**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.

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