HP Prime: Thermal Noise (Johnson-Nyquist Noise)
02-18-2015, 01:30 PM
Post: #1 Eddie W. Shore Senior Member Posts: 1,134 Joined: Dec 2013
HP Prime: Thermal Noise (Johnson-Nyquist Noise)
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
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