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Dharma5 proposed a metric with the following list of situations to be counted: di ci do co gd gc w r = = = = = = = = Number Number Number Number Number Number Number Number of of of of of of of of input data parameters input control parameters output data parameters output control parameters global variables used as data global variables used as control modules called (fan-out) modules calling this module (fan-in)

Obtain the equivalent inductance of the parallel-connected, coupled coils shown in Fig. 14-25.

Theorem 5-1 states that the expected value of the sample mean is the population mean. Theorem 5-2 If a population is infinite and the sampling is random or if the population is finite and sampling 2 is with replacement, then the variance of the sampling distribution of means, denoted by sX , is given by # E [(X where

m)2]

Currents I1 and I2 are selected as shown on the diagram; then Zin V1 =I1 : j!0:3 j!0:043 Z j!0:043 j!0:414 and or Leq is 0.296 H. Zin Z j!0:3 j!0:414 j!0:043 2 j!0:296 11 j!0:414

is the variance of the population. N,

Fig. 14-25

Theorem 5-3 If the population is of size N, if sampling is without replacement, and if the sample size is n then (5) is replaced by

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14.10 For the coupled circuit shown in Fig. 14-26, show that dots are not needed so long as the second loop is passive.

while mX is still given by (4). Note that (6) reduces to (5) as N S `. Theorem 5-4 If the population from which samples are taken is normally distributed with mean m and variance s2, then the sample mean is normally distributed with mean m and variance s2>n. Theorem 5-5 Suppose that the population from which samples are taken has a probability distribution with mean m and variance s2 that is not necessarily a normal distribution. Then the standardized vari# able associated with X, given by # X m s>!n

Dharma s module coupling indicator is the inverse of the sum of the preceding items times a proportionality constant: mc k= di 2 ci do 2 co gd 2 gc w r There are two di culties with this metric. One is that an inverse means that the greater the number of situations that are counted, the greater the coupling that this module has with other modules and the smaller will be the value of mc. The other issue is that the parameters and calling counts o er potential for problems but do not guarantee that this module is linked to the inner workings of other modules. The use of global variables almost guarantees that this module is tied to the other modules that access the same global variables.

Z is asymptotically normal, i.e., lim P(Z nS` z)

Fig. 14-26 Currents I1 and I2 are selected as shown. 50 j4 0 5 j10 250 j500 10:96 54:648 A I1 2 j5 j4 24 j45 j4 5 j10 2 j5 50 j4 0 3:92 118:07 908 A I2 Z The value of Z is una ected by the sign on M. Since the numerator determinant for I1 does not involve the coupling impedance, I1 is also una ected. The expression for I2 shows that a change in the coupling polarity results in a 1808 phase shift. With no other phasor voltage present in the second loop, this change in phase is of no consequence.

Theorem 5-5 is a consequence of the central limit theorem, page 112. It is assumed here that the population is infinite or that sampling is with replacement. Otherwise, the above is correct if we replace s> !n in (7) by sX as given by (6).

14.11 For the coupled circuit shown in Fig. 14-27, nd the ratio V2 =V1 which results in zero current I1 .

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