Op amps problem Gain Calculation

[N]

Hi,
Note to view the schematic below, change your font to fixed Courier.


I have a problem I am trying to work out on simple Op Amps gain,
and I am having trouble trying to prove what the gain is.
I know what the gain is supposed to be (see below), but
I am stumped as to how to actually go about proving it. When
I try to setup the Kirchoff node equations I get a really
ugly polynomial.

I can put the design into a spice deck and prove it, but I want to
understand the design from an analytical point of view.

Gain = 2*R2/R1 * (1 + R2/Rg)(V2-V1) (GAIN FOR THE OP AMP BELOW)

Now looking at the above equation it is obvious if you
eliminate resistor Rg, the equation becomes a simple
differential amplifier gain, which I can easily solve and
prove. However when you add the positive feedback from
the output, you get a different Beta for the loop gain
that is hard to figure out.

Anybody want to take a stab at proving this?

Nick ------------
| |
V1---------R1-----------------------R2-------R2---| |
| | |
| ___ | |
| | \ | |
|--Vn| \ | |
| \ Vout | Rg
| |------------------ |
|--Vp| / |
| | _ / -----------
| |
| |
V2----------R1-----------------------R2-------R2---|GND

 

[Figaro]

"N" <caprice24 at no spam yahoo dot com> wrote in message
| Hi,
| Note to view the schematic below, change your font to fixed Courier.
|
|
| I have a problem I am trying to work out on simple Op Amps gain,
| and I am having trouble trying to prove what the gain is.
| I know what the gain is supposed to be (see below), but
| I am stumped as to how to actually go about proving it. When
| I try to setup the Kirchoff node equations I get a really
| ugly polynomial.
|
| I can put the design into a spice deck and prove it, but I want to
| understand the design from an analytical point of view.
|
| Gain = 2*R2/R1 * (1 + R2/Rg)(V2-V1) (GAIN FOR THE OP AMP BELOW)
|
| Now looking at the above equation it is obvious if you
| eliminate resistor Rg, the equation becomes a simple
| differential amplifier gain, which I can easily solve and
| prove. However when you add the positive feedback from
| the output, you get a different Beta for the loop gain
| that is hard to figure out.
|
| Anybody want to take a stab at proving this?
|
| Nick ------------
| | |
| V1---------R1-----------------------R2-------R2---| |
| | | |
| | ___ | |
| | | \ | |
| |--Vn| \ | |
| | \ Vout | Rg
| | |------------------ |
| |--Vp| / |
| | | _ / -----------
| | |
| | |
| V2----------R1-----------------------R2-------R2---|GND
|

write the loop equations, apply the following op-amp tricks:

1) currents into the inputs Vn and Vp are zero because op-amps have very
input impedance
2) Vn-Vp is zero because op-amps have very high gain

and you will get your gain equation