~ Thermal Noise ~ Johnson Noise Calculator ~

Calculates the root mean square Thermal Noise or Johnson Noise Voltage Vn-rms in a given bandwidth at a specific temperature that is passively generated across the resistive part 'R' of a circuit element ~ There may be additional 'excess noise' generated by current flowing through the resistance due to the type of material and its purity hence the extra pink noise from old carbon resistors or shot noise in active devices ~ Click here for other calculators

Input Variables in yellow
Boltzmann constant — k 1.3806x10-23 J/K — Joules per degree Kelvin
Temperature — T °C
High Pass Response –3dB — f l Hz — Can be zero for d.c. coupled
Low Pass Response –3dB — f h Hz — See notes below
f l and f h Filter order — m — Assumed Butterworth response
Resistance — R Ω
Calculated results using the values entered above
Noise Bandwidth — Bn
Noise Voltage — Vn-rms nV = √4kTBnR  =  nV/√Hz
Noise Level — ref. 1V dBV = 20 log Vn-rms/1V
Noise Level — ref. 0.775V dB(0.775) or dBu = 20 log Vn-rms/0.775V
Noise Level — ref. 1mW in 50Ω dBm = 10 log (Vn-rms)2/50 x10-3
Reference Voltage ~ for calculating Signal/Noise ratio SNR in dB relative
Reference Voltage V dBr = 20 log (Vn-rms)/Vref

Nota Bene The noise bandwidth is not the same as a known or measured −3dB response which is why you enter −3dB points for f l and f h and the order m which is based on the slope of the response of the measuring equipment or the device [amplifier] being measured

The default values for f l and f h and filter order m are for the Tektronix AA501 audio analyser or similar equipment with an IEC 22.4kHz audio filter with 3rd order Butterworth response ~ Most audio equipment is measured with similar filters in place to indicate the percieved noise output but may generate noise beyond audio which could annoy your pets

Nota Bene The Reference Voltage input can be useful for establishing a theoretical limit for SNR ~ If for example the total resistance around a low noise transistor input is say 10Ω [ including rbb and source R ] and the source voltage is 100µV the best possible SNR in the audio band will be about 64dB ~ which could be 3dB better if the amplifier is a well designed passive RIAA phono stage as seen using this Excel calculator

For more information about noise in components and amplifiers see:

The Art of Electronics 3rd edition chapter 8 ~ By Paul Horowitz and Winfield Hill
Noise in Transistor Circuits ~ By P. J. Baxandall ~ Wireless World November 1968
Designing low–noise audio amplifiers ~ By Wilfried Adam ~ Wireless World June 1989
Introduction to low–noise amplifier design ~ By A. Foord ~ Wireless World April 1981
The design of Low-noise audio frequency amplifiers ~ By E. A. Faulkner ~ The R & E E July 1968

These articles along with the book 'Low-Noise Electronic System Design' By C. D. Motchenbacher and J. A. Connelly should answer most questions about electronic noise ~ Click here for other calculators

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