LM1117IMPX-3.3 National Semiconductor, LM1117IMPX-3.3 Datasheet - Page 4

• Manufacturer Part Number: LM1117IMPX-3.3
• Description: IC,VOLT REGULATOR,FIXED,+3.3V,BIPOLAR,SOT-223,3PIN,PLASTIC
• Manufacturer: National Semiconductor

Specifications of LM1117IMPX-3.3

• Rohs Compliant: NO

www.national.com
Statistical Variation of Resistors,
Semiconductors, and Systems
A similar histogram supporting our assumption for 0805
general purpose surface mount resistors is shown in Figure
4. The nominal value for a 1% resistor is shown here con-
trolled to greater than
sian.
Note: Figure 3 and Figure 4 are presented to support the assumption that
The RSS Method
The RSS (root sum squares) method is only valid for the
case when independent Gaussian random variables are
combined as sums. Since equation 1 contains products,
quotients and sums of random variables, this method is not
valid for equation 1.
Random Variable Theory vs. Worst
Case Over PVT
In the worst case method, we saw that total output voltage
tolerances could be substantially larger than expected (Table
1). Is it realistic to use these limits? Random variable theory
can be used to show that these excessive limits are not
necessary. In particular, the concept of “worst case” is not
exactly appropriate when dealing with random processes
where there is always a (very small) probability that a sample
could fall outside of the worst case limits.
Rather than look at worst case limits, it is more appropriate
to look at the equivalent
voltage. For this purpose, let’s look again at the output
voltage equation.
Be reminded that V
random variables. As such, V
(Continued)
FIGURE 4. Typical Resistor Variation: 1% General
V
on the order of six sigma or better.
ref
and the voltage setting resistors are Gaussian and have variations
Purpose 0805 SMD
ref
±
, R1, and R2 are all independent
6σ and is also approximately Gaus-
±
6σ points for the regulator’s output
out
is a function of three random
20148211
4
variables. To complicate matters, summation, multiplication,
and division are all involved. Although summation of two
Gaussian random variables produces a Gaussian result, this
is not the case for multiplication or division. As such, the true
distribution of V
approximations exist for calculating the mean value and
deviation for sums, products, and quotients. These approxi-
mations are especially accurate for the case where V(x)
E(x) which is the case for linear regulators and resistors. In
particular, consider these relationships:
For uncorrelated Gaussian random variables, the following
relationships apply:
Notice that the resulting distribution after these operations is
not always Gaussian. It is possible to calculate the distribu-
tion function for the resulting random variable, however, this
is quite complicated and unnecessary since we are only
interested in the mean and variance of the result. Since V(x)
<<
Gaussian distribution so our Gaussian based SPC (Statisti-
cal Process Control) concepts will still be valid.
Since equation 1 involves a sum, product, and quotient, we
cannot use the relationships above and, instead, must cal-
culate a specific approximating equation for E(V
V(V
Equations 7 and 8 originate from Taylor series expansion
(see Mood, Graybill, and Boes).
Notice that the expected value for V
ent than the simple value calculated in equation 1. The third
and fourth terms in equation 7 are zero. However, there is a
very small positive error caused by the second term which is
not exactly zero. Since we are working with six sigma pro-
cesses, it is easy to show that this second term is virtually
zero and the expected value of V
lated with equation 1.
To evaluate equations 7 and 8, we will need the following
partial derivatives of equation 1.
QUOTIENT
PRODUCT
Operation
out
E(x), the resulting distribution will somewhat resemble a
SUM
) using these relationships.
Gaussian Random Variable Operations
E(x + y) = E(x) + E(y)
V(x + y) = V(x) + V(y)
E(x • y) = E(x) • E(y)
V(x • y) = E(x)
E(y)
out
V(x) = variance(x) = σ
could be quite complicated. Fortunately,
Mean and Variance
2
x V(x) + V(x) x V(y)
E(x) = mean(x)
2
x V(y) +
out
out
is essentially as calcu-
will be slightly differ-
2
Distribution
zero mean x
Gaussian &
Cauchy for
Resulting
Gaussian
Modified
Bessel
and y
out
) and
<<
(7)
(8)