I am trying to solve a few example questions relating to input voltage and input noise for the following questions.

Question 1


Question 2

I understand that I need to calculate the maximum noise voltage acceptable for the required SNR using the equation, SNR = 20log(Signal/Noise).

The thing I am having trouble understanding is for the first question, in the solutions the input noise voltage is calculated using:

SNR for question 1

Whilst in the solution for the second problem it uses:

SNR for Question 2

I cannot see any difference in the question as to why one would be squared and the other not. Thanks in advance.


Let's assume that 500 uV input is 500 uV RMS. We are allowed 40 dB SNR, meaning the ratio of Vinsignal/Vinnoise is 100:1. We now know the allowed input noise is 5 uVrms. This 5 uV input noise must be from all the sources attached to that input node.

To make the math easy, assume the bandwidth is 1,000,000 Hz. (the 1.2 MHz is about 2 dB error; I'll let you correct for that).

We need the input noise density for 1Hertz bandwidth. Power of noise changes linearly with bandwidth. Voltage of noise changes with square-root of bandwidth.

The 1 hertz noise density is 5uV/sqrt(1,000,000) = 5uV/1,000 = 5 nanovolts.

The noise floor of the signal source must be included in this; that 1 kΩ resistor provides 4 nanovolts RMS in a 1 hertz bandwidth.

Your budget allows only 5 nanovolts. Will the extra factor of 1.2x bandwidth cause this to be an impossible design task, intended as a learning experience by your teacher?

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