Calculating Closed Loop Gain in a Noisy System

[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

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.

 

[rbj]

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

I've got the following so far:

$$V_{out} = \frac{A_1 A_2}{1 + A_1 A_2 B} V_{in} + \frac{A_2}{1 + A_1 A_2 B} V_n$$

But the question is asking for the closed loop gain.

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.

 

[name]

What if i do this:

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

and then...

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

Is this logically correct?