noise output in a voltage source

[kbcheong]

A non-ideal voltage source can be modeled by a series combination of an ideal DC voltage source, a resistance, and a small-signal voltage source. The small-signal source is included to represent the noise inherent in the source.
In practice, connecting the non-ideal voltage source to a load may result in undesirable effects due to the noise voltage vo appearing across the load.

(Diagram as file attached)

This problem studies such effects and how a Zener diode may be used to ameliorate the problem.
Assume that VI= 12.5 V, RIN=1 k ilo ohm , and vi = 20.0 mV.
In the figure above, calculate the DC output voltage VO , and the output noise voltage vo for two values of the load resistance, for RL = 2 kilo ohm and 4 kilo ohm.

I obtained the output DC for 2 kiloohm as 8.32 and for 4 kilo ohm is 9.984. What about the noise output, is it any formula for it?

 

[timothy48342]

Ahhh, an image to look at. Images makes a post much more inviting to respond compared to any post that didn't have the image.

First regarding your 2nd part. The calculation for noise output. I don't know for sure, so hopefully someone else will chime in on that. I would think that the formula is the same and that you would calculate the noise across the load the same as you did for the main voltage.

The answers you gave for the first part are close. 8.32 is not comletely incorrect, but you could improve it a bit. I want to mention significant digits and also suggest one good habit when making calculations.

The values you were given:
12.5 and 20.0 both have 3 significant digits.
The resistors 1K, 2K, and 4K all seem to have just 1, but I think there is a reason to ignore that and report your answers to 3 digits. (For the life of me, now that I am typing, I can't seem to come up with "why" the 1 digit of significance can be ignored there.)
Still, you don't have 4 significant digits anywhere, so yor answer of 9.984 has too many digits.
The other thing I wanted to mention is just a good calculation habit.
At some point during your calculation to get 8.32 I think you dropped the extra digits. You should never round or drop digits until your done. For instance if I take 12.5 and divide by 3000 (1K resistor + 2K resistor) I get .00416667 and if I truncate that to .00416 and multiplty by 2000, I get 8.32 which is what you got, but I should not have dropped the extra digits in the middle of the calculation.

This is better:
12.5 / 3000 = .00416667
.00416667 * 2000 = 8.3333333
8.3333333 should then be rounded to the correct number of digits

Now 9.984 is further off. How did you get that? It is close enough that I think you are using the formula correctly, but are your rounding in the middle of your calculation.
Could yhou show your work?

-tim