I want to examine the equations of a differential Operational Amplifier, specifically I want to examine how the tolerances of the resistors affect the resulting differential gain and common mode voltage gain. Specifically in the equations I have I examine the differential gain.
I have two equations, one for the gain and the other for the gain variation.
I want to use Mathematica to find the relation between the two. How can I do this?
The first equation is an equation of 4 resistors. The gain variation is an equation of the 4 same resistors plus another 4 variables which is the tolerances. I want to examine how the two behave and possible plot a curve when varying the above 8 variables.
To be more specific, most of the times one uses resistors of the same tolerance and the resistors come in pairs, meaning that the nominal value of these resistors are the same in pairs (e.g. r1 = r3 and r2 = r4). And this is exactly the occasion I want to study.
The equations that I have are the following:
r3 = r1 r4 = r2 T = 0.05 T1 = T T2 = T T3 = T T4 = T GainD[r1, r2, r3, r4] = (r4*(r1 + r2) + r2*(r3 + r4))/(2*r1*(r3 + r4)) GainDiv[r1, r2, r3, r4, T1, T2, T3, T4] = (((((r4/(2 r1 (r3 + r4)) - ((r1 + r2) r4 + r2 (r3 + r4))/( 2 r1^2 (r3 + r4)))*r1* T1)^2) + (((-((r3 + 2 r4)/(2 r1^2 (r3 + r4))))*r2* T2)^2) + (((-(1/(2 r1^2 (r3 + r4))) + (r3 + 2 r4)/( 2 r1^2 (r3 + r4)^2))*r3* T3)^2) + (((3/(2 r1^2 (r3 + r4)^2) - (r3 + 2 r4)/( r1^2 (r3 + r4)^3))*r4*T4)^2))^(1/2)) GainRes = (GainDiv[r1, r2, r3, r4, T1, T2, T3, T4]/ GainD[r1, r2, r3, r4])*100
How can I find the relationship between GainD and GainDiv?
How can I plot the graph that has GainD and GainRes as the axis while varying r1 r2 r3 and r4?
I need r1 - r3 and r2 - r4 to vary together during the value sweep, meaning to have the same value as r1 = r3 = Ra and r2 = r4 = Rb and plot while varying Ra and Rb as these are the resistors on which the gain depends on.
I am pretty new to Mathematica and it would be indeed a really useful tool when I can examine things like this.