## Friday, January 4, 2019

### HP Prime and HP 42S: Noise Figure and Noise Voltage

HP Prime and HP 42S:  Noise Figure and Noise Voltage

Notes:  The programs for the HP 42S format are designed to work with the HP 42S's solver.  The programs were created using Thomas Okken's Free42, and should also be compatible with the Swiss Micros DM42.

Noise Figure

Given system temperature (in Kelvins), this program calculates the noise figure (in Decibels), which describes the noise performance of an amplifier.  The noise figure is described as the difference between the noise output of an actual receiver to an ideal, noiseless receiver.  A noiseless receiver is said to have a resistor operating at room temperature, 290 K (about 16.85°C or 62.33°F). The lower the noise figure, the better.

Formula:

F = 10 * log(T/290 + 1)

where:

F = noise figure (dB)
T = system temperature (K)

HP Prime Program Function:  NOISEDB

EXPORT NOISEDB(T)
BEGIN
// Noise Figure in dB
// Input: T: Temperature (K)
// 2019-01-04 EWS
10*LOG(T/290+1);
END;

HP 42S Program for Solver:  NSEFG

00 { 35-Byte Prgm }
01▸LBL "NSEFG"
02 MVAR "F"
03 MVAR "T"
04 RCL "T"
05 290
06 ÷
07 1
08 +
09 LOG
10 10
11 ×
12 RCL "F"
13 -
14 END

Example (Fix 4):

Input:  T = 57.8°F, convert it to Kelvins, enter 287.4833 K (approximately)
Result:  F = 2.9914 dB

Noise Voltage

Given the noise bandwidth (in Hertz) and the resistance (in Ω), calculate the open-circuit voltage (in RMS volts).

Formula:

e_n = √(1.6*10^-20 * B * R)

where:

e_n = open circuit voltage noise (RMS volts)
B = bandwidth (Hz)
R = resistance (Ω)

HP Prime Program Function: NOISEVOLT

EXPORT NOISEVOLT(b,r)
BEGIN
// Noise Voltage in V
// Input: B=bandwidth (Hz)
// Input: R=resistor (Ω)
// input numbers only
√(1.6ᴇ−20*b*r);
END;

HP 42S Program for Solver:  NSEVT

00 { 37-Byte Prgm }
01▸LBL "NSEVT"
02 MVAR "B"
03 MVAR "R"
04 MVAR "En"
05 16ᴇ-21
06 RCL× "B"
07 RCL× "R"
08 SQRT
09 RCL- "En"
10 .END.

Example (FIX 4):

Input:  B = 31,000 Hz, R = 950 Ω
Result:  e_n = 6.8644e-7 V

Sources:

Ball, John A.  Algorithms For RPN Calculators  John Wiley & Sons: New York  1978.  ISBN 0-471-03070-8

Eddie

All original content copyright, © 2011-2018.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

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