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Chap16-1-NMOS-Inverter.pdf

1. The document discusses NMOS and CMOS inverter circuits. It describes the operation of an NMOS inverter using an enhancement load, depletion load, and resistor load. 2. A CMOS inverter uses both an NMOS and PMOS transistor to provide complementary output signals. It has advantages over NMOS inverters like zero static power dissipation and full voltage swing at the output. 3. The voltage transfer curve of a CMOS inverter is discussed along with the load lines showing the different operating regions of the NMOS and PMOS transistors.

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1 Chapter 16 NMOS Inverter Chapter 16.1 ¾ In the late 70s as the era of LSI and VLSI began, NMOS became the fabrication technology of choice. ¾ Later the design flexibility and other advantages of the CMOS were realized, CMOS technology then replaced NMOS at all level of integration. ¾ The small transistor size and low power dissipation of CMOS circuits, demonstration principal advantages of CMOS over NMOS circuits. MOSFET Digital Circuits NMOS Inverter • For any IC technology used in digital circuit design, the basic circuit element is the logic inverter. • Once the operation and characterization of an inverter circuits are thoroughly understood, the results can be extended to the design of the logic gates and other more complex circuits. MOSFET Digital Circuits
2 n-channel MOSFET n-channel MOSFET n-Channel MOSFET Formulas ‰ Transition points ‰ Saturation region ‰ Nonsaturation region Æ Æ Chap.3 NMOS Inverter • For any IC technology used in digital circuit design, the basic circuit element is the logic inverter. • Once the operation and characterization of an inverter circuits are thoroughly understood, the results can be extended to the design of the logic gates and other more complex circuits.
3 + + VGS= NMOS Inverter ¾ As the input voltage increases (VGS ), the drain to source voltage (VDS) decreases and the transistor inter into the nonsaturation region. ¾ If VI <VTN , the transistor is in cutoff and iD = 0, there is no voltage drop across RD, and the output voltage is Vo=VDD=VDS =VDD=VDS VI <VNT Transistor off VI >VNT Transistor on ¾ If VI >VTN , the transistor is on and initially is biased in saturation region, since VDS < VGS -VTN . + + VGS= =VDD=VDS Cut-off NMOS Inverter with Resister Load ¾ If VI <VTN , the transistor is in cutoff and iD = 0, there is no voltage drop across RD, and the output voltage is Vo=VDD=VDS ¾ As the input is increased slightly above the VTN , the transistor turns on and is in the saturation region. + + VGS= =VDS Saturation Region NMOS Inverter with Resister Load Saturation region Transition Region NMOS Inverter with Resister Load ¾ The Q-point of the transistor moves up the load line. ¾ As the input voltage is further increases and voltage drop across the RD become sufficient to reduce the VDS such that TN GS DS V V V − ≤ + + VGS= =VDS At the transition point, Saturation region
4 ¾ As the input voltage becomes greater than VIt , the Q-point continues to move up the load line, and the transistor becomes biased in the nonsaturation region. Nonsaturation Region Saturation region + + VGS= =VDS Nonsaturation region NMOS Inverter with Resister Load VGS= vI VDS= vO NMOS Inverter with Resister Load + + VGS= =VDS The sharpness of the transition region increases with increasing load resistance. The minimum output voltage, or the logic 0 level, for a high input decreases with increasing load resistance. Input-Output Relationship Summary of NMOS inverter with Resister Load Current-Voltage Relationship Nonsaturation Region Saturation Region Transition Region Æ Example For the NMOS inverter shown in Fig. VDD = 3V. Assume transistor parameters of K’ n = 60 µA/v2, W/L = 5, and VTN = 0.5 V. (a) Find the value of RD such that vo = 0.1 V when vI = 3 V. (b) Using the results of part (a) determine the transition point for the driver transistor
5 n-Channel MOSFET connected as saturated load device • An n-channel enhancement-mode MOSFET with the gate connected to the drain can be used as load device in an NMOS inverter. • Since the gate and drain of the transistor are connected, we have VGS=VDS When VGS=VDS>VTN, a non zero drain current is induced in the transistor and thus the transistor operates in saturation only. And following condition is satisfied. VDS>(VGS-VTN) VDS (sat)= (VDS-VTN) because VGS=VDS or VDS (sat)= (VGS-VTN) In the saturation region the drain current is iD=Kn(VGS-VTN)2 = Kn(VDS-VTN)2 The iD versus vDS characteristics are shown in Figure 16.7(b), which indicates that this device acts as a nonlinear resistor. NMOS Inverter with Enhancement Load ¾ This basic inverter consist of two enhancement-only NMOS transistors ¾ Much more practical than the resister loaded inverter, because the resistors are thousand of times larger size than a MOSFET. NMOS Inverter with Enhancement Load ¾ An n-channel enhancement-mode MOSFET with gate connected to the drain can be used as a load device. Device acts as a Nonlinear resistor !!! Nonlinear resistor !!!
6 NMOS Inverter with Enhancement Load When vI < VTND NMOS Inverter with Enhancement Load When vI > VTND Just greater than NMOS Inverter with Enhancement Load NMOS Inverter with Enhancement Load When vI > VIt
7 NMOS Inverter with Enhancement Load NMOS Inverter with Resister Load + + VGS= =VDS The sharpness of the transition region increases with increasing load resistance. The minimum output voltage, or the logic 0 level, for a high input decreases with increasing load resistance. Input-Output Relationship c.f. NMOS Inverter with Enhancement Load Limitation of Enhancement Load inverter Example P1014
8 Limitation of Enhancement Load inverter Example 16.3 P1014 Example The enhancement-load NMOS inverter shown in Fig. is biased at VDD = 3 V. The transistor parameters are VTND = VTNL = 0.4 V, k’ n = 60 mA/V2, (W/L)D = 16 and (W/L)L = 2. (a) Find vo when (i) vI = 0, (ii) vI = 2.6, (b) Calculate the power dissipated in the inverter when vI = 2.6 V.
9 NMOS Inverter with Depletion Load ¾ This is an alternate form of the NMOS inverter that uses an depletion-mode MOSFET load device with gate and source terminal connected. ¾ This inverter has the advantage of VO= VDD , as well as more abrupt transition region even though the W/L ratio for the output MOSFET is small. Depletion mode : Channel exists even with zero gate voltage. A negative voltage must be applied to the gate to turn the device off. Threshold voltage is always negative. N-Channel Depletion-Mode MOSFET • In n- channel depletion mode MOSFET, an n- channel region or inversion layer exists under the gate oxide layer even at zero gate voltage and hence term depletion mode. • A negative voltage must be applied to the gate to turn the device off. • The threshold voltage is always negative for this kind of device. NMOS Inverter with Depletion Load Gate and source are connected, Since the threshold voltage of load transistor is negative. Load NMOS Inverter with Depletion Load
10 NMOS Inverter with Depletion Load (cont.) Case I: when VI<VTND (drive is cutoff): No drain current conduct in either transistor. That means the load transistor must be in the linear region of the operation and the output current can be expressed as fellows iDL(linear)=KL[2(VGSL - VTNL)VDSL - VDSL 2] Since VGSL=0, and iDL=0 0=-KL[2VTNLVDSL + VDSL 2] Which gives VDSL=0 thus VO= VDD This is the advantage of the depletion load inverter over the enhancement load inverter. When vI > VTND Just greater than NMOS Inverter with Depletion Load NMOS Inverter with Depletion Load This implies that input voltage is constant as the Q-point passes this region. NMOS Inverter with Depletion Load This implies that input and output voltages are not linear in this region.
11 NMOS Inverter with Depletion Load Q1 Q2 (Nonsaturation) More abrupt transition region can be achieved even though the W/L ratio for the output MOSFET is small. NMOS Inverter with Depletion Load Example 16.4 P1014 Example 16.4 P1014 See next slide vGS=0 See slide 34
12 Example 16.4 P1014 See next slide vGS=0 Summary of NMOS inverter with Resister Load Current-Voltage Relationship Nonsaturation Region Saturation Region Transition Region Example 16.4 P1014 Design 16.5 P1018
13 Design 16.5 P1018 short Load transistor is in Saturation mode Design 16.5 P1018 (i) (ii) Example 16.14 P1098
14 (i) (ii) Example 16.14 P1098 Example 16.14 P1098 (i) (ii) 1160µW 825µW 200µW Example 16.14 P1098 Depletion Load Resister Load Enhancement Load NMOS Inverter Chapter 16 NMOS Logic Circuit Chapter 16.2
15 NMOS logic circuits are constructed by connecting driver transistor in parallel, series or series-parallel combinations to produce required output logic function NMOS Logic Circuit Logic Gates In 0 1 Out AND Gate OR Gate In 0 1 Out XOR Gate In 0 1 Out In Out NOT Gate Logic Gates NMOS NOR Gate ¾ NMOS NOR gate can be constructed by connecting an additional driver transistor in parallel with a depletion load inverter.
