What do you need a proof for?
Mathematic Puzzle
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#3
- well normally some times I can harbour a guess but when I think about this I draw a blank - but lets say R1 = R2 = one million ohms - so with one percent tolerance
each resistor could be plus or minus 10 000 with the worse case being
gain = ( 1 000 000 + 10 000 ) / ( 1 000 000 - 10 000 )
if R1 = R2 = 100 ohms - then with one percent tolerance
each resistor could be plus or minus 1 ohm
with a worse case being Gain = 101/99
- well I think in theory that the numbers would be the same and that the value of the resistor would not matter however
- however I am wondering about " practical " resistors and resistance values
- like if in achieving 1% tolerance manufacturers find it easier to achieve that with smaller resistors values or higher resistance values
- and the current in the circuit is a function of the resistance feedback - so I am wondering if in fact in trying to achieve a " perfect " gain of one - that one would have some kind of indication as to whether one would select a high value or low value of resistor or whether or not it just would not matter
- like I am just wondering here - I haven't got a clue - but I am guessing I will select a resistor value which would let me play with a current of 100 micro amperes ( just to save on batteries )
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#4
- I just wanted to add something -
- like someone might think it makes no difference what size
- however, many people must have seen that show - " HOW IT'S MADE "
- so essentially I am trying to get two perfectly "matched" resistors
- so I am asking for help in terms of a mathematical opinion -
- that being mathematically speaking if it would make a difference -
would you have a better chance of getting perfectly matched resistors
with high resistance one percent resistors or a better chance with low resistance
one percent resistors - ( or once again would it make no difference )
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on first glance one could say that one percent is one percent and one percent
across the board should mean that it would make no different HOWEVER
- supposing you were to try to design a Unity Gain inverting amplifier for mass
production - now it would cost a fortune for precision resistors - so assume then
that you decide to go with resistors that have a 1% tolerance
- assume further than R1 should equal R2 so as to get a Gain of 1 ( Unity Gain )
- then assume further that the resistor value will be chosen to be from 10 000 ohms ( 10k ohms ) - to - 50 000 ohms ( 50k ohms )
- my question involves wondering if there is a maxima minima thing here
- that being if a higher or lower value of resistor would possibly have an effect of negating the 1% tolerance error
- if the tolerance of R1 was one percent positive and the tolerance of R2 was one percent negative - the total error would be like 2 percent -
- so the question would be like in theory one percent is one percent - but in practise - if the Gain is R1/R2 - and you wanted a gain of one - would you use large resistance values or low resistance values - or would you say the value of the resistors doesn't not matter - ( and if you know mathematics like I don't might you beable to offer a written mathematical " proof " )