# ~ 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

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

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