designing an amplifier using the 741...

Hi

Could you please help me with the query included in the attachment? Thank you.

Regards
PG

hi PG,
Consider this,

If we have two 2% tolerance resistors in series, what is the possible tolerance of the series pair.???

E.

first design the amplifier irregardless of resistor tolerances

THEN, do a sensitivity analysis on each resistor...in otherwords, find the sensitivity of each resistor to the overall gain, and add up those sensitivities....adjust resistor values as necessary to get the gain you want

see this document for an intro to sensitivity...its not as simple as just "adding" things up...the analysis involved is actually very heavy and mathematical:

https://www.electro-tech-online.com/custompdfs/2012/06/sprp524.pdf

Hi,

You can also do it this way...

Choose d1 to represent the tolerance of the first resistor X, and d2 to represent the tolerance of the second resistor Y. Now calculate lower case x and y from:

x=X*d1
y=Y*d2

Now we can find the combinations for any operation like add, subtract, multiply, etc., from:

F1(x,y)/F1(X,Y)

which for the three cases where F1 is either addition, multiplication, or division, gives us:

(x+y/(X+Y)=(d2*Y+d1*X)/(X+Y)
(x*y)/(X*Y)=(d1*d2*X*Y)/(X*Y)=d1*d2
(x/y)/(X/Y)=((d1*X)/(d2*Y))/(X/Y)=d1/d2

(Note how simple it is to get the expressions on the left in each of the three above. It's just the x and y with the operator divided by the X and Y with the same operator).

Now choose your exact values X and Y and the tolerances d1 and d2, where d1=1.02 or 0.98 and d2 same, and that gives us four expressions for each set above. Note that the multiplication and division simplify to just d1 and d2, so you dont need the actual exact values for them.

Once you calculate the four values, you select the highest one. That's the worst case tolerance.

Forget what's on the +ve on the amplifier. Take the worst case of low gain where R1 is -% and Rf is +%.
Do the same with the opposites and come up with the resistor values.

Technically known as Monty Carlo analysis. It is defunct on many designs as you can buy highly calibrated 1% resistors for peanuts.

IMHO if you are designing circuits that use such junk resistors these days then you are just asking for problems. They might have been 2% when they left the factory but experience tells me they can be 20% out later.

Any system that requires a gain specifically of 68 is a badly designed system. An academic design but not a real world one.