Supplement to Logic and Computer Design Fundamentals 3rd Edition 1 CMOS CIRCUITS elected topics not covered in the third edition of Logic and Computer Design Fundamentals are provided here for optional coverage and for self study if desired This material fits well with the desired coverage in some programs but not may not fit within others due to time constraints or local preferences This supplement referenced in Chapter 2 as a part of the coverage Other Gate Types presents a functional view of the implementation of gates as CMOS electronic circuits It is particularly appropriate for coverage by electrical or computer engineering students S So far we have dealt largely with implementing logic circuits in terms of gates In this supplement we briefly explore implementing the gates themselves using CMOS technology In addition we study how structures other than primitive logic gates can be implemented directly in terms of electronic elements called transistors CMOS implementation is important because we often design CMOS logic from Boolean equations directly to the transistor level skipping the logic gate level Switch Models for CMOS Transistors CMOS technology employs two types of transistor n channel and p channel The two differ in the characteristics of the semiconductor materials used in their implementation and in the mechanism governing the conduction of a current through them Most important to us however is the difference in behavior of the two types of transistor We will model this behavior using switches controlled by voltages corresponding to logic 0 and logic 1 Such a model ignores complex electronic devices and captures only logical behavior The symbol for an n channel transistor is shown in Figure 1 a The transistor has three terminals the gate G the source S and the drain D as shown in Figure 1 b The voltage applied between G and S determines whether a path for current to flow exists between D and S If a path exists we say that the transistor is 1 Pearson Education 2004 All rights reserved 1 D G X X X S b a X X c d FIGURE 1 Symbol and Switch Model for n Channel Transistor ON and if a path does not exist we say that the transistor is OFF The n channel transistor is ON if the applied gate to source voltage is H and OFF if the applied voltage is L Here we will make the usual assumption that a 1 represents the H voltage range and a 0 represents the L voltage range The notion of whether a path for current to flow exists is easily modeled by a switch as shown in Figure 1 c The switch consists of two fixed terminals corresponding to the S and D terminals of the transistor In addition there is a movable contact that depending on its position determines whether the switch is open or closed The position of the contact is controlled by the voltage applied to the gate terminal G Since we are looking at logic behavior this control voltage is represented on the symbol by the input variable X on the gate terminal For an n channel transistor the contact is open no path exists for the input variable X equal to 0 and closed a path exists for the input variable X equal to 1 Such a contact is traditionally referred to as being normally open that is open without a positive voltage applied to activate or close it Figure 1 d shows a shorthand notation for the n channel switch model with the variable X applied This notation represents the fact that a path between S and D exists for X equal to 1 and does not exist for X equal to 0 The symbol for a p channel transistor is shown in Figure 2 a In Figure 2 b the positions of the source S and drain D are seen to be interchanged relative to their positions in the n channel transistor The voltage applied between the gate G and the source S determines whether a path exists between the drain and source Note in Figure 2 a that the negation indicator or bubble appears as a part of the symbol This is because in contrast to the behavior of an n channel transistor a path exists between S and D in the p channel transistor for input variable X equal to 0 at value L and does not exist for input variable X equal to 1 at value H This behavior is represented by the model in Figure 2 c which has a normally S X G X a X D b X X c FIGURE 2 Symbol and Switch Model for p Channel Transistor 2 d closed contact through which a path exists for X equal to 0 No path exists through the contact for X equal to 1 In addition the shorthand notation of the p channel switch model with variable X applied is given in Figure 2 d Since a 0 on input X causes a path to exist through the switch and a 1 on X produces no path the literal shown on the switch is X instead of X Networks of Switches A network made up of switches that model transistors can be used to design CMOS logic The network implements a function F if there is a path through the network for F equal to 1 and no path through the network for F equal to 0 A simple network of p channel transistor switch models is shown in Figure 3 a The function G1 implemented by this network can be determined by finding the input combinations for which a path exists through the network In order for the path to exist through G1 both switches must be closed that is the path exists for X and Y both 1 This implies that X 0 and Y 0 Thus the function G1 of the network is X Y X Y in other words the NOR function In Figure 3 b for function G2 a path exists through the n channel switch model network if either switch is closed that is for X 1 or Y 1 Thus the function G2 is X Y In general switches in series give an AND function and switches in parallel give an OR function The function for the preceding network that models p channel transistors is a NOR function because of the complementation of the variables and the application of DeMorgan s law By using these network functions to produce paths in a circuit that attach logic 1 H or logic 0 L to an output we can implement a logic function on the output as discussed next Fully Complementary CMOS Circuits The subfamily of CMOS circuits that we will now consider has the general structure shown in Figure 4 a Except during transitions there is a path to the output of the circuit F either from the power supply V logic 1 or from ground logic 0 Such a circuit is called static CMOS In order to have a static circuit the transistors must implement networks of switches for both function F and function F In other …
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