Patent Application
20090076775
The present invention relates a method of increasing precision. More particularly, the present invention relates to a method of converting a low precision into high precision.
Currently in order to obtain products of high precision, machines with higher precision are used to produce high-precision manufacture equipments for producing, in which the precision of the finished products completely depend on the precision of the machines themselves; and if the machines can not fulfill this object, the finished products fail naturally. Accordingly, solutions for overcoming this limitation, elevating the precision, and making it easy to manufacture and simple to accomplish have become the important issues.
The object of the present invention is to provide a method for increasing precision, which is simple and easy. The method may be able to achieve the required precision when in use.
Serial Connection Mode:
According to an aspect of the present invention, the semi-finished product is assumed to have a precision of negative 1%. For example:
99.X is −1% precision of 100
0.099X is −1% precision of 0.1
198.X is −1% precision of 200
594.X is −1% precision of 600
It can be seen that one character of negative 1% is the second digit is always 9, which can be formulated as below:
in which a9bcdef represents bigger rough precision, g9hik represent smaller rough precision, and a99nmop represents the value with higher precision. Now, the cases for bc may be observed as below:
In order to make b+g=9, so g=9−b;
In order to make b+g+1=9, so g=8−b;
In order to make b+g+1=9, so g=8−b.
Hence, g can be either 9−b or 8−b, and 8−b takes the possibility of 0.9.
It can be concluded that, independent of the value b, a 9 can be acquired as long as select g=9−b or g=8−b. We can say that after the addition of the original value a9bcdef to g9hik, the value a99 nmop can be derived, which is referred by the applicant as “Full-9 Principle”.
Thus using this Full-9 Principle, it is possible to derive a combination of a9999 . . . 9, which consists of n 9's, achieving the required precision, and meanwhile such precision is negative; in case a positive precision is needed, then add one 1 to the last 9. As for other precision, a similar value is added to or subtracted from the last 9.
The precision product generated by this Full-9 Principle has a999999 . . . 9, and if other values should be obtained, then other products can be added. For example, to derive the value 234, it is possible first to generate 199.9, 29.9, 3.9, such that 199.9+29.9+3.9=233.7, or 199.99+29.99+3.99=233.97, completely depending on the precision requited to select each values.
To produce the product of negative 1% rough precision, it is certainly inevitable that sometimes it might fall out of such a range. In general, factories will determine this as a bad condition and thus abandon; however, by using the Full-9 Principle, it can be preserved.
For example, 199.9+29.9+3.9=199.9+28.9+4.9=other cases with the same sum. Therefore, as long as the sum remains unchanged, negative 1% rough precision represents merely consistent manufacture quality, facilitates to foresee related ranges, and provides better strategies; meanwhile the deviated or accidental items can be detected by measurement apparatus to know the errors thereof, and got corrected in the next level.
Serial connection multiplication is analogous to addition, Q=Z+W=Z+R*Y, in which make sure the R times, then sift Y to the required precision.
Parallel Connection Mode:
R means idea value.
F means semi-finished value, which must be a positive rough precision, so F>R.
T means additional ideal value.
T1 means rough new value.
R1 mean rough ideal value.
in which equation (A) is with a known F, to solve for a value T bigger than F and belong to division. Equation (A1) whereas is with a known T, to solve for a value smaller than T and belong to subtraction, then sifting the value K to the required precision.
T=R/(R/N+1) (B)
N=F−R (C)
R1=1/(1/F+1/T1) (D)
Since T1 is just slightly bigger than R/(R/N+1), R1 is necessarily situated within the positive error, and never in the range of negative error. If T1 is smaller than T, then it will become a negative error, and once it is a negative error, it will never return to positive error, thus, at this moment the serial connection addition can be applied.
M means how many decimal digits behind the decimal dot.
I means number of digits for F−R
G means maximum range for error, 0<G<1.
H means error before correction.
Based the following equation:
R(R/N+1)<=T<(G*(10 of power I−1)+R)*F/(F−R−G*(10 of power I−1)) (E)
herein such equation (E) is referred as Error Sifting equation.
T is equal to left hand, more precise; T is equal to right hand, i.e. equal to the maximum of error.
For example, F=1234, R=1000, then F−R=234, of 3 digits, thus I=3. Input in the equation L, hence H=2.34.
From H, it can be seen that it is required to correct 2 to zero, and the corrected value needs to be smaller than G
Hereunder the content of the present invent will be further illustrated with embodiments. However, the application of the present technique is not limited to the described embodiments. Other examples to which the present technique can be applied will be also herein incorporated as reference.
Serial Connection Mode:
Take an example of producing resistors of 1,000,000 ohm with precision 0.9999, the last 9 occurs at the hundred-digit position, thus the semi-product needs to be produced from this hundred-digit. For clear illustration, assuming each semi-product had been measured and results thereof have the values enlisted in the Table as below. Certainly each value in the Table may differ from the real manufacture value; however this will not affect the purpose of the present invention.
