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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)