HP Prime: Thermal Noise (Johnson-Nyquist Noise)

[Eddie W. Shore]

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)

Example:

R = 1040 Ω
T = 300 K
B = 19000 Hz

Results:
V = 5.721708 * 10^-7 V
P = -131.040419 dB

Code:

Code:

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;

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%...uist_noise Retrieved 2015-2-15