16 NMOS NOR Gate NMOS NOR Gate When all Inputs are at logic 1 When A = B = logic 1 Both driver transistors are switched into nonsaturation region and load transistor is biased in saturation region. Suppose two driver transistors are identical, higher the aspect ratio lower the output. Example 16.7 p1030 NMOS NAND Gate Additional driver transistor connected in Series
17 For the NOR gate the effective width of the drivers transistors doubles. The effective aspect ratio is increased. For the NAND gate the effective length of the driver transistors doubles. The effective aspect ratio is decreased. Parallel combination Series combination NMOS Logic Circuit Concept of Effective Width-to-Length Ratios Design 16.20 p1099 (a) Design 16.20 p1099 (b) (c)
18 ¾ The Fan-in of a gate is the number of its inputs. Thus a four input NOR gate has a fan-in of 4. ¾ Similarly, Fan-Out is the maximum number of similar gates that a gate can drive while remaining within guaranteed specifications. Fan-In and Fan-Out The rate at Transient Analysis of NMOS Inverters ¾The constant current over a wide range of VDS provided by the depletion load implies that this type of inverter switch a capacitive load more rapidly than the other two types inverter configurations. ¾The source of capacitance CT2 and CT3 are the transistor input capacitances and parasitic capacitances due to interconnect lines between the inverter stages. ¾ The raise time is longer because the load capacitor is charged by the current through the smaller load transistor. ¾ The fall time relatively short, because the load capacitor discharges through the large driver transistor. (W/L)L= 1 (W/L)D= 4 0.5pF Transient Analysis of NMOS Inverters Chapter 16 CMOS Inverter Chapter 16.3
19 p-Channel MOSFET p p n p n ¾ In p-channel enhancement device. A negative gate-to-source voltage must be applied to create the inversion layer, or channel region, of holes that, “connect” the source and drain regions. ¾ The threshold voltage VTP for p-channel enhancement-mode device is always negative and positive for depletion-mode PMOS. p-Channel MOSFET Cross-section of p-channel enhancement mode MOSFET Complementary MOS CMOS The most abundant devices on earth ¾ Although the processing is more complicated for CMOS circuits than for NMOS circuits, CMOS has replaced NMOS at all level of integration, in both analog and digital applications. ¾ The basic reason of this replacement is that the power dissipation in CMOS logic circuits is much less than in NMOS circuits.
20 CMOS Properties ‰ Full rail-to-rail swing Î high noise margins z Logic levels not dependent upon the relative device sizes transistors can be minimum size ratio less ‰ Always a path to VDD or GND in steady state Î low output impedance (output resistance in kΩ range) large fan-out. ‰ Extremely high input resistance (gate of MOS transistor is near perfect insulator) nearly zero steady-state input current ‰ No direct path steady-state between power and ground no static power dissipation ‰ Propagation delay function of load capacitance and resistance of transistors Î Î Î Î Î ¾ In the fabrication process, a separate p-well region is formed within the starting n-substrate. ¾ The n-channel MOSFET is fabricated in the p-well region and p-channel MOSFET is fabricated in the n-substrate. CMOS Inverter Steady State Response VDD Rn VOut = 0 VIn = V DD VDD Rp VOut = VDD VIn = 0 CMOS Inverter DD OH OL V V V = = 0 PMOS NMOS PMOS NMOS
21 Voltage Transfer Curve
22 HW solution 16.4
23 CMOS Inverter Load Lines 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 I DN (A) Vout (V) X10 -4 Vin = 1.0V Vin = 1.5V Vin = 2.0V Vin = 2.5V 0.25um, W/Ln = 1.5, W/Lp = 4.5, VDD = 2.5V, VTn = 0.4V, VTp = -0.4V Vin = 0V Vin = 0.5V Vin = 1.0V Vin = 1.5V Vin = 0.5V Vin = 2.0V Vin=1.0V PMOS NMOS Vin=0V Vin=0.5V Vin=2.5V Vin=2.0V Vin=1.5V I DP (A) NMOS off PMOS in non sat NMOS in sat PMOS in non sat NMOS in sat PMOS in sat NMOS in non sat PMOS in sat NMOS in nonsat PMOS off
24 vSDP is small vI and vO relationship as long as NMOS: saturation, PMOS: nonsaturation from below graph vOPt or from above graph vONt vIt B C
25 NMOS: nonsaturation PMOS: off NMOS: nonsaturation PMOS: saturation NMOS: saturation PMOS: saturation NMOS: saturation PMOS: nonsaturation NMOS: off PMOS: nonsaturation Example 16.9 p1041 vIt vOPt vONt For VDD=5V Example 16.9 p1041 vIt vOPt vONt vOPt vONt vIt VDD=5V VDD=10V
26 ¾ The transistor KN is also known as “pull down” device because it is pulling the output voltage down towards ground. ¾ The transistor KP is known as the “pull up” device because it is pulling the output voltage up towards VDD. This property speed up the operation considerably. The static power dissipation during both extreme cases (logic 1 or 0) is almost zero because iDP= iDN= 0. 1 0 0 1 VOut VIn ¾ CMOS inverter: series combination of PMOS and NMOS ¾ To form the input, gates of the two MOSFET are connected. ¾ To form the output, the drains are connected together. (ideal case) Ideally, the power dissipation of the CMOS inverter is zero. Practical device CMOS inverter (∼ nW) NMOS inverter (∼mW) CMOS Inverter in either High or Low State CMOS Inverter Design Consideration ‰ The CMOS inverter usually design to have, 9 This can achieved if width of the PMOS is made two or three times than that of the NMOS device. 9 This is very important in order to provide a symmetrical transition, results in wide noise margin. But (because µN>µP) (1) (2) TP TN V V =       =       L W k L W k P N ' ' ' ' P N k k > ¾ How equation (2) can be satisfied ?
27 NMOS: nonsaturation PMOS: off NMOS: nonsaturation PMOS: saturation NMOS: saturation PMOS: saturation NMOS: saturation PMOS: nonsaturation NMOS: off PMOS: nonsaturation Symmetrical Properties of the CMOS Inverter vOPt vONt 2 DD It V V = p1101 vIt vOPt vONt       = L W k K n N 2 ' (a) (i) Transition points VOPt VONt (ii)
28 Example 16.29 p1101 (b) (i) (ii) Transition points VOPt VONt       = L W k K P P 2 ' Increase W of PMOS ¼ kP increases ¼ VIt moves to right VDD VDD VIn VOut kp=5kn kp=kn kp=0.2kn CMOS Inverter VTC Increase W of NMOS ¼ kN increases ¼ VIt moves to left P N P N DD It W W k k V V for ≈ = → = , 2 VIt ‰ Result from changing kP/kN ratio: ¾ Inverter threshold VIt ≠ VDD/2 ¾ Rise and fall delays unequal ¾ Noise margins not equal ‰Reasons for changing inverter threshold: ¾ Want a faster delay for one type of transition (rise/fall) ¾ Remove noise from input signal: increase one noise margin at expense of the other CMOS Inverter VTC Effects of VIt adjustment Problem 16.31 p1101 (a)
29 Problem 16.31 p1101 vIt Example 16.31 p1101 (b) CMOS inverter currents ¾ When the output of a CMOS inverter is either at a logic 1 or 0, the current in the circuit is zero. ¾ When the input voltage is in the range both transistors are conducting and a current exists in the inverter. CMOS inverter currents ‰ When NMOS transistor is biased in the saturation region ¾ The current in the inverter is controlled by vGSN and the PMOS vSDP adjusts such that iDP = iDN . As long as NMOS transistor is biased in the saturation region the square root of the inverter current is linear function of the input voltage.
30 CMOS inverter currents ‰ When PMOS transistor is biased in the saturation region ¾ The current in the inverter is controlled by vSGP and the NMOS vDSN adjusts such that iDP = iDN . As long as PMOS transistor is biased in the saturation region the square root of the inverter current is linear function of the input voltage. NMOS: saturation PMOS: saturation NMOS: off PMOS: nonsaturation NMOS: saturation PMOS: nonsaturation CMOS inverter currents NMOS: nonsaturation PMOS: off NMOS: nonsaturation PMOS: saturation Problem 16.33 p1102 (a) (b) Power Dissipation ¾ There is no power dissipation in the CMOS inverter when the output is either at logic 0 or 1. However, during switching of the CMOS inverter from low logic 0 to logic 1, current flows and power is dissipated. ¾ Usually CMOS inverter and logic circuit are used to drive other MOS devices by connecting a capacitor across the output of a CMOS inverter. This capacitor must be charged and discharged during the switching cycle.
