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Saturation denotes operation (with jvCE j % 0:2 V and jvBC j % 0:5 V for Si devices) such that maximum collector current ows and the transistor acts much like a closed switch from collector to emitter terminals. [See Figures 3-2(c) and 3-3(c).] Cuto denotes operation near the voltage axis of the collector characteristics, where the transistor acts much like an open switch. Only leakage current (similar to Io of the diode) ows in this mode of operation; thus, iC ICEO % 0 for CB connection, and iC ICBO % 0 for CE connection. Figures 3-2(c) and 3-3(c) indicate these leakage currents. The inverse mode is a little-used, ine cient active mode with the emitter and collector interchanged. The active or linear mode describes transistor operation in the region to the right of saturation and above cuto in Figs. 3-2(c) and 3-3(c); here, near-linear relationships exist between terminal currents, and the following constants of proportionality are de ned for dc currents: IC ICBO IE I ICEO C hFE 1 IB hFB where the thermally generated leakage currents are related by ICEO 1 ICBO 3:3 3:1 3:2

Proof of Theorem A.6 on page 323: If 1 < r < 1, then as n increases without bound, rn shrinks down to zero. Let rn =0 in the formula in Theorem A.5. Proof of Theorem A.7 on page 323: + n . Then S = n + + 3 + 2 + 1 also. Add these two equations, Let S = 1 + 2 + 3 + summing the 2n terms on the right pairwise: (1 + n), (2 + (n 1)), etc. There are n pairs, and each pair has the same sum of n + 1. So the total sum on the right is n(n + 1). Then, since the sum on the left is 2S, the correct value of S must be n(n + 1)/2.

The constant < 1 is a measure of the proportion of majority carriers (holes for pnp devices, electrons for npn) injected into the base region from the emitter that are received by the collector. Equation (3.2) is the dc current ampli cation characteristic of the BJT: Except for the leakage current, the base current is increased or ampli ed times to become the collector current. Under dc conditions KCL gives IE IC IB 3:4

Q k lg n Classification Constant: run time is fixed, and does not depend upon n. Most instructions are executed once, or only a few times, regardless of the amount of information being processed. Logarithmic: when n increases, so does run time, but much more slowly than n does. When n doubles, lg n increases by a constant, but does not double until n increases to n2. Common in programs which solve large problems by transforming them into smaller problems. Linear: run time varies directly with n. Typically, a small amount of processing is done on each element. When n doubles, run time slightly more than doubles. Common in programs which break a problem down into smaller subproblems, solve them independently, and then combine solutions. Quadratic: when n doubles, runtime increases fourfold. Practical only for small problems; typically the program processes all pairs of input (e.g., in a double nested loop). Exponential: when n doubles, run time squares. This is often the result of a natural, brute force solution. Such problems are not computable in a reasonable time when the problem becomes at all large.

which, in conjunction with (3.1) through (3.3), completely describes the dc current relationships of the BJT in the active mode.

The output is:

Example 3.5. Determine and for the transistor of Example 3.1 if leakage currents ( ow due to holes) are negligible and the described charge ow is constant.

{22, 33, 44, 55, 66, 77, 88, 99} search(a, 44): 2 search(a, 50): -1 search(a, 77): 5 search(a, 100): -1

If we assume ICBO ICEO 0, then and iC iE iB 1:602 0:016 0:99 1:602 iE iE i i iB 1:602 0:016 C E 99:125 0:016 iB iB

CHAP. 2]

CHAP. 2]

Example 3.6. A BJT has 0:99; iB IB 25 A, and ICBO 200 nA. Find (a) the dc collector current, (b) the dc emitter current, and (c) the percentage error in emitter current when leakage current is neglected. (a) With 0:99, (3.2) gives Using (3.3) in (3.2) then gives IC IB 1 ICBO 99 25 10 6 99 1 200 10 9 2:495 mA (b) The dc emitter current follows from (3.1): IE (c) IC ICBO 2:495 10 3 200 10 9 2:518 mA 0:99 IC 2:475 2:5 mA 0:99 99 1

The search() method returns the index of the target x: search(a, 44) returns 2, because a[2] = 44; search(a, 77) returns 5, because a[5] = 77. The method returns 1 when the target is not in the array: search(a, 50) returns 1, because 50 is not in the array.

Neglecting the leakage current, we have IC IB 99 25 10 6 2:475 mA giving an emitter-current error of 2:518 2:5 100% 0:71% 2:518 so IE