)

Introduction

The following program calculates the RMS (root-mean-square) voltage of a resistor at a certain temperature.  Thermal noise, also known as Johnson-Nyquist Noise is generated when the resistor has a temperature above absolute zero.  The equation to calculate the voltage is:

V = √(4*k*T*R*B) where

k = Boltzmann’s Constant = 1.3806488 * 10^-23 J/K

T = temperature in degrees Kelvin (K)

R = resistance in ohms (Ω)

B = noise bandwidth (Hz)

This program also calculates the noise power in decibels.  Yes, the power for most calculations for this application will be a negative quantity.   (I did a double take when I first learned about noise power.)   The equation for the noise power is:

P = −198.599167802+10*LOG(T*B)

where -198.599167802 = 10*LOG(k*1000) (see above)

HP Prime:  THNOISE

EXPORT THNOISE(R,T,B)

BEGIN

// 2015-2-18

// R = resistor (ohms)

// T = temp (°K)

// B = bandwidth (Hz)

LOCAL V,P;

// Boltzmann′s constant:

// can get retrieved by pressing Shift, Units, Const, 2, 2

V:=√(4*1.3806488ᴇ−23*T*R*B);

// volts

P:=−198.599167802+10*LOG(T*B);

// dBs

RETURN {V,P}; 

END;

TI-84+:  THNOISE

Disp "R=RESIS. (OHM)"

Disp "T=TEMP. (°K)"

Disp "B=BANDWIDTH (HZ)"

Prompt R,T,B

√(4*1.3806488ᴇ−23*T*R*B)→V

−198.599167802+10*LOG(T*B)→P

Disp "V=VOLTAGE"

Pause V

Disp "P = POWER"

Pause P

Example:

R = 1040 Ω

T = 300 K

B = 19000 Hz

Results:

V » 5.721708 * 10^-7 V

P » -131.040419 dB

Sources:  

John A. Ball.  "Algorithms for RPN Calculators"  John Wiley & Sons, Inc.  New York.  1978.  pg. 267

Johnson-Nyquist Noise.  http://en.wikipedia.org/wiki/Johnson%E2%80%93Nyquist_noise  Retrieved 2015-2-15

This blog is property of Edward Shore - 2015.