31 Triode Region NMOS Transistor Capacitances Cox” = Gate-Channel capacitance per unit area(F/m2) CGC = Total gate channel capacitance CGS = Gate-Source capacitance CGD = Gate-Drain capacitance CGSO and CGDO = overlap capacitances (F/m) Saturation Region NMOS Transistor Capacitances ¾ Drain is no longer connected to channel. Cutoff Region NMOS Transistor Capacitances ¾ Conducting channel region is completely gone. CGB = Gate-Bulk capacitance CGBO = Gate-Bulk capacitance per unit width. VDD Rn Vout CL VIn = VDD VDD Rp Vout CL VIn = 0 ¾ Gate response time is determined by the time to charge CL through Rp (discharge CL through Rn) Switch Model of Dynamic Behavior CMOS Inverter
32 ‰ Power has three components ¾ Static power: when input isn’t switching ¾ Dynamic capacitive power: due to charging and discharging of load capacitance ¾ Dynamic short-circuit power: direct current from VDD to Gnd when both transistors are on CMOS Inverter Power ™ Static current: in CMOS there is no static current as long as VIn < VTN or VIn > VDD+VTP ™ Leakage current: determined by “off” transistor ™ Influenced by transistor width, supply voltage, transistor threshold voltages VDD VI<VTN Ileak,N VDD VDD Ileak,P Vo(low) VDD Static Power Consumption CMOS Inverter Power Case I: When the input is at logic 0 PMOS is conducting and NMOS is in cutoff mode and the load capacitor must be charged through the PMOS device. Power dissipation in the PMOS transistor; PP=iLVSDp= iL(VDD-VO) The current and output voltages are related by, iL=CLdvO/dt Similarly the energy dissipation in the PMOS device can be written as the output switches from low to high, 2 2 0 2 0 0 0 0 0 2 1 ) 0 2 ( ) 0 ( , 2 , ) ( DD L P DD L DD DD L P V O L V O DD L P O V O L V O DD L P O O DD L P P V C E V C V V C E C V C E d C d V C E dt dt d V C P E DD DD DD DD = − − − = − = − = − = = ∫ ∫ ∫ ∫ ∞ ∞ ν ν ν ν ν ν ν Dynamic Capacitive Power and Energy stored in the PMOS CMOS Inverter Power the energy stored in the capacitor CL when the output is high. Case II: when the input is high and out put is low: During switching all the energy stored in the load capacitor is dissipated in the NMOS device because NMOS is conducting and PMOS is in cutoff mode. The energy dissipated in the NMOS inverter; The total energy dissipated during one switching cycle; The power dissipated in terms frequency; 2 2 1 DD L N V C E = 2 2 2 2 1 2 1 DD L DD L DD L N P T V C V C V C E E E = + = + = 2 DD L T T T V fC fE P t E P t P E → = → = → ⋅ = This implied that the power dissipation in the CMOS inverter is directly proportional to switching frequency and VDD 2 Dynamic Capacitive Power and Energy stored in the PMOS CMOS Inverter Power
33 ¾ Does not (directly) depend on device sizes ¾ Does not depend on switching delay ¾ Applies to general CMOS gate in which: • Switched capacitances are lumped into CL • Output swings from GND to VDD • Input signal approximated as step function • Gate switches with frequency f f V C P DD L dyn 2 = Dynamic Capacitive Power CMOS Inverter Power Formula for dynamic power ¾ Short-circuit current flows from VDD to GND when both transistors are on saturation mode. VDD VDD Vin Vout ID Imax Imax: depends on saturation current of devices Dynamic Short-Circuit Power CMOS Inverter Power f V C P I V f t t I V f V C P P P P P DD L tot leak DD f r DD DD L tot stat sc dyn tot 2 max 2 ~ 2 +         + + = + + = Inverter Power Consumption Total Power Consumption f V C P DD L dyn 2 = Power Reduction ‰ Reducing dynamic capacitive power ¾ Lower the voltage!! ™ Quadratic effect on dynamic power ¾ Reduce capacitance!! ™ Short interconnect lengths ™ Drive small gate load (small gates, small fan-out) ¾ Reduce frequency!! ™ Lower clock frequency ™ Lower signal activity
34 ‰ Reducing short-circuit current ¾ Fast rise/fall times on input signal ¾ Reduce input capacitance ¾ Insert small buffers to “clean up” slow input signals before sending to large gate ‰ Reducing leakage current ¾ Small transistors (leakage proportional to width) ¾ Lower voltage Power Reduction Chapter 16 CMOS Inverter Noise Margin Chapter 16.3.4 Concept of Noise Margins Noise Margin for low input Noise Margin for high input OLU IL L V V NM − = IH OHU H V V NM − =
35 CMOS Inverter Noise Margins of CMOS when CMOS Inverter Noise Margins of CMOS when If CMOS is symmetrical, CMOS Inverter Noise Margins CMOS Inverter Noise Margins of CMOS when
36 If CMOS is symmetrical, CMOS Inverter Noise Margins CMOS Inverter Noise Margins Summary Noise Margin of a Symmetrical CMOS Inverter Noise Margin for low input Noise Margin for high input OLU IL L V V NM − = IH OHU H V V NM − = Æ P1047 Example 16.11 Chapter 16 CMOS Logic Circuits Chapter 16.4
37 CMOS Logic Circuits ¾ Large scale integrated CMOS logic circuits including watches, calculators, and microprocessors are constructed by using basic CMOS NOR and NAND gates. Therefore, understanding of these basic gates is very important for the designing of very large scale integrated (VLSI) logic circuits. CMOS Logic Circuits ‰ CMOS NOR gate can be constructed by using two parallel NMOS devices and two series PMOS transistors. ¾ The output is at logic 1 when all inputs are low. ¾ For all other possible inputs, output is low or at logic 0. CMOS Logic Circuits ‰ CMOS NAND gate can be constructed by using two parallel PMOS devices and two series NMOS transistors. ¾ The is at logic 0 when all inputs are high. ¾ For all other possible inputs, output is high or at logic 1. CMOS Logic Circuits How can we design CMOS NOR symmetrical gate? To obtained symmetrical switching times for the high-to-low and low-to-high output transitions, the effective conduction (design) parameters of the composite PMOS and composite NMOS device must be equal. For the CMOS NOR gate, In order to get the symmetrical switching properties, the width to length ratio of PMOS transistor must be approximately eight times that of the NMOS device. For asymmetrical case, switching time is longer!!
38 CMOS Logic Circuits How can we design CMOS NOR symmetrical gate? Only one PMOS and one NMOS are working. Two PMOS and two NMOS are working. For the NOR gate the effective width of the drivers transistors doubles. The effective aspect ratio is increased. For the NAND gate the effective length of the driver transistors doubles. The effective aspect ratio is decreased. Parallel combination Series combination Concept of Effective Width to Length Ratios
39 CMOS Logic Circuits Fan-In and Fan-Out ¾ Fan-in of a gate is the number of its inputs. Thus a four input NOR gate has a fan-In of 4. ¾ Fan-Out is the maximum number of load gates that may be connected to the output. ™ Each additional load gate increases the load capacitance their must be charge and discharge as the driver gate changes state. This place a practical limit on the maximum allowable number of load gates. However, Switching Time and Propagation Delay Time • The dynamic performance of a logic circuit family is characterized by propagation delay of its basic inverter. The propagation delay time is define as the average of low- to-high propagation delay time and the high-to-low propagation delay time. • The propagation delay time is directly proportional to the switching time and increases as the Fan-out increases. Therefore, the maximum Fan- out is limited by the maximum acceptable propagation delay time. Each additional load gate increases the load capacitance their must be charge and discharge as the driver gate changes state. This place a practical limit on the maximum allowable number of load gates. CMOS Logic Circuits Switching Time and Propagation Delay Time Propagation Delay Time Switching Time Propagation Delay Estimate • The two modes of capacitive charging/discharging that contribute to propagation delay
40 Switch-level model Delay estimation using switch- level model (for general RC circuit): Rn CL [ ]         = − = = = − = → = = → = ∫ 0 1 0 1 0 1 ln ) ln( ) ln( 1 0 V V RC V V RC t dV V RC t t t dV V RC dt R V I dV I C dt dt dV C I p V V p Switch-level model • For fall delay tphl, V0=Vcc, V1=Vcc/2 L p plh L n phl p CC CC p C R t C R t RC t V V RC V V RC t 69 . 0 69 . 0 ) 5 . 0 ln( ln ln 2 1 0 1 = = =         =         = Standard RC-delay equations Chapter 16 Transmission Gates Chapter 16.6 Transmission Gates ¾ Use of transistors as switches between driving circuits and load circuits are called transmission gates because switches can transmit information from one circuit to another. ¾ NMOS and CMOS transmission gate.
