Fig. 1 CMOS Transistor Circuits (a) Inverter Out = NOT In, (b) NORgate C = NOT (A or B)


 Katrina Cross
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1 1 Introduction to TransistorLevel Logic Circuits 1 By Prawat Nagvajara At the transistor level of logic circuits, transistors operate as switches with the logic variables controlling the open or closed state of the switches. Figure 1 shows a transistorlevel diagram of an inverter (Fig. 1 a) and a 2input NORgate (Fig. 1b). The parallel and series structures for the ntype transistor(s) (the structure connecting the output to ground 0 volt for Logic 0) and the ptype transistor(s) (the structure connecting the output to V DD V DD volts for Logic 1), respectively, result in the NOR function of the control variables at the output of the gate. (a) (b) Fig. 1 CMOS Transistor Circuits (a) Inverter Out = NOT In, (b) NORgate C = NOT (A or B) The transistors are the Field Effect Transistors (FET). The terminals of the transistor are source, gate and drain terminals. The logic variables are the input voltages at the gateterminals controlling the switch state. Figure 2 shows a cross section of the transistors diagram of the ptype (left) and ntype (right) transistor. The terminals of the transistors can be connected (wired) by a layer of conductors (metal). The input and output wires are not shown. Fig. 2 CMOS inverter layout Cross Section 1 Figures were taken from presentations with their sources cited in the references. Only for student use.
2 2 Fig.3 CMOS Inverter Circuit and Layout Cross Section Diagram Figure 3 shows the terminal S of the ptype is connected to V DD which is the voltage for Logic 1. The S terminal of the ntype transistor is connected to ground. The D and D of ntype and ptype are connected and an output is wired at the connection. The input is wired to both G terminals. The diagrams include terminals for the substrate (Bulk) voltages for the operation of the transistors. They do not represent the logic variables. Steadystate Circuit model In the ptype transistor, when the gate voltage is 0V a conducting channel is formed between D and S (fieldeffect transistor), that is, the ptype switch is closed (Fig. 4). With the ntype transistor, when the gate voltage is V DD the ntype switch is closed (Fig. 5). The ptype and ntype are complementary with respect to the control logic variables. Fig. 4 CMOS Inverter Steadystate Circuit (V SGp = V DD, V GSn = 0) Fig. 5 CMOS Inverter Steadystate Circuit (V SGp = 0, V GSn = V DD )
3 3 Figure 4 and Figure 5 show the CMOS inverter steadystate output voltage V out due input voltage V in = V GSn, for the ntype and V in = V SGp + V DD, for the ptype. V GSn and V SGp denote the ntype and ptype gate voltages. For the NORgate (Fig. 1), the ptype (top structure) the output C = not A and not B, i.e., when both A and B are logic zero the output is a logic one a series structure. For the ntype (bottom structure), not C = A or B, i.e., the output is a logic zero when either A or B or both is a logic one a parallel structure. The ptype (top structure) and the ntype (bottom structure) are complementary. Switching Electrical Characteristic: This technology is called CMOS. The name MOS transistor, metal oxide silicon, came from the first version of the transistor where metal was used for the gate terminal over silicon dioxide and substrate. Shortly after the early design, polysilicon was used replacing metal. Fig. 6 ntype MOSFET Figure 6 shows the geometry of the gate terminal at which the control logic voltage is applied in charging or discharging the parallel plates of the gate terminal. The channel length L is fixed for a given technology and W varies for different sizes for transistors in the circuit. Box. 1 nmos I ds v.v ds Equations Box 1 shows the equations for I DS as a function of V DS for nmos which consists of two operating regions  nonsaturated and saturated. The transistor is in nonsaturation when V GS  V tn V DS 0 and in saturation when V DS V GS  V tn 0, where V tn is the NMOS threshold voltage. The saturation voltage is when V DSn = V sat = V GS  V tn. The parameter β n is a function of the widthlength ratio (W/L) n and the process parameters the electron mobility μ, the oxide permittivity ε and the oxide thickness t ox.
