# Transfer function with noise?

1. Oct 28, 2007

### name

Hi,

Is it possible to calculate the gain of a closed loop system with Noise? Here's a diagram describing what i mean:

http://img206.imageshack.us/img206/8955/cltfmh8.png [Broken]

I've got the following so far:

$$Vout = \frac{A1A2Vin}{1 + A1A2B} +$$ $$\frac{AVn}{1 + A1A2B}$$

But the question is asking for the closed loop gain. Would that just be:

$$Vout / Vin = \frac{A1A2}{1 + A1A2B} +$$ $$\frac{AVn}{Vin(1 + A1A2B)}$$

Thanks.

Last edited by a moderator: May 3, 2017
2. Oct 28, 2007

### rbj

if the question is well posed, it needs to still specify the gain (closed loop or not) from some specified input to a specified output. your first equation (i prettied it up a little) actually shows two different transfer functions.

Last edited by a moderator: May 3, 2017
3. Oct 29, 2007

### name

What if i do this:

$$A' = A2 (A1 + Vn)$$

and then...

$$Vout / Vin = \frac{A'}{1 + A'B}$$

Is this logically correct?