41 ¾ The bias applied to the transistor determines which terminal acts as the drain and which terminal acts as the source. ¾ ¾ As an Open Switch When gate voltage φ =0, the n-channel transistor is cut-off and the transistor acts as an open switch As an Open Switch Drain Source Gate If φ =VDD, vI=VDD, and vO is initially (t=0) zero, terminal a acts as the drain since its bias is VDD. terminal b acts as the source since its bias is zero. Current enters the drain from the input charging up the capacitor. VDD zero =VDD @ High input As CL charges up and Vo increases, the gate to source voltage decreases. When the gate to source voltage VGS become equal to threshold voltage VTN, the capacitance stop charging and current goes to zero. This implies that the VO=VO(max) when VGS=VTN Or VO(max) = VDD-VTN This implies that output voltage never will be equal to VDD. ; rather it will be lower by VTN. This is one of the disadvantage of an NMOS transmission gate when VI=high As an Open Switch Drain Source Gate VDD zero =VDD @ High input
42 Characteristics of NMOS transmission gate (at low input) • When VI=0 and φ=VDD and VO=VDD-VTN at t=o (initially). It is to be noted that in the present case terminal b acts as the drain and terminal a acts as the source. Under these conditions the gate to source voltage is, VGS=φ-VI VGS=VDD-o vGS=vDD This implies that value of VGS is constant. In this case the capacitor is fully discharge to zero as the drain current goes to zero. VO=0 This implies that the NMOS transistor provide a “good” logic 0 when VI=low VDD-Vt G S D source drain gate As an Open Switch Source Drain Gate When φ =VDD, vI=0, and vO =VDD-VTN, at t=0, terminal a acts as the source since its bias is zero. terminal b acts as the drain since its bias is high. Capacitor discharges as current enters the drain. Stop discharging drain current goes zero. zero VDD-VTN =VDD @ Low input VDD-VTN “Good” logic 0 when VI=low In this case the capacitor is fully discharge to zero as the drain current goes to zero. VO=0 This implies that the NMOS transistor provide a “good” logic 0 when VI=low ‰ Why NMOS transmission gate does not remain in a static condition? ¾ The reverse leakage current due to reverse bias between terminal b and ground begins to discharge the capacitor, and the circuit does not remain in a static condition. VDD-VTN Source Drain Gate Example 16.13 p1060
43 VO(max) = VDD-VTN (a) Example 16.52 p1106
44 Example 16.52 p1106 (b) ¾ A CMOS transmission gate can be constructed by parallel combination of NMOS and PMOS transistors, with complementary gate signals. ¾ The main advantage of the CMOS transmission gate compared to NMOS transmission gate is to allow the input signal to be transmitted to the output without the threshold voltage attenuation. Charging path NMOS terminal a acts as the drain terminal b acts as the source PMOS terminal c acts as the drain terminal d acts as the source Case I: Input High condition In order to charge the load capacitor, current enters the NMOS drain and the PMOS source. NMOS VGSN continuously change PMOS VGSP remains constant Source Drain Source Drain In PMOS, IDP=0, when VSDP=0, which would be possible only, if, VO=VI=5V logic ‘1’ is unattenuated Case II: Input Low condition NMOS terminal a acts as the source terminal b acts as the drain PMOS terminal c acts as the source terminal d acts as the drain In order to discharge the load capacitor, current enters the NMOS drain and the PMOS source. NMOS PMOS Finally, VO=0, which is a good logic 0. O O O SGP v v v v = − = − = 0 φ Discharging path Drain Source Drain Source
45 CMOS transmission gate remains in a dynamic condition. ¾ If VO=VDD and φ=0, then NMOS substrate to terminal ‘b’ pn junction is reverse biased and capacitor CL can discharge. ¾ If VO=0, then the PMOS terminal c- to-substrate pn junction is reverse biased and capacitance CL can be charge to a positive voltage. ¾ This implies that the output high or low of CMOS transmission gate circuit do not remain constant with time (dynamic behavior). Test your understanding p1067 NMOS conducting for 0 ≤ vI ≤ 4.2V NMOS conducting for 0 ≤ t ≤ 8.4 sec NMOS cutoff for 8.4 ≤ t ≤ 10 sec Exercise 16.29 (a) Given that VTN=0.8V, VTP=-1.2V. When φ = 5V, input vI varies with time as vI =0.5t for 0 ≤ t ≤ 10 sec. Let VO=0 and CL=1pF. Determine the range of the times that the NMOS and PMOS devices are conducting or cutoff. p10XX
46 HW solution
47 Chapter 16 Sequential Logic Circuit Chapter 16.7 • The logic circuits considered thus far are called combinational logic circuits. Their output depend only on the present value of input. This implies that these circuit do not have memory. • Another class of the logic circuit that incorporate memory are called sequential logic circuits; that is, their output depend not only the present value of the input, but also on the previous history of inputs. Shift registers and flip-flops are typical examples of such circuits.
48 • A shift register can be constructed by the combination of transmission gates and inverters. • If VI=VDD and φ1=VDD, then a logic 1=VDD-VTN would exist at VO1. • The CL charges through MN1. As VO1 goes high, VO2 goes low. If φ2 is high low will transmitted through MN2 and VO4 would be at logic 1. Thus logic 1 shifted from input to output. In shift register the input signal is transmitted, or shifted, from the input to the output during one clock cycle. NMOS Suppose VDD=5V and VTN=1V. At t=t1 , V1=φ1=5V, vO2 goes low At this time MN2 is still in cutoff (φ2=0) even though input of MN2 has been changed. This implies that vO3 and vO4 depend on the previous history. Similarly at t=t3, φ2 is high, and logic 0 at vO2 is transmitted to vO3, which force vO4 to 5V. Thus the input information is transmitted to output during one clock cycle. Transparent mode Hold mode Dynamic Shift Registers at Various Time • Consider when t=t4, vI=0, and φ1=5V, so VO1=0 and VO2=5V.Vo3 and Vo4 depend on previous history • At t=t5, φ2=5V, vO3 charges to VDD- VTN=4V and VO4 goes low. • Thus logic 0 is shifted (transmitted) from input to output. • Also note that vO3 and vO4 are depend on previous history of their inputs instead of current inputs (they are having memory). Dynamic Shift Registers at Various Time NMOS shift register is also dynamic (why?) • The output charged capacitor does not remain constant with time because it is discharge through the transmission gate transistor. • In order to prevent logic errors, the clock signal period T must be small compared to effective RC discharge time constant. For example at t = t2, VO1=4V, φ1=0 and MN1 is cutoff.VO1 will start to to decay and VO2 will begin to increase.
49 CMOS Dynamic Shift Registers • The operation of the CMOS shift register is similar to the NMOS register except for the voltage levels. • For example, when vI=φ1=VDD. Then vO1=VDD and vO2=0. when φ2 goes high, then vo3 switch to zero, vo4=vDD. • Thus input signal is shifted to the output during one clock cycle. NMOS R-S Flip Flop • Flip- flops are bistable circuits usually formed by cross-coupling two NOR gates. The output of the two NOR circuits are connected back to the inputs of the opposite NOR gates. When S=logic 1 and R=logic 0 =logic 0 and Q=logic 1=VDD Transistor M2 is then also biased in conducting state. If S returns to logic 0, nothing in the circuit can force a change and flip flop stores the previous logic states, although M1 turned off (but M2 remains tuned on). Q NMOS R-S Flip Flop (cont.) • When R=logic 1 and S=logic 0 • Then M4 turn on so output goes low. With S=Q=Logic 0, both M1 and M2 are cutoff and goes high. The flip-flop is now in reset state. • If both S and R inputs go high. Then both outputs Q and would go low, which implies that output is not complementary. This condition is forbidden or nonallowed condition. Q CMOS R-S Flip-Flop • The operation sequence of CMOS R-S flip flop is same as NMOS. • For example: If S = logic 1 and R = logic 0, then MN1, is turned on, Mp1, is cut off, and goes low. • With = R = logic 0, then both MN3 and MN4 are cut off, both MP3 and Mp4 are biased in a conducting state so that the output Q goes high. • With Q = logic 1, MN2 is biased on, Mp2 is biased off, and the flip-flop is in a set condition. • When S goes low, MN1, turns off, but MN2 remains conducting, so the state of the flip-flop does not change. • Q Q
50 CMOS R-S Flip-Flop (cont.) • When S = logic 0 and R = logic 1, then output Q is forced low, output goes high, and the flip- flop is in a reset condition. • Again, a logic 1 at both S and R is considered to be a forbidden or a nonallowed condition, since the resulting outputs are not complementary. Q Static vs Dynamic Storage • Static storage – preserve state as long as the power is on – have positive feedback (regeneration) with an internal connection between the output and the input – useful when updates are infrequent (clock gating) • Dynamic storage – store state on parasitic capacitors – only hold state for short periods of time (milliseconds) – require periodic refresh – usually simpler, so higher speed and lower power Static D-type Flip-Flop • A D-type flip-flop is used to provide a delay. The logic bit on the D input is transferred to the output at the next clock pulse. When the CMOS transmission gate turn off (φ=0), the pn junction in the MN1 transmission gate transistor is reverse biased.

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Chap16-1-NMOS-Inverter.pdf

  • 1.
