1. Jun 12, 2015

### MrBondx

1. The problem statement, all variables and given/known data

A simplified model of ADC noise refers the noise to a noisy source resistance Rn while assuming the rest of the signal path to be noiseless. Figure 3 represents a particular 18-bit ADC that has a 10 V input voltage range. The ADC has a bandwidth of 1 MHz.

Calculate the maximum value of Rn if the resolution of the ADC is not to be adversely affected by thermal noise. Assume the ADC operates at 25 degrees C.

[N.b. The voltage resolution of an ADC is equal to its overall voltage measurement range divided by the number of discrete values possible on its output.] FIG. 3

2. Relevant equations

3. The attempt at a solution

The issue of resolution has totally thrown me off but here is what I'm thinking.

Rn = (Vn \ 4kTRB), where k is the Boltzmann constant.

Vn = ? I'm not sure whether Vn = resolution or full scale voltage.

Last edited by a moderator: Jun 12, 2015
2. Jun 12, 2015

### Staff: Mentor

That equation does not look correct. What is the equation for the thermal noise voltage in terms of of k and T and R and B?

3. Jun 12, 2015

### MrBondx

Thanks, Yea my mistake

Vn = sqrt(4kTBR)

Re-arranging

R = (Vn^2 / 4kTB)

4. Jun 12, 2015

### Staff: Mentor

Ah, much better. I was getting vertigo trying to decipher what you wrote.

So now you're pretty much done. Take the input voltage range and divide by the total resolution (18 bits is how many steps?). Then apply the formula...

5. Jun 12, 2015

### Staff: Mentor

Oh, and remember that T is absolute temperature...

6. Jun 12, 2015

### MrBondx

Input voltage resolution

18bits = 2^18 steps = 262144

Voltage range / steps = (10 / 262144)

Vn = 38.14697 x 10^-6 V

Is that correct?

7. Jun 12, 2015

### Staff: Mentor

Yes, I get 38.15uV as well. So what is the equivalent resistance to make that noise voltage at (absolute) room temperature?

8. Jun 12, 2015

### MrBondx

Converting Celsius to Kelvin

25degrees = 298.15 K

Plugging numbers into equation

Rn = (38.15 x 10^-6)^2 / (4 x (1.38 x 10^-23) x 298.15 x 1000000)

= 88433.17

Rn = 88.4 kOhms

9. Jun 12, 2015

### Staff: Mentor

Looks like a reasonable value. Do you know if it's correct?

10. Jun 12, 2015

### MrBondx

I hope it is correct, will send it for marking. Thanks for your help, much appreciated.