Fundamentals-of-Microelectronics-Behzad-Razavi.pdf

Example 316 plot the inputoutput characteristic of

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Example 3.16 Plot the input/output characteristic of the circuit shown in Fig. 3.18(a) using the constant-voltage diode model. Solution We begin with , predicting intuitively that is on. We also (blindly) assume that
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 78 (1) 78 Chap. 3 Diode Models and Circuits D 1 V D,on R out V in V 1 X R = in V R 1 D 2 Y V B = 2 V R 1 V D,on V B X Y 2 I R2 = I R1 I = 1 out V V D,on R = in V R 1 V B X Y 2 out V D 1 R out V in V 1 X R 1 D 2 Y V B D 1 R out V in V 1 X R 1 D 2 Y V B = 2 V = V D,on V out V in V D,on D 1 turns off. D 1 R out V in V 1 X R 1 D 2 Y V B = 2 V V out V in V D,on (c) (a) (b) (d) (e) (f) (g) (h) Figure 3.18 (a) Diode circuit, (b) possible equivalent circuit for very negative inputs, (c) simplified circuit, (d) equivalent circuit, (e) equivalent circuit for , (f) section of input/output characteristic, (g) equivalent circuit, (f) complete input/output characteristic. is on, thus reducing the circuit to that in Fig. 3.18(b). The path through and creates a difference of between and , i.e., . This voltage difference also appears across the branch consisting of and , yielding (3.27) and hence (3.28) That is, is independent of . We must now analyze these results to determine whether they agree with our assumptions regarding the state of and . Consider the current flowing through : (3.29)
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 79 (1) Sec. 3.4 Large-Signal and Small-Signal Operation 79 (3.30) which approaches for . The large value of and the constant value of indicate that the branch consisting of and carries a large current with the direction shown. That is, must conduct current from its cathode to it anode, which is not possible. In summary, we have observed that the forward bias assumption for translates to a current in a prohibited direction. Thus, operates in reverse bias for . Redrawing the circuit as in Fig. 3.18(c) and noting that , we have (3.31) We now raise and determine the first break point, i.e., the point at which turns off or turns on. Which one occurs first? Let us assume turns off first and obtain the corresponding value of . Since is assumed off, we draw the circuit as shown in Fig. 3.18(d). Assuming that is still slightly on, we recognize that at , approaches zero, yielding a zero current through , , and hence . The diode therefore turns off at . We must now verify the assumption that remains off. Since at this break point, , the voltage at node is equal to whereas the cathode of is at [Fig. 3.18(e)]. In other words, is indeed off. Fig. 3.18(f) plots the input-output characteristic to the extent computed thus far, revealing that after the first break point because the current flowing through and is equal to zero. At what point does turn on? The input voltage must exceed by . Before turns on, , and ; i.e., must reach , after which the circuit is configured as shown in Fig. 3.18(g). Consequently, (3.32) Figure 3.18(h) plots the overall result, summarizing the regions of operation.
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