    1 Chapter 16 NMOS Inverter Chapter16.1 ¾ In the late 70s as the era of LSI and VLSI began, NMOS became the fabrication technology of choice. ¾ Later the design flexibility and other advantages of the CMOS were realized, CMOS technology then replaced NMOS at all level of integration. ¾ The small transistor size and low power dissipation of CMOS circuits, demonstration principal advantages of CMOS over NMOS circuits. MOSFET Digital Circuits NMOS Inverter • For any IC technology used in digital circuit design, the basic circuit element is the logic inverter. • Once the operation and characterization of an inverter circuits are thoroughly understood, the results can be extended to the design of the logic gates and other more complex circuits. MOSFET Digital Circuits
  • 2.
    2 n-channel MOSFET n-channelMOSFET n-Channel MOSFET Formulas ‰ Transition points ‰ Saturation region ‰ Nonsaturation region Æ Æ Chap.3 NMOS Inverter • For any IC technology used in digital circuit design, the basic circuit element is the logic inverter. • Once the operation and characterization of an inverter circuits are thoroughly understood, the results can be extended to the design of the logic gates and other more complex circuits.
  • 3.
    3 + + VGS= NMOS Inverter ¾ Asthe input voltage increases (VGS ), the drain to source voltage (VDS) decreases and the transistor inter into the nonsaturation region. ¾ If VI <VTN , the transistor is in cutoff and iD = 0, there is no voltage drop across RD, and the output voltage is Vo=VDD=VDS =VDD=VDS VI <VNT Transistor off VI >VNT Transistor on ¾ If VI >VTN , the transistor is on and initially is biased in saturation region, since VDS < VGS -VTN . + + VGS= =VDD=VDS Cut-off NMOS Inverter with Resister Load ¾ If VI <VTN , the transistor is in cutoff and iD = 0, there is no voltage drop across RD, and the output voltage is Vo=VDD=VDS ¾ As the input is increased slightly above the VTN , the transistor turns on and is in the saturation region. + + VGS= =VDS Saturation Region NMOS Inverter with Resister Load Saturation region Transition Region NMOS Inverter with Resister Load ¾ The Q-point of the transistor moves up the load line. ¾ As the input voltage is further increases and voltage drop across the RD become sufficient to reduce the VDS such that TN GS DS V V V − ≤ + + VGS= =VDS At the transition point, Saturation region
  • 4.
    4 ¾ As theinput voltage becomes greater than VIt , the Q-point continues to move up the load line, and the transistor becomes biased in the nonsaturation region. Nonsaturation Region Saturation region + + VGS= =VDS Nonsaturation region NMOS Inverter with Resister Load VGS= vI VDS= vO NMOS Inverter with Resister Load + + VGS= =VDS The sharpness of the transition region increases with increasing load resistance. The minimum output voltage, or the logic 0 level, for a high input decreases with increasing load resistance. Input-Output Relationship Summary of NMOS inverter with Resister Load Current-Voltage Relationship Nonsaturation Region Saturation Region Transition Region Æ Example For the NMOS inverter shown in Fig. VDD = 3V. Assume transistor parameters of K’ n = 60 µA/v2, W/L = 5, and VTN = 0.5 V. (a) Find the value of RD such that vo = 0.1 V when vI = 3 V. (b) Using the results of part (a) determine the transition point for the driver transistor
  • 5.
    5 n-Channel MOSFET connectedas saturated load device • An n-channel enhancement-mode MOSFET with the gate connected to the drain can be used as load device in an NMOS inverter. • Since the gate and drain of the transistor are connected, we have VGS=VDS When VGS=VDS>VTN, a non zero drain current is induced in the transistor and thus the transistor operates in saturation only. And following condition is satisfied. VDS>(VGS-VTN) VDS (sat)= (VDS-VTN) because VGS=VDS or VDS (sat)= (VGS-VTN) In the saturation region the drain current is iD=Kn(VGS-VTN)2 = Kn(VDS-VTN)2 The iD versus vDS characteristics are shown in Figure 16.7(b), which indicates that this device acts as a nonlinear resistor. NMOS Inverter with Enhancement Load ¾ This basic inverter consist of two enhancement-only NMOS transistors ¾ Much more practical than the resister loaded inverter, because the resistors are thousand of times larger size than a MOSFET. NMOS Inverter with Enhancement Load ¾ An n-channel enhancement-mode MOSFET with gate connected to the drain can be used as a load device. Device acts as a Nonlinear resistor !!! Nonlinear resistor !!!
  • 6.
    6 NMOS Inverter withEnhancement Load When vI < VTND NMOS Inverter with Enhancement Load When vI > VTND Just greater than NMOS Inverter with Enhancement Load NMOS Inverter with Enhancement Load When vI > VIt
  • 7.
    7 NMOS Inverter withEnhancement Load NMOS Inverter with Resister Load + + VGS= =VDS The sharpness of the transition region increases with increasing load resistance. The minimum output voltage, or the logic 0 level, for a high input decreases with increasing load resistance. Input-Output Relationship c.f. NMOS Inverter with Enhancement Load Limitation of Enhancement Load inverter Example P1014
  • 8.
    8 Limitation of EnhancementLoad inverter Example 16.3 P1014 Example The enhancement-load NMOS inverter shown in Fig. is biased at VDD = 3 V. The transistor parameters are VTND = VTNL = 0.4 V, k’ n = 60 mA/V2, (W/L)D = 16 and (W/L)L = 2. (a) Find vo when (i) vI = 0, (ii) vI = 2.6, (b) Calculate the power dissipated in the inverter when vI = 2.6 V.
  • 9.
    9 NMOS Inverter withDepletion Load ¾ This is an alternate form of the NMOS inverter that uses an depletion-mode MOSFET load device with gate and source terminal connected. ¾ This inverter has the advantage of VO= VDD , as well as more abrupt transition region even though the W/L ratio for the output MOSFET is small. Depletion mode : Channel exists even with zero gate voltage. A negative voltage must be applied to the gate to turn the device off. Threshold voltage is always negative. N-Channel Depletion-Mode MOSFET • In n- channel depletion mode MOSFET, an n- channel region or inversion layer exists under the gate oxide layer even at zero gate voltage and hence term depletion mode. • A negative voltage must be applied to the gate to turn the device off. • The threshold voltage is always negative for this kind of device. NMOS Inverter with Depletion Load Gate and source are connected, Since the threshold voltage of load transistor is negative. Load NMOS Inverter with Depletion Load
  • 10.
    10 NMOS Inverter withDepletion Load (cont.) Case I: when VI<VTND (drive is cutoff): No drain current conduct in either transistor. That means the load transistor must be in the linear region of the operation and the output current can be expressed as fellows iDL(linear)=KL[2(VGSL - VTNL)VDSL - VDSL 2] Since VGSL=0, and iDL=0 0=-KL[2VTNLVDSL + VDSL 2] Which gives VDSL=0 thus VO= VDD This is the advantage of the depletion load inverter over the enhancement load inverter. When vI > VTND Just greater than NMOS Inverter with Depletion Load NMOS Inverter with Depletion Load This implies that input voltage is constant as the Q-point passes this region. NMOS Inverter with Depletion Load This implies that input and output voltages are not linear in this region.
  • 11.
    11 NMOS Inverter withDepletion Load Q1 Q2 (Nonsaturation) More abrupt transition region can be achieved even though the W/L ratio for the output MOSFET is small. NMOS Inverter with Depletion Load Example 16.4 P1014 Example 16.4 P1014 See next slide vGS=0 See slide 34
  • 12.
    12 Example 16.4 P1014 Seenext slide vGS=0 Summary of NMOS inverter with Resister Load Current-Voltage Relationship Nonsaturation Region Saturation Region Transition Region Example 16.4 P1014 Design 16.5 P1018
  • 13.
    13 Design 16.5 P1018 short Loadtransistor is in Saturation mode Design 16.5 P1018 (i) (ii) Example 16.14 P1098
  • 14.
    14 (i) (ii) Example 16.14 P1098Example 16.14 P1098 (i) (ii) 1160µW 825µW 200µW Example 16.14 P1098 Depletion Load Resister Load Enhancement Load NMOS Inverter Chapter 16 NMOS Logic Circuit Chapter 16.2
  • 15.
    15 NMOS logic circuitsare constructed by connecting driver transistor in parallel, series or series-parallel combinations to produce required output logic function NMOS Logic Circuit Logic Gates In 0 1 Out AND Gate OR Gate In 0 1 Out XOR Gate In 0 1 Out In Out NOT Gate Logic Gates NMOS NOR Gate ¾ NMOS NOR gate can be constructed by connecting an additional driver transistor in parallel with a depletion load inverter.
  • 16.
    16 NMOS NOR GateNMOS NOR Gate When all Inputs are at logic 1 When A = B = logic 1 Both driver transistors are switched into nonsaturation region and load transistor is biased in saturation region. Suppose two driver transistors are identical, higher the aspect ratio lower the output. Example 16.7 p1030 NMOS NAND Gate Additional driver transistor connected in Series
  • 17.
