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Figure 811 illustrates how, on a large scale, the i-v characteristic of a typical diode may be approximated by an open circuit when vD < 0 and by a short circuit when vD 0 (recall the i-v curves of the ideal short and open circuits presented in 2) The analysis of a circuit containing a diode may be greatly simpli ed by using the short-circuit open-circuit model From here on, this diode model will
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iD (mA)
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be known as the ideal diode model In spite of its simplicity, the ideal diode model (indicated by the symbol shown in Figure 811) can be very useful in analyzing diode circuits
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Actual diode characteristic
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In the remainder of the chapter, ideal diodes will always be represented by the lled (black) triangle symbol shown in Figure 811
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vD (V)
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Consider the circuit shown in Figure 812, which contains a 15-V battery, an ideal diode, and a 1-k resistor A technique will now be developed to determine whether the diode is conducting or not, with the aid of the ideal diode model Assume rst that the diode is conducting (or, equivalently, that vD 0) This enables us to substitute a short circuit in place of the diode, as shown in Figure 813, since the diode is now represented by a short circuit, vD = 0 This is consistent with the initial assumption (ie, diode on ), since the diode is assumed to conduct for vD 0 and since vD = 0 does not contradict the assumption The series current in the circuit (and through the diode) is iD = 15/1,000 = 15 mA To summarize, the assumption that the diode is on in the circuit of Figure 813 allows us to assume a positive (clockwise) current in the circuit Since the direction of the current and the diode voltage are consistent with the assumption that the diode is on (vD 0, iD > 0), it must be concluded that the diode is indeed conducting
+ vD + 15 V _ 1 k iD 15 V + _ 1 k iD + vD _
+ vD _ Circuit models for vD 0 (short) and vD < 0 (open) + vD _
Symbol for ideal diode
Figure 811 Large-signal on-off diode model
Figure 812 Circuit containing ideal diode
Figure 813 Circuit of Figure 812, assuming that the ideal diode conducts
Suppose, now, that the diode had been assumed to be off In this case, the diode would be represented by an open circuit, as shown in Figure 814 Applying KVL to the circuit of Figure 814 reveals that the voltage vD must equal the battery voltage, or vD = 15 V, since the diode is assumed to be an open circuit and no current ows through the circuit Equation 88 must then apply 15 = vD + 1,000iD = vD (88)
+ vD _ + 15 V _ 1 k iD
But the result vD = 15 V is contrary to the initial assumption (ie, vD < 0) Thus, assuming that the diode is off leads to an inconsistent answer Clearly, the assumption must be incorrect, and therefore the diode must be conducting This method can be very useful in more involved circuits, where it is not quite so obvious whether a diode is seeing a positive or a negative bias The method is particularly effective in these cases, since one can make an educated guess whether the diode is on or off and solve the resulting circuit to verify the
Figure 814 Circuit of Figure 812, assuming that the ideal diode does not conduct
8
Semiconductors and Diodes
correctness of the initial assumption Some solved examples are perhaps the best way to illustrate the concept
F O C U S O N M E T H O D O L O G Y
Determining the Conduction State of an Ideal Diode 1 Assume a diode conduction state (on or off) 2 Substitute ideal circuit model into circuit (short circuit if on, open circuit if off) 3 Solve for diode current and voltage using linear circuit analysis techniques 4 If the solution is consistent with the assumption, then the initial assumption was correct; if not, the diode conduction state is opposite to that initially assumed For example, if the diode has been assumed to be off but the diode voltage computed after replacing the diode with an open circuit is a forward bias, then it must be true that the actual state of the diode is on
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