Voltage is being read by 1 kHz ADC in a circuit above a running engine (T=40°C, R=1000 Ohms.

Boltzmann’s constant = 1.38064852 × 10^(−23) J/K

Assume the ADC has 32 bits with a range of 5V.

Estimate the Johnson-Nyquist noise, check if noise would be an issue.

Hint: Compare the calculated noise with the minimum voltage the ADC can output.

 
A. Yes

B. No

C. Cannot be determined with the given data

D. Noise is irrelevant

To solve this problem, we need to estimate the Johnson-Nyquist noise and compare it with the minimum voltage resolution of the ADC to determine if the noise would be an issue.

### Step 1: Calculate the Johnson-Nyquist Noise Voltage
The Johnson-Nyquist noise voltage can be calculated using the formula:

\[
V_{n} = \sqrt{4 k_B T R \Delta f}
\]

Where:
- \( V_n \) is the RMS noise voltage
- \( k_B = 1.38064852 \times 10^{-23} \, \text{J/K} \) (Boltzmann constant)
- \( T = 40^\circ \text{C} = 313.15 \, \text{K} \) (temperature in Kelvin)
- \( R = 1000 \, \Omega \) (resistance)
- \( \Delta f = 1 \, \text{kHz} = 1000 \, \text{Hz} \) (bandwidth)

Let's calculate the noise voltage.

\[
V_n = \sqrt{4 \times (1.38064852 \times 10^{-23}) \times 313.15 \times 1000 \times 1000}
\] 

We can now calculate this value.The Johnson-Nyquist noise voltage is approximately \( 1.315 \times 10^{-7} \, \text{V} \) (or 131.5 nV).

### Step 2: Calculate the ADC's Minimum Voltage Resolution
The ADC has 32 bits and a range of 5V, so the minimum voltage resolution is:

\[
\text{Resolution} = \frac{5 \, \text{V}}{2^{32}} = \frac{5}{4294967296}
\]

Let’s calculate this next.The minimum voltage resolution of the 32-bit ADC is approximately \( 1.164 \times 10^{-9} \, \text{V} \) (or 1.16 nV).

### Step 3: Compare the Noise Voltage with the ADC Resolution
The Johnson-Nyquist noise voltage (\( 131.5 \, \text{nV} \)) is significantly larger than the ADC's minimum voltage resolution (\( 1.16 \, \text{nV} \)).

### Conclusion:
Since the noise voltage is much greater than the ADC resolution, the noise would be an issue, and the correct answer is:

**A. Yes**

---

Would you like any further details or have any questions? Here are 5 related questions to deepen your understanding:
1. How does temperature affect Johnson-Nyquist noise?
2. What role does the resistance play in calculating thermal noise?
3. How does increasing the ADC resolution improve measurement accuracy in noisy environments?
4. What other types of noise might affect measurements in this circuit?
5. How can you reduce the impact of Johnson-Nyquist noise in practical circuits?

**Tip:** Shielding your circuit and reducing bandwidth can help mitigate the impact of noise.

Voltage is being read by 1 kHz ADC in a circuit above a running engine (T=40°C, R=1000 Ohms). Boltzmann’s constant = 1.38064852 × 10^(−23) J/K. Assume the ADC has 32 bits with a range of 5V. Estimate the Johnson-Nyquist noise, check if noise would be an issue.

Learn how to calculate Johnson-Nyquist noise in a circuit operating at 40°C with a 1 kHz ADC and 32-bit resolution. This problem involves understanding thermal noise, resistance, temperature, and ADC resolution, with step-by-step calculations for determining if noise is an issue in the circuit.

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