4 4 (a) nmos I Dn v V DSn (b) pmos I Dp v V SDp Fig. 7 Drain Current v Drain Voltage Characteristics for CMOS Invertor Analysis Figure 7 shows nmos I Dn v.v DSn plot and pmos I Dp v V SDp plot for an analysis of the steadystate characteristic of the CMOS invertor. These characteristic consists of multiple plots correspond to different gate voltages. When the gate voltage is less than the threshold voltage the devices are in the cutoff mode. These are modeled by an open switch in Fig. 4 and Fig. 5. In Fig. 4, the nmos is in cutoff. For the pmos the drain current I Dp is zero but the gate voltage, V SGp = V DD, whose characteristic is the curve B in Fig. 8. The pmos is in nonsaturation region in the vicinity of the origin where V SDp is also zero, hence, V O = V DD  V SDp = V DD. This characteristic of the CMOS technology gives its verylow (no) static power dissipation advantage. Similarly in Fig. 5 the pmos is in nonsaturate with V DSn = 0 and I Dn = 0, V O = V DD  V DSn. Fig. 8 CMOS Switching Inverter Characteristic: Input Voltage v Output Voltage The switching characteristic of the CMOS inverter in terms of V O v V i (Fig. 8) consists of the transitions of the nmos operating regions from the cutoff region, saturated region, saturated region, nonsaturated region and nonsaturated region as the invertor input voltage (nmos gate voltage) varies from 0 to VDD. Table 1 summarizes pmos and nmos transitions of operating regions as the intervals of the input voltage V i, where V TN and V TP denote the threshold voltage for the pmos and nmos, respectively. Recall also that V i = V GSn, and V i = V SGp + V DD. When V i = V It, the critical voltage, both transistors are in the
5 5 saturated region a short circuit occurs between V DD and ground). With the nmos and pmos transistor widths, W n = W p, V It = V DD /2. Table1. Operating Regions of CMOS Transistors V i pmos nmos 0 V i V TN Nonsaturated Cutoff V TN V i V It Nonsaturated Saturated V It Saturated Saturated V It V i V DD  V TP Saturated Nonsaturated V DD  V TP V i Cutoff Nonsaturated Switching Delay and Frequency: Important parameters associating with the performance of logic circuits are the risetime and the falltime of circuit output voltages (logic values) due to input changes. These time durations determine the clock frequency or the clock period of a synchronous digital system, that is, the maximal delay in the switching logic circuit for the output voltages to reach steady state values dictates how fast these values can be updated into registers. Rise time of the RC circuit is defined as the duration for a response voltage across the capacitor, v(t) = 1 e (1/ )t, where = RC is the time constant, to reach 0.9 V (90%) from 0.1 V (10%). Figure 9 shows the capacitor voltage v time. The rise time is approximately ( ) = Fig. 9 Rise Time for RC Circuit Definition
6 6 Fig. 10 Falltime Analysis Circuit Models (a) nmos: Saturated (b) nmos: NonSaturated The CMOS inverter analysis of the fall time involves the circuit models (Fig. 10) where the nmos operates in the saturated region V out V DD  V Tn and then the nonsaturated region 0 < V out V DD  V Tn as the output voltage V out = V DSn transitions (see Fig. 7(a)). Initially, the pmos is in the saturated region with I DSp = 0, and the nmos is in the cutoff where the input V in = V GSn = 0 and V out = V DD. When the input changes from 0 to V DD, the pmos moves to the cutoff state I DSp = 0, and the nmos moves to the saturated region V GS = V DD and a constant I DSn equals to the capacitor current I C (Fig. 10(a)). When the voltage across C L, V out = V DS drops below V DD V Tn the nmos is the nonsaturated region until V out reaches the steadystate value of 0 volt and I DSn reaches 0 Amp. Fig. 11 Risetime Analysis Circuit Models (a) pmos: Saturation (b) pmos: NonSaturation Similarly, the CMOS inverter analysis for the rise time is based on the circuit model shown in Fig. 11, where Fig. 11(a) the nmos is in the cutoff region and the pmos transitions from the saturated region V out V Tp (Fig. 11(a)) to the nonsaturated region V Tp < V out V DD (Fig. 11(b)) as the output voltage V out = V DD  V SDp transitions to steadystate, i.e., V SDp = 0 and I SDp = 0 (see Fig. 7(b)). The results from the above analyses are that the rise time t r =[k/β p V DD ]C L and the fall time t f =[k/β n V DD ]C L. The RC circuit models are used, omitting the saturated and nonsaturated region models, for analyzing the rise time and fall time. In this RCcircuit model t r = R p C L and t f = R n C L, (the time constants are approximately the rise time and fall time with the 2.2 factor included). The resistors R p = k/β p V DD and R n = k/β n V DD are functions of the constant k and β p (or β n ) and V DD. In Box 1, beta varies with the ratio W/L and the mobility μ. Since the mobility μ n = 2μ p, for equal rise time and fall time, t r = t f, β p = β n, which means that (W/L) p = 2(W/L) n. In other words, for a fixed channel length L, an equal risetime and falltime means the pmos width is twice the nmos width (pmos is twice larger than nmos).
7 7 (a) Nonequal Rise/Fall Times (b) Equal Rise/Fall Times Fig. 12 Series Inverters Risetime and Falltime RC Circuit Model Analysis Figure12 shows two inverters in series. The W/L sizing parameters and the equivalent load capacitors are indicated. The rise time is the time from when the input changes from 0V to V DD to the time the output of the circuit reaches 0.9 V DD. Similarly, the fall time is calculated as the time from when the input changes from V DD to 0Vto the time the output of the circuit reaches 0.1V. For the circuit (a) with the load capacitor at the output equals 2C, the rise time t r = (2R)(2C) + R(2C) = 6RC, the first inverter fall time plus the second inverter rise time, where R n = 2R, R p = R, C n = C and C p = C. With the ration (W/L) p = (W/L) n = 2/1 which means that 2β p = β n and R n = 2R p. The fall time for the circuit (a) is t f = R(2C) + (2R)(2C) = 6RC. Similarly for the circuit (b) with the load capacitor at the output equals 3C, the rise time t r = R(3C) + R(3C) = 6RC, the first inverter fall time plus the second inverter rise time, where R n = R, R p = R, C n = C and C p = 2C when (W/L) p = 2/1 and (W/L) n = 4/1. The fall time is t f = R(3C) + R(3C) = 6RC. Power Dissipation: Power dissipation in the CMOS inverter comprises the dynamic capacitive power, the power dissipated during the short circuit condition (see Fig. 8) and the static dissipation due to the leakage current. The dominant dissipation is the capacitive power equals to C L V DD 2 f, where f is the clock frequency determined by the switching delay. References )/Lecture%20notes/Chap162CMOSinvertermodified.pdf
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