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# June StudentZone Quiz Solution

Here are the answers for the June 2017 StudentZone Quiz

Q: Which Noise is generated in a Resistor?

A: White Noise

Thermal noise in an ideal resistor is approximately white noise. The power spectral density is nearly constant throughout the frequency spectrum.

Q: What is the rms noise generated by a 10kΩ resistor at room temp (20°C) over an equivalent noise bandwidth of 20 kHz.

Solution:

Keep in mind this model

with V(rms)=sqrt(4*KB*T*R*B)

B= Bandwidth (F2-F1) [Hz]

R= Resistor [Ohm]

T= Temperature [Kelvin]

KB= Boltzmann Constant

Vrms=1.79uVrms

Q: Having a 24Bit Audio ADC with an Input span of 2.5V – how many flickering Bits we would get with this Vnoise from above?

Calculation:

For the calculation we need Vp-p.

I convert the 1.79uVrms into 11.87uVp-p by multiplying by ~ 6.6

(A factor of 6 is sometimes used here instead of 6.6, but ADI has standardized on 6.6)

1 LSB for a 24bit ADC and 2.5V Fullscale equals to 0.149uV.

So there are 11.87uV/0.149uV = 80  -> this means 80LSBs flickering which is around 6.2 bits being not stable.

Remark:

There is the argument that since the noise is Gaussian, there is a probability that more bits will occasionally flicker.

(but you can’t really see that effect with the eye)

Parents
• It may be worth adding Johnson and Nyquist noise to the first answer, as they were the first to measure and explain this type of noise, back in 1928.

J.B. Johnson, “Thermal agitation of electric charge in conductors,” Phys. Rev., vol. 32, no. 1, pp. 97–109, Jul. 1928.

H. Nyquist, “Thermal agitation of electric charge in conductors,” Phys. Rev., vol. 32, no. 1, pp. 110–113, Jul. 1928.