For the initial value 994253, since b=4 and c=2, thus g=8-4=4, and from the Table, the value 4958, and 994253+4958=999211 can be chosen. Now b=2 and c=1, hence g=8−2=6, in the Table the value 696, and 999211+696=999907 can be chosen, in which the value satisfies the precision requirement.
Supposing the initial value is 995321, since b=5 and c=3, therefore g=8−5=3, in the Table the value 3961, and 995321+3961=999282 may be picked. Now b=2 and c=1, hence g=8−2=6, in the Table, the value 696, and 999282+0.696=999978 can be chosen, in which the value satisfies the precision requirement.
Now, as the precision is altered to be 1.0001, for the initial value 991234, since b=1 and c=2, thus g=8−1=7, and in the Table the value 7981, and 991234+7981=999215 can be chosen. Now b=2 and c=1, hence g=8−2=6, in the Table the value 696 can be chosen, but since the positive precision requires to add 1, hence the value 798 is selected, resulting in 999215+798=1000013, which satisfies the precision requirement.
Parallel Connection Mode:
For example, F=1234, R=1000, F−R=234 which value presents 3 digits, thus I=3.
Assuming G=0.56, which can be set based on manufacture precision or other conditions, placed into equation (E):
5273.5<=T<7320.8
T1=6125 may be arbitrarily chosen and put into equation (D), thus R1=1027. Let the original 1234 can be connected in parallel to 6125 and obtain 1027, thus H=2.34 becomes 0.27, which is smaller than G, accordingly narrows down the positive error.
Now F=1027, R=1000, F−R=27, which has two digits, thus I=2.
Assuming G=0.56, put into equation (E),
38037.04<=T<48259.
T1=40000 may be arbitrarily chosen and put into equation (D), thus R1=1001.3.
In case the precision is not good enough, the method may be repeated in the parallel connection mode process several times to obtain the ideal positive error.
In practical operation, it is possible to use both the serial connection and the parallel connection mode to achieve better combination.
Another advantage of the present invention is that, when the original precision is to be increased to a higher level of precision, it can be accomplished by first measuring the original values, then use serial connection or parallel connection to add new resistors.
For example, originally the production line was equipped with 1% machines; without the present invention, it would have been unavoidable to entirely repurchase new 0.1% machines for upgrading production line. To subsequently manufacture 0.01% products, it would have been inevitable to buy new 0.01% machines again. However, with the present invention, when 0.1% products are desired but machines in the factory remain 1%, then this can be accomplished by simply adding one extra resistor; again, while 0.01% is needed but machines remains 1%, this can be solved by adding another resistor after the 0.1%. Suppose originally, in the spare parts of the machine, there is space preserved for future use, then the advantage of using the present invention can be fully leveraged, arbitrarily adding or removing number of resistors, thus achieving the desired precision.
Another application for the present invention is integral circuits in semiconductor field. Similarly, assuming the precision of machine for producing integral circuit is 1%. Since the volume becomes smaller but rough precision for resistance remains unchanged, hence the spare part box for originally preserved space does not work completely, which is now replaced by switches, as shown in
Suppose these switches are controlled by CPU, this will become a variable resistor with variable precision and resistance. Such a variable resistor can substitute any known resistor, which is suitable for maintenance or automatic control system.
Another usage of the present invention is in the military field. Taking serial connection mode for example, as long as each series of resistance is produced (with MSB for different digit, from 1 to 9, and each 9 resistors multiplied by total number of digits) and got measured beforehand, when no other tools are available or no way to acquire the same resistor, it is possible to use the present method, calculate, take out the corresponding resistance and perform connection for achieving the desired resistance. Repeat the method to produce multiple times, the resistance will remain unchanged.
The measurement results of the present method are completely determined by measurement apparatus. Whatever feature that the measurement apparatus possesses, the measurement value is the precision under such a feature.
From the capacitor parallel connection equation, we know that it is equal to the serial connection mode addition of the present invention; hence the present invention can be directly applied to achieve higher precision. As for the capacitor serial connection equation, it is equal to the parallel connection mode addition of the present invention, thus the present invention is also applicable.
In addition to resistors and capacitors, the present invention can be also applied in the manufacture of other items such as inductors, chemical formulations, alloy formulations, medicine controls, weights for weight measurement, gold ornaments for weight measurement . . . , and so forth.
R11-R19 resistance of same digits, for MSB=1 to MSB=9
R21-R29 resistance of same digits with one less digit than R11, for MSB=1 to MSB=9
R31-R39 resistance of same digits with one less digit than R21, for MSB=1 to MSB=9
in which MSB refers to the number of the highest digit in the value, e.g., for 1234, its MSB is 1; for 905, MSB is 9.
R11-R19 resistance of same digits, for MSB=1 to MSB=9
R21-R29 resistance of same digits with one less digit than R11, for MSB=1 to MSB=9
R31-R39 resistance of same digits with one less digit than R21, for MSB=1 to MSB=9
