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Fig. 4-22 By symmetry, IDQ1 IDQ2 . KCL at the source node requires that ISQ IDQ1 IDQ2 2IDQ1 With iG1 0, KVL around the left gate-source loop gives VGSQ1 VSS ISQ RS VSS 2IDQ1 RS Solving (4.2) for VGSQ and equating the result to the right side of (2) gives " # IDQ1 1=2 1 VSS 2IDQ1 RS Vp0 IDSS Rearranging (3) results in a quadratic in IDQ : " # VSS Vp0 Vp0 2 1 VSS Vp0 2 2 0 IDQ1 IDQ1 RS 2RS IDSS 2RS Substituting known values into (4) yields

(4.3)

2 IDQ1 3:04 10 3 IDQ1 2:25 10 6 0

The output is:

We shall sometimes double-subscript voltages and currents to show the terminals that are of interest. Thus, V13 is the voltage across terminals 1 and 3, where terminal 1 is at a higher potential than terminal 3. Similarly, I13 is the current that ows from terminal 1 to terminal 3. As an example, VL in Fig. 1-6(a) could be labeled V12 (but not V21 ). Note also that an active element (either independent or controlled) is restricted to its assigned, or stated, current or voltage, no matter what is involved in the rest of the circuit. Thus the controlled source in Fig. 1-6(a) will provide VL A no matter what voltage is required to do so and no matter what changes take place in other parts of the circuit.

set.isEmpty(): true [FR, US, RU, GB, CN] set.size(): 5 set.contains("GB"): true set.contains("JP"): false set.isEmpty(): false [FR, US, RU, BR, GB, CN] [US, RU, BR, GB, CN] US RU BR GB CN

To write a procedure to perform this calculation, one might write a program to do the following: Set SUM and SUMSQUARES equal to 0.0 Set n = size of the array of scores Start with the first score, and continue until all the scores have been processed Set SUM = SUM + score Set SUMSQUARES = SUMSQUARES + score2 End of loop Set MEAN = SUM/n Return the SquareRoot of (SUMSQUARES n * MEAN2) / (n 1) This is the recipe, the procedure, the pseudocode, for calculating the standard deviation of an array of numbers. Here is a Java class called Sd that implements such a procedure in a routine called stdDev: import java.lang.Math; class Sd { public static void main( String args[] ){ float[] numbers = { 3, 5, 7, 9 }; System.out.println( "Std. dev. = " + stdDev( numbers) ); } public static float stdDev( float scores[] ) { float sum = 0; float sumSquares = 0; int n = scores.length; for( int i = 0; i < n; i++ ) { sum = sum + scores[i]; sumSquares = sumSquares + scores[i]*scores[i]; } float mean = sum / n; float variance = (sumSquares - n*mean*mean) / (n - 1); return (float)Math.sqrt( variance ); } }

The network of Fig. 1-8 is a two-port network if I1 I10 and I2 I20 . It can be characterized by the four variables V1 ; V2 ; I1 , and I2 , only two of which can be independent. If V1 and V2 are taken as independent variables and the linear network contains no independent sources, the independent and dependent variables are related by the open-circuit impedance parameters (or, simply, the z parameters) z11 ; z12 ; z21 ; and z22 through the equation set V1 z11 I1 z12 I2 V2 z21 I1 z22 I2

[JP, [US, [BR, [US, []

I1 1 + V1 _ I1 Linear network I2 I2 + V2 _ 2

CHAP. 4]

FR, US, RU, GB, DE, IT, CA] RU, GB] CN] RU, BR, GB, CN]

1:8 1:9

The set object is instantiated at line 3 as a HashSet of String elements. The isEmpty() method is tested at line 4 and again at line 10. At line 5, the collection is loaded with five elements. This is done by the static addAll() method defined in the java.util.Collections class. Note that the order with which the five elements are printed at line 6 is different from the order with which they were added to the set. This illustrates the hash nature of the set. The size() and contains() methods are tested at lines 7 9. The add() method is tested at line 11, and the remove() method is tested at line 13. At line 15, the one-argument toArray() method is used to generate a String array of the same elements that are in the collection. The for loop at lines 16 18 confirms that the array contains the same elements. Lines 20 21 create and load a second set, named g8. This is then used together with the set collection to test the retainAll(), removeAll(), and addAll() methods at lines 23 28. Finally, the clear() method is tested at line 29.

Fig. 1-8