    17 For the NORgate the effective width of the drivers transistors doubles. The effective aspect ratio is increased. For the NAND gate the effective length of the driver transistors doubles. The effective aspect ratio is decreased. Parallel combination Series combination NMOS Logic Circuit Concept of Effective Width-to-Length Ratios Design 16.20 p1099 (a) Design 16.20 p1099 (b) (c)
  • 18.
    18 ¾ The Fan-inof a gate is the number of its inputs. Thus a four input NOR gate has a fan-in of 4. ¾ Similarly, Fan-Out is the maximum number of similar gates that a gate can drive while remaining within guaranteed specifications. Fan-In and Fan-Out The rate at Transient Analysis of NMOS Inverters ¾The constant current over a wide range of VDS provided by the depletion load implies that this type of inverter switch a capacitive load more rapidly than the other two types inverter configurations. ¾The source of capacitance CT2 and CT3 are the transistor input capacitances and parasitic capacitances due to interconnect lines between the inverter stages. ¾ The raise time is longer because the load capacitor is charged by the current through the smaller load transistor. ¾ The fall time relatively short, because the load capacitor discharges through the large driver transistor. (W/L)L= 1 (W/L)D= 4 0.5pF Transient Analysis of NMOS Inverters Chapter 16 CMOS Inverter Chapter 16.3
  • 19.
    19 p-Channel MOSFET p p n p n ¾ Inp-channel enhancement device. A negative gate-to-source voltage must be applied to create the inversion layer, or channel region, of holes that, “connect” the source and drain regions. ¾ The threshold voltage VTP for p-channel enhancement-mode device is always negative and positive for depletion-mode PMOS. p-Channel MOSFET Cross-section of p-channel enhancement mode MOSFET Complementary MOS CMOS The most abundant devices on earth ¾ Although the processing is more complicated for CMOS circuits than for NMOS circuits, CMOS has replaced NMOS at all level of integration, in both analog and digital applications. ¾ The basic reason of this replacement is that the power dissipation in CMOS logic circuits is much less than in NMOS circuits.
  • 20.
    20 CMOS Properties ‰ Fullrail-to-rail swing Î high noise margins z Logic levels not dependent upon the relative device sizes transistors can be minimum size ratio less ‰ Always a path to VDD or GND in steady state Î low output impedance (output resistance in kΩ range) large fan-out. ‰ Extremely high input resistance (gate of MOS transistor is near perfect insulator) nearly zero steady-state input current ‰ No direct path steady-state between power and ground no static power dissipation ‰ Propagation delay function of load capacitance and resistance of transistors Î Î Î Î Î ¾ In the fabrication process, a separate p-well region is formed within the starting n-substrate. ¾ The n-channel MOSFET is fabricated in the p-well region and p-channel MOSFET is fabricated in the n-substrate. CMOS Inverter Steady State Response VDD Rn VOut = 0 VIn = V DD VDD Rp VOut = VDD VIn = 0 CMOS Inverter DD OH OL V V V = = 0 PMOS NMOS PMOS NMOS
  • 21.
  • 22.
  • 23.
    23 CMOS Inverter LoadLines 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 I DN (A) Vout (V) X10 -4 Vin = 1.0V Vin = 1.5V Vin = 2.0V Vin = 2.5V 0.25um, W/Ln = 1.5, W/Lp = 4.5, VDD = 2.5V, VTn = 0.4V, VTp = -0.4V Vin = 0V Vin = 0.5V Vin = 1.0V Vin = 1.5V Vin = 0.5V Vin = 2.0V Vin=1.0V PMOS NMOS Vin=0V Vin=0.5V Vin=2.5V Vin=2.0V Vin=1.5V I DP (A) NMOS off PMOS in non sat NMOS in sat PMOS in non sat NMOS in sat PMOS in sat NMOS in non sat PMOS in sat NMOS in nonsat PMOS off
  • 24.
    24 vSDP is small vIand vO relationship as long as NMOS: saturation, PMOS: nonsaturation from below graph vOPt or from above graph vONt vIt B C
  • 25.
    25 NMOS: nonsaturation PMOS: off NMOS:nonsaturation PMOS: saturation NMOS: saturation PMOS: saturation NMOS: saturation PMOS: nonsaturation NMOS: off PMOS: nonsaturation Example 16.9 p1041 vIt vOPt vONt For VDD=5V Example 16.9 p1041 vIt vOPt vONt vOPt vONt vIt VDD=5V VDD=10V
  • 26.
    26 ¾ The transistorKN is also known as “pull down” device because it is pulling the output voltage down towards ground. ¾ The transistor KP is known as the “pull up” device because it is pulling the output voltage up towards VDD. This property speed up the operation considerably. The static power dissipation during both extreme cases (logic 1 or 0) is almost zero because iDP= iDN= 0. 1 0 0 1 VOut VIn ¾ CMOS inverter: series combination of PMOS and NMOS ¾ To form the input, gates of the two MOSFET are connected. ¾ To form the output, the drains are connected together. (ideal case) Ideally, the power dissipation of the CMOS inverter is zero. Practical device CMOS inverter (∼ nW) NMOS inverter (∼mW) CMOS Inverter in either High or Low State CMOS Inverter Design Consideration ‰ The CMOS inverter usually design to have, 9 This can achieved if width of the PMOS is made two or three times than that of the NMOS device. 9 This is very important in order to provide a symmetrical transition, results in wide noise margin. But (because µN>µP) (1) (2) TP TN V V =       =       L W k L W k P N ' ' ' ' P N k k > ¾ How equation (2) can be satisfied ?
  • 27.
    27 NMOS: nonsaturation PMOS: off NMOS:nonsaturation PMOS: saturation NMOS: saturation PMOS: saturation NMOS: saturation PMOS: nonsaturation NMOS: off PMOS: nonsaturation Symmetrical Properties of the CMOS Inverter vOPt vONt 2 DD It V V = p1101 vIt vOPt vONt       = L W k K n N 2 ' (a) (i) Transition points VOPt VONt (ii)
  • 28.
    28 Example 16.29 p1101 (b) (i) (ii) Transitionpoints VOPt VONt       = L W k K P P 2 ' Increase W of PMOS ¼ kP increases ¼ VIt moves to right VDD VDD VIn VOut kp=5kn kp=kn kp=0.2kn CMOS Inverter VTC Increase W of NMOS ¼ kN increases ¼ VIt moves to left P N P N DD It W W k k V V for ≈ = → = , 2 VIt ‰ Result from changing kP/kN ratio: ¾ Inverter threshold VIt ≠ VDD/2 ¾ Rise and fall delays unequal ¾ Noise margins not equal ‰Reasons for changing inverter threshold: ¾ Want a faster delay for one type of transition (rise/fall) ¾ Remove noise from input signal: increase one noise margin at expense of the other CMOS Inverter VTC Effects of VIt adjustment Problem 16.31 p1101 (a)
  • 29.
    29 Problem 16.31 p1101 vIt Example16.31 p1101 (b) CMOS inverter currents ¾ When the output of a CMOS inverter is either at a logic 1 or 0, the current in the circuit is zero. ¾ When the input voltage is in the range both transistors are conducting and a current exists in the inverter. CMOS inverter currents ‰ When NMOS transistor is biased in the saturation region ¾ The current in the inverter is controlled by vGSN and the PMOS vSDP adjusts such that iDP = iDN . As long as NMOS transistor is biased in the saturation region the square root of the inverter current is linear function of the input voltage.
  • 30.
    30 CMOS inverter currents ‰When PMOS transistor is biased in the saturation region ¾ The current in the inverter is controlled by vSGP and the NMOS vDSN adjusts such that iDP = iDN . As long as PMOS transistor is biased in the saturation region the square root of the inverter current is linear function of the input voltage. NMOS: saturation PMOS: saturation NMOS: off PMOS: nonsaturation NMOS: saturation PMOS: nonsaturation CMOS inverter currents NMOS: nonsaturation PMOS: off NMOS: nonsaturation PMOS: saturation Problem 16.33 p1102 (a) (b) Power Dissipation ¾ There is no power dissipation in the CMOS inverter when the output is either at logic 0 or 1. However, during switching of the CMOS inverter from low logic 0 to logic 1, current flows and power is dissipated. ¾ Usually CMOS inverter and logic circuit are used to drive other MOS devices by connecting a capacitor across the output of a CMOS inverter. This capacitor must be charged and discharged during the switching cycle.
  • 31.
    31 Triode Region NMOS TransistorCapacitances Cox” = Gate-Channel capacitance per unit area(F/m2) CGC = Total gate channel capacitance CGS = Gate-Source capacitance CGD = Gate-Drain capacitance CGSO and CGDO = overlap capacitances (F/m) Saturation Region NMOS Transistor Capacitances ¾ Drain is no longer connected to channel. Cutoff Region NMOS Transistor Capacitances ¾ Conducting channel region is completely gone. CGB = Gate-Bulk capacitance CGBO = Gate-Bulk capacitance per unit width. VDD Rn Vout CL VIn = VDD VDD Rp Vout CL VIn = 0 ¾ Gate response time is determined by the time to charge CL through Rp (discharge CL through Rn) Switch Model of Dynamic Behavior CMOS Inverter
  • 32.
