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4x 2 3 for 0 x < 1. Find the absolute extrema, if any, of f on [0, 1), x 1 f (x) = (x 1)Dx (4x 2 3) (4x 2 3)Dx (x 1) (x 1)(8x) (4x 2 3)(1) = (x 1)2 (x 1)2 2 8x 4x 2 + 3 2 8x + 3 8x 4x (2x 3)(2x 1) = = = 2 2 (x 1) (x 1) (x 1)2

General hybrid-parameter analysis of two-port networks was introduced in Section 1.7. Actually, di erent sets of h parameters are de ned, depending on which element of the transistor (E, B, or C) shares a common point with the ampli er input and output terminals. Common-Emitter Transistor Connection From Fig. 3-3(b) and (c), we see that if iC and vBE are taken as dependent variables in the CE transistor con guration, then vBE f1 iB ; vCE iC f2 iB ; vCE 163

6:1 6:2

To nd the critical numbers, set f (x) = 0,

If the total emitter-to-base voltage vBE goes through only small excursions (ac signals) about the Q point, then vBE vbe ; iC ic , and so on. Therefore, after applying the chain rule to (6.1) and (6.2), we have, respectively, @v @v vbe vBE % dvBE BE ib BE vce 6:3 @iB Q @vCE Q @i @i ic iC % diC C ib C vce 6:4 @i @v

The cash disbursements journal is used to record all transactions that re duce cash. These transactions may arise from payments to creditors, from cash purchases, and from the payment of expenses, as well as personal withdrawals. The procedure for recording and posting the cash disbursements journal parallels that of the cash receipts journal: 1. A check is written each time a payment is made; the check num bers provide a convenient reference, and they help in controlling cash and in reconciling the bank account. 2. The cash credit column is posted in total to the general ledger at the end of the month. 3. Debits to Accounts Payable represent cash paid to creditors. These individual amounts will be posted to the creditors accounts in the ac counts payable subsidiary ledger. At the end of the month, the total of the accounts payable column is posted to the general ledger. 4. The Sundry column is used to record debits for any account that cannot be entered in the other special columns. These would include pur chases of equipment, inventory, payment of expenses, and cash with drawals. Each item is posted separately to the general ledger. The total of the Sundry column is not posted.

The four partial derivatives, evaluated at the Q point, that occur in (6.3) and (6.4) are called CE hybrid parameters and are denoted as follows: @v vBE Input resistance hie BE % 6:5 @iB Q iB Q @v vBE Reverse voltage ratio hre BE % 6:6 @vCE Q vCE Q @i i 6:7 Forward current gain hfe C % C @iB Q iB Q @i @ iC Output admittance hoe C % 6:8 @v v

Let us apply the rst-derivative test (Theorem 23.4), f (x) =

The equivalent circuit for (6.3) and (6.4) is shown in Fig. 6-1(a). The circuit is valid for use with signals whose excursion about the Q point is su ciently small so that the h parameters may be treated as constants.

hoe (S)

3 1 2(x 3 ) 2(x 1 ) (2x 3)(2x 1) 2 2 = 4(x 2 )(x 2 ) = 2 2 2 (x 1) (x 1) (x 1)

ie + hrb Lcb _ B (b) CB small-signal equivalent circuit hfb ie hob (S)

Fig. 6-1

Some companies, primarily for convenience, prefer to record all cash transactions (receipts and disbursements) in one journal. This combina tion cash journal uses basically the same account columns as the cash re ceipts and cash disbursements journals, but with a different arrangement of accounts. This journal makes it easier to keep track on a day-to-day basis of changes in the Cash account, since the debit and credit to Cash are adja cent to one another.