Question

Here is the question:

Noise produced by resistor is to be amplified by noiseless amplifier having voltage gain 75 and bandwidth 100kHz. A sensitive meter at output reads 240uV rms. Assuming operations at 37 degrees Celsius, calculate resistors resistance.

I know K= 1.38 x10^-23 J/K

I used equation 1-9 associated with this problem from the textbook:

e_n²/4 = kT(bandwidth)R

Where R = (e_n²/4) / kT(bandwidth)

R = ((240*10^-6)²/4) / (1.38*10^-23) * (37+273) * (100*10³)

R= (1.44*10^-8) / (4.14*10^-16)

R= 34.78 M Ohm

The book answer is 5.985 k Ohm for this first part. I do not know how they did that.

The question shows the gain at 75 gain. I know Gain = Vout/Vin.

So I used the formula and found Vin was 3.2uV rms.

I tried inserting that into e_n but I get a resistance value of 6.2 k Ohm. Its closer, but the book answer looks pretty exact.

Am I doing this wrong? Is e_n suppose to be the output noise? Looking at the diagram, e_n looks like it can be input noise on page 28. But since its e_n/2 then its output noise. And is that meter in the question stating that's noise? It is not very clear and pretty confusing.

Textbook is Electronic Communications a systems approach by Beasley, Hymer, Miller. ISBN: 13: 978-0-13-298863-6

Please let me know what I am doing wrong.

Thank you.