    32 ‰ Power hasthree components ¾ Static power: when input isn’t switching ¾ Dynamic capacitive power: due to charging and discharging of load capacitance ¾ Dynamic short-circuit power: direct current from VDD to Gnd when both transistors are on CMOS Inverter Power ™ Static current: in CMOS there is no static current as long as VIn < VTN or VIn > VDD+VTP ™ Leakage current: determined by “off” transistor ™ Influenced by transistor width, supply voltage, transistor threshold voltages VDD VI<VTN Ileak,N VDD VDD Ileak,P Vo(low) VDD Static Power Consumption CMOS Inverter Power Case I: When the input is at logic 0 PMOS is conducting and NMOS is in cutoff mode and the load capacitor must be charged through the PMOS device. Power dissipation in the PMOS transistor; PP=iLVSDp= iL(VDD-VO) The current and output voltages are related by, iL=CLdvO/dt Similarly the energy dissipation in the PMOS device can be written as the output switches from low to high, 2 2 0 2 0 0 0 0 0 2 1 ) 0 2 ( ) 0 ( , 2 , ) ( DD L P DD L DD DD L P V O L V O DD L P O V O L V O DD L P O O DD L P P V C E V C V V C E C V C E d C d V C E dt dt d V C P E DD DD DD DD = − − − = − = − = − = = ∫ ∫ ∫ ∫ ∞ ∞ ν ν ν ν ν ν ν Dynamic Capacitive Power and Energy stored in the PMOS CMOS Inverter Power the energy stored in the capacitor CL when the output is high. Case II: when the input is high and out put is low: During switching all the energy stored in the load capacitor is dissipated in the NMOS device because NMOS is conducting and PMOS is in cutoff mode. The energy dissipated in the NMOS inverter; The total energy dissipated during one switching cycle; The power dissipated in terms frequency; 2 2 1 DD L N V C E = 2 2 2 2 1 2 1 DD L DD L DD L N P T V C V C V C E E E = + = + = 2 DD L T T T V fC fE P t E P t P E → = → = → ⋅ = This implied that the power dissipation in the CMOS inverter is directly proportional to switching frequency and VDD 2 Dynamic Capacitive Power and Energy stored in the PMOS CMOS Inverter Power
  • 33.
    33 ¾ Does not(directly) depend on device sizes ¾ Does not depend on switching delay ¾ Applies to general CMOS gate in which: • Switched capacitances are lumped into CL • Output swings from GND to VDD • Input signal approximated as step function • Gate switches with frequency f f V C P DD L dyn 2 = Dynamic Capacitive Power CMOS Inverter Power Formula for dynamic power ¾ Short-circuit current flows from VDD to GND when both transistors are on saturation mode. VDD VDD Vin Vout ID Imax Imax: depends on saturation current of devices Dynamic Short-Circuit Power CMOS Inverter Power f V C P I V f t t I V f V C P P P P P DD L tot leak DD f r DD DD L tot stat sc dyn tot 2 max 2 ~ 2 +         + + = + + = Inverter Power Consumption Total Power Consumption f V C P DD L dyn 2 = Power Reduction ‰ Reducing dynamic capacitive power ¾ Lower the voltage!! ™ Quadratic effect on dynamic power ¾ Reduce capacitance!! ™ Short interconnect lengths ™ Drive small gate load (small gates, small fan-out) ¾ Reduce frequency!! ™ Lower clock frequency ™ Lower signal activity
  • 34.
    34 ‰ Reducing short-circuitcurrent ¾ Fast rise/fall times on input signal ¾ Reduce input capacitance ¾ Insert small buffers to “clean up” slow input signals before sending to large gate ‰ Reducing leakage current ¾ Small transistors (leakage proportional to width) ¾ Lower voltage Power Reduction Chapter 16 CMOS Inverter Noise Margin Chapter 16.3.4 Concept of Noise Margins Noise Margin for low input Noise Margin for high input OLU IL L V V NM − = IH OHU H V V NM − =
  • 35.
    35 CMOS Inverter NoiseMargins of CMOS when CMOS Inverter Noise Margins of CMOS when If CMOS is symmetrical, CMOS Inverter Noise Margins CMOS Inverter Noise Margins of CMOS when
  • 36.
    36 If CMOS issymmetrical, CMOS Inverter Noise Margins CMOS Inverter Noise Margins Summary Noise Margin of a Symmetrical CMOS Inverter Noise Margin for low input Noise Margin for high input OLU IL L V V NM − = IH OHU H V V NM − = Æ P1047 Example 16.11 Chapter 16 CMOS Logic Circuits Chapter 16.4
  • 37.
    37 CMOS Logic Circuits ¾Large scale integrated CMOS logic circuits including watches, calculators, and microprocessors are constructed by using basic CMOS NOR and NAND gates. Therefore, understanding of these basic gates is very important for the designing of very large scale integrated (VLSI) logic circuits. CMOS Logic Circuits ‰ CMOS NOR gate can be constructed by using two parallel NMOS devices and two series PMOS transistors. ¾ The output is at logic 1 when all inputs are low. ¾ For all other possible inputs, output is low or at logic 0. CMOS Logic Circuits ‰ CMOS NAND gate can be constructed by using two parallel PMOS devices and two series NMOS transistors. ¾ The is at logic 0 when all inputs are high. ¾ For all other possible inputs, output is high or at logic 1. CMOS Logic Circuits How can we design CMOS NOR symmetrical gate? To obtained symmetrical switching times for the high-to-low and low-to-high output transitions, the effective conduction (design) parameters of the composite PMOS and composite NMOS device must be equal. For the CMOS NOR gate, In order to get the symmetrical switching properties, the width to length ratio of PMOS transistor must be approximately eight times that of the NMOS device. For asymmetrical case, switching time is longer!!
  • 38.
    38 CMOS Logic Circuits Howcan we design CMOS NOR symmetrical gate? Only one PMOS and one NMOS are working. Two PMOS and two NMOS are working. For the NOR gate the effective width of the drivers transistors doubles. The effective aspect ratio is increased. For the NAND gate the effective length of the driver transistors doubles. The effective aspect ratio is decreased. Parallel combination Series combination Concept of Effective Width to Length Ratios
  • 39.
    39 CMOS Logic Circuits Fan-Inand Fan-Out ¾ Fan-in of a gate is the number of its inputs. Thus a four input NOR gate has a fan-In of 4. ¾ Fan-Out is the maximum number of load gates that may be connected to the output. ™ Each additional load gate increases the load capacitance their must be charge and discharge as the driver gate changes state. This place a practical limit on the maximum allowable number of load gates. However, Switching Time and Propagation Delay Time • The dynamic performance of a logic circuit family is characterized by propagation delay of its basic inverter. The propagation delay time is define as the average of low- to-high propagation delay time and the high-to-low propagation delay time. • The propagation delay time is directly proportional to the switching time and increases as the Fan-out increases. Therefore, the maximum Fan- out is limited by the maximum acceptable propagation delay time. Each additional load gate increases the load capacitance their must be charge and discharge as the driver gate changes state. This place a practical limit on the maximum allowable number of load gates. CMOS Logic Circuits Switching Time and Propagation Delay Time Propagation Delay Time Switching Time Propagation Delay Estimate • The two modes of capacitive charging/discharging that contribute to propagation delay
  • 40.
    40 Switch-level model Delay estimationusing switch- level model (for general RC circuit): Rn CL [ ]         = − = = = − = → = = → = ∫ 0 1 0 1 0 1 ln ) ln( ) ln( 1 0 V V RC V V RC t dV V RC t t t dV V RC dt R V I dV I C dt dt dV C I p V V p Switch-level model • For fall delay tphl, V0=Vcc, V1=Vcc/2 L p plh L n phl p CC CC p C R t C R t RC t V V RC V V RC t 69 . 0 69 . 0 ) 5 . 0 ln( ln ln 2 1 0 1 = = =         =         = Standard RC-delay equations Chapter 16 Transmission Gates Chapter 16.6 Transmission Gates ¾ Use of transistors as switches between driving circuits and load circuits are called transmission gates because switches can transmit information from one circuit to another. ¾ NMOS and CMOS transmission gate.
  • 41.
    41 ¾ The biasapplied to the transistor determines which terminal acts as the drain and which terminal acts as the source. ¾ ¾ As an Open Switch When gate voltage φ =0, the n-channel transistor is cut-off and the transistor acts as an open switch As an Open Switch Drain Source Gate If φ =VDD, vI=VDD, and vO is initially (t=0) zero, terminal a acts as the drain since its bias is VDD. terminal b acts as the source since its bias is zero. Current enters the drain from the input charging up the capacitor. VDD zero =VDD @ High input As CL charges up and Vo increases, the gate to source voltage decreases. When the gate to source voltage VGS become equal to threshold voltage VTN, the capacitance stop charging and current goes to zero. This implies that the VO=VO(max) when VGS=VTN Or VO(max) = VDD-VTN This implies that output voltage never will be equal to VDD. ; rather it will be lower by VTN. This is one of the disadvantage of an NMOS transmission gate when VI=high As an Open Switch Drain Source Gate VDD zero =VDD @ High input
  • 42.
    42 Characteristics of NMOS transmissiongate (at low input) • When VI=0 and φ=VDD and VO=VDD-VTN at t=o (initially). It is to be noted that in the present case terminal b acts as the drain and terminal a acts as the source. Under these conditions the gate to source voltage is, VGS=φ-VI VGS=VDD-o vGS=vDD This implies that value of VGS is constant. In this case the capacitor is fully discharge to zero as the drain current goes to zero. VO=0 This implies that the NMOS transistor provide a “good” logic 0 when VI=low VDD-Vt G S D source drain gate As an Open Switch Source Drain Gate When φ =VDD, vI=0, and vO =VDD-VTN, at t=0, terminal a acts as the source since its bias is zero. terminal b acts as the drain since its bias is high. Capacitor discharges as current enters the drain. Stop discharging drain current goes zero. zero VDD-VTN =VDD @ Low input VDD-VTN “Good” logic 0 when VI=low In this case the capacitor is fully discharge to zero as the drain current goes to zero. VO=0 This implies that the NMOS transistor provide a “good” logic 0 when VI=low ‰ Why NMOS transmission gate does not remain in a static condition? ¾ The reverse leakage current due to reverse bias between terminal b and ground begins to discharge the capacitor, and the circuit does not remain in a static condition. VDD-VTN Source Drain Gate Example 16.13 p1060
  • 43.
  • 44.
    44 Example 16.52 p1106 (b) ¾A CMOS transmission gate can be constructed by parallel combination of NMOS and PMOS transistors, with complementary gate signals. ¾ The main advantage of the CMOS transmission gate compared to NMOS transmission gate is to allow the input signal to be transmitted to the output without the threshold voltage attenuation. Charging path NMOS terminal a acts as the drain terminal b acts as the source PMOS terminal c acts as the drain terminal d acts as the source Case I: Input High condition In order to charge the load capacitor, current enters the NMOS drain and the PMOS source. NMOS VGSN continuously change PMOS VGSP remains constant Source Drain Source Drain In PMOS, IDP=0, when VSDP=0, which would be possible only, if, VO=VI=5V logic ‘1’ is unattenuated Case II: Input Low condition NMOS terminal a acts as the source terminal b acts as the drain PMOS terminal c acts as the source terminal d acts as the drain In order to discharge the load capacitor, current enters the NMOS drain and the PMOS source. NMOS PMOS Finally, VO=0, which is a good logic 0. O O O SGP v v v v = − = − = 0 φ Discharging path Drain Source Drain Source
  • 45.
    45 CMOS transmission gateremains in a dynamic condition. ¾ If VO=VDD and φ=0, then NMOS substrate to terminal ‘b’ pn junction is reverse biased and capacitor CL can discharge. ¾ If VO=0, then the PMOS terminal c- to-substrate pn junction is reverse biased and capacitance CL can be charge to a positive voltage. ¾ This implies that the output high or low of CMOS transmission gate circuit do not remain constant with time (dynamic behavior). Test your understanding p1067 NMOS conducting for 0 ≤ vI ≤ 4.2V NMOS conducting for 0 ≤ t ≤ 8.4 sec NMOS cutoff for 8.4 ≤ t ≤ 10 sec Exercise 16.29 (a) Given that VTN=0.8V, VTP=-1.2V. When φ = 5V, input vI varies with time as vI =0.5t for 0 ≤ t ≤ 10 sec. Let VO=0 and CL=1pF. Determine the range of the times that the NMOS and PMOS devices are conducting or cutoff. p10XX
  • 46.
  • 47.
    47 Chapter 16 Sequential LogicCircuit Chapter 16.7 • The logic circuits considered thus far are called combinational logic circuits. Their output depend only on the present value of input. This implies that these circuit do not have memory. • Another class of the logic circuit that incorporate memory are called sequential logic circuits; that is, their output depend not only the present value of the input, but also on the previous history of inputs. Shift registers and flip-flops are typical examples of such circuits.
  • 48.
    48 • A shiftregister can be constructed by the combination of transmission gates and inverters. • If VI=VDD and φ1=VDD, then a logic 1=VDD-VTN would exist at VO1. • The CL charges through MN1. As VO1 goes high, VO2 goes low. If φ2 is high low will transmitted through MN2 and VO4 would be at logic 1. Thus logic 1 shifted from input to output. In shift register the input signal is transmitted, or shifted, from the input to the output during one clock cycle. NMOS Suppose VDD=5V and VTN=1V. At t=t1 , V1=φ1=5V, vO2 goes low At this time MN2 is still in cutoff (φ2=0) even though input of MN2 has been changed. This implies that vO3 and vO4 depend on the previous history. Similarly at t=t3, φ2 is high, and logic 0 at vO2 is transmitted to vO3, which force vO4 to 5V. Thus the input information is transmitted to output during one clock cycle. Transparent mode Hold mode Dynamic Shift Registers at Various Time • Consider when t=t4, vI=0, and φ1=5V, so VO1=0 and VO2=5V.Vo3 and Vo4 depend on previous history • At t=t5, φ2=5V, vO3 charges to VDD- VTN=4V and VO4 goes low. • Thus logic 0 is shifted (transmitted) from input to output. • Also note that vO3 and vO4 are depend on previous history of their inputs instead of current inputs (they are having memory). Dynamic Shift Registers at Various Time NMOS shift register is also dynamic (why?) • The output charged capacitor does not remain constant with time because it is discharge through the transmission gate transistor. • In order to prevent logic errors, the clock signal period T must be small compared to effective RC discharge time constant. For example at t = t2, VO1=4V, φ1=0 and MN1 is cutoff.VO1 will start to to decay and VO2 will begin to increase.
  • 49.
    49 CMOS Dynamic ShiftRegisters • The operation of the CMOS shift register is similar to the NMOS register except for the voltage levels. • For example, when vI=φ1=VDD. Then vO1=VDD and vO2=0. when φ2 goes high, then vo3 switch to zero, vo4=vDD. • Thus input signal is shifted to the output during one clock cycle. NMOS R-S Flip Flop • Flip- flops are bistable circuits usually formed by cross-coupling two NOR gates. The output of the two NOR circuits are connected back to the inputs of the opposite NOR gates. When S=logic 1 and R=logic 0 =logic 0 and Q=logic 1=VDD Transistor M2 is then also biased in conducting state. If S returns to logic 0, nothing in the circuit can force a change and flip flop stores the previous logic states, although M1 turned off (but M2 remains tuned on). Q NMOS R-S Flip Flop (cont.) • When R=logic 1 and S=logic 0 • Then M4 turn on so output goes low. With S=Q=Logic 0, both M1 and M2 are cutoff and goes high. The flip-flop is now in reset state. • If both S and R inputs go high. Then both outputs Q and would go low, which implies that output is not complementary. This condition is forbidden or nonallowed condition. Q CMOS R-S Flip-Flop • The operation sequence of CMOS R-S flip flop is same as NMOS. • For example: If S = logic 1 and R = logic 0, then MN1, is turned on, Mp1, is cut off, and goes low. • With = R = logic 0, then both MN3 and MN4 are cut off, both MP3 and Mp4 are biased in a conducting state so that the output Q goes high. • With Q = logic 1, MN2 is biased on, Mp2 is biased off, and the flip-flop is in a set condition. • When S goes low, MN1, turns off, but MN2 remains conducting, so the state of the flip-flop does not change. • Q Q
  • 50.
    50 CMOS R-S Flip-Flop(cont.) • When S = logic 0 and R = logic 1, then output Q is forced low, output goes high, and the flip- flop is in a reset condition. • Again, a logic 1 at both S and R is considered to be a forbidden or a nonallowed condition, since the resulting outputs are not complementary. Q Static vs Dynamic Storage • Static storage – preserve state as long as the power is on – have positive feedback (regeneration) with an internal connection between the output and the input – useful when updates are infrequent (clock gating) • Dynamic storage – store state on parasitic capacitors – only hold state for short periods of time (milliseconds) – require periodic refresh – usually simpler, so higher speed and lower power Static D-type Flip-Flop • A D-type flip-flop is used to provide a delay. The logic bit on the D input is transferred to the output at the next clock pulse. When the CMOS transmission gate turn off (φ=0), the pn junction in the MN1 transmission gate transistor is reverse biased.