# CMOS Digital Integrated Circuits Analysis and Design

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1 CMOS Digital Integrated Circuits Analysis and Design Chapter 8 Sequential MOS Logic Circuits 1

2 Introduction Combinational logic circuit Lack the capability of storing any previous events Non-regenerative circuit There is no feedback relationship between the output and the input Sequential circuits The output is determined by the current inputs as well as the previously applied input variables Regenerative circuit Bistable circuits Two stable states Most widely used and important All basic latch, flip-flop circuits, registers, and memory elements Monostable circuits Only one stable operating point Astable circuits No stable operating point Oscillate, without settling into a stable operating mode

3 Behavior of bistable elements Two identical cross-coupled inverter circuits v o1 =v i, v o =v i1 The two voltage transfer characteristics, v o1 -v i1, and v o -v i Intersecting at three points If the circuit is initially operating at one of these two stable point Preserve this state unless it is forced externally to change its operating point Gain is smaller than unity (at the two operating points)» Need sufficiently large voltage perturbation The third operating point The voltage gains are larger than unity A small perturbation at the input of any of the inverters will be amplified Causing the operating to move to one of the stable operating point 3

4 CMOS two-inverter bistable element At the unstable operating point All four the transistor are in saturation Resulting in maximum loop gain for the circuit Small voltage perturbation Output voltage diverse and eventually settle at V OH and V OL 4

5 Assume C Small-signal input and output, propagation of a transient Initially operating at v Small signal drain current, i g1 g C m g d q1 d q 1 g m q1 = = q 1 Cg gm dt dt C g This equation can also be expressed in a more simplified form by usingτ, the transit time constant d q dt 1 1 = q τ The time - domain solution for where the initial condition is v v o o1 0 1 ' () t = v ( 0) τ v ( 0) 1 g >> C dvg1 = Cg, i dt 1 with τ ( 0) = C v ( 0), τ 1 0 ' ( ) e + ( v ( 0) + τ v ( 0) ) o τ 1 0 ' ( ) e + ( v ( 0) + τ v ( 0) ) ' () t = v ( 0) τ v ( 0) o1 g d for each inverter = C 0 g o1 C = g = v dv g dt g m o i g1 t = v, i.e. at the unstable operating point = i g q ' t ' ( 0) τ q ( 0) q ( 0) τ q ( 0) t + τ 0 t + τ 0 + τ 1 0 ' ( ) e, v () t ( v ( 0) + τ v ( 0) ) 1 ' vo 1() t vo 1( 0) + τ 0v01( 0) o o 0 0 e Note that the magnitude of both output voltages increases exponentially with time Depending on the polarity of the initial small perturbations t 1 d m g t 1 th v = g q q (t) = o o1 m g g τ0 note that v t + τ 0 t + τ0 ( 0) and dv ( 0), the output voltages of both inverters will diverge from their initial value of V 1 v, i g1 g = i d1 dvg1 = Cg, g v dt m g1 e = g e e v m g1 g1 where v dv = Cg dt + 1 dv g o o1 0 = v, v g1 1 g q1 =, v C g 0 e = v 01 g o th g gm dq1 gm q =, q1 C dt C q =, q1 and q are the gate charge C g g to either V dq = dt OL or V OH While the bistable circuit is settling from its unstable operating point into one of we can envison a signal traveling the loop consisting of the two cascaded inverters several times. The time - domain behavior of If during a time interval along a cascaded inverter chain consisting of The loop gain A n = e T + τ0 T the output voltage v o1, the signal travels the loop n times, n inverters. v during this period is v o1 o1 () t ( 0) then the equivalent its stable operating points, = e t + τ o to the same signal propagating 5

6 SR latch circuit The bi-stable element Consisting two cross-coupled inverters has two stable operating states Preserving its state as long as the power supply is provided A simple memory function of holding its state However, no provision for allowing its state to be changed externally from one stable operating mode to another CMOS SR latch Having two triggering inputs, S and R Triggering the circuit from one operating point to the other SR flip-flop Two stable states can be switched back and forth Consisting Two CMOS NOR gates One input cross-couple to the output of other NOR gate Another input enables triggering of the circuit 6

7 SR latch circuit The SR latch has two complementary outputs, Q and Q Q=1 in its set state Q=0 in its reset state Gate level schematic Two NOR gates If both inputs = 0 Operating like the simple cross-coupled bistable element Holding either one of its two stable operating points (states) as determined by the previous inputs If S=1 Forcing the output Q=1 If R=1 Forcing the output Q=0 S=1 and R=1, not allowed 7

8 Operation modes of the transistors in the NOR-based CMOS SR latch circuit If S=V OH, R=V OL M1, M on node Q=V OL =0 M3, M4 off node Q=V OH If S=V OH, R=V OL, the situation will reverse If S=V OL, R=V OL, there are two possibilities Depending on the previous state of the SR latch Either M or M3 on (while M1, M4 off) Generating a logic low level of V OL =0 at one of the output nodes While the complementary output node is at V OH 8

9 Transient analysis of the SR latch circuit C C Assuming that the latch is initially reset and that a set operation is being performed by applying S = "1"and R = "0", the rise time associated with node Q can now be estimated as follows τ Q Q rise, Q = C = C gb, gb,3 + C + C gb,5 gb,7 + C + C (SR - latch) = τ The calculation of the switching timeτ and fall times of the NOR gates First, M1turn on db,3 db,1 rise, Q + C + C db,4 db, + C + C db,5 (NOR) + τ db,7 + C fall, Q + C Q falling from high to low; followed M3 turn off both M and M4 can be assumed to be off in this process (although M can be turned on as Q rises) ( NOR) rise,q SB,7 SB,5 + C + C db,8 db,6 requires two separate calculations for the rise Q rising from low to high 9

10 Depletion load nmos SR latch circuit The operation principle is identical to that of the CMOS SR latch In terms of power dissipation and noise margins 10

11 CMOS SR latch circuit based on NAND gates S=1, R=1 holding state S=0, R=1 Q=1, -Q=0 (set the latch) S=1, R=0 Q=0, -Q=1 (reset the latch) The NAND-based SR latch responds to active low input signals The NOR-based SR latch, which responds to active high inputs S=0, R=0 Q=0, -Q=0 (not allowed) Depletion-load NAND gates The same operation Poor static power dissipation and noise margins 11

12 Clocked SR latch Asynchronous sequential circuit Responding to the changes occurring in input signals at a circuit-delay-dependent time point during their operation Synchronous operation By adding a gating clock signal to the circuit The outputs will respond to the input levels only during the active period of a clock pulse A clocked NOR-based SR latch CK=0 The input signal have no influence upon the circuit response Output hold its current state CK=1 S and R inputs are permitted to reach the SR latch The circuit is strictly level-sensitive during active clock phases Any changes occurring in the S and R input voltage when the CK level is equal to 1 1

13 AOI based implementation of the clocked NOR-based SR latch Very small transistor counts 13

14 Active low The changes in the input signal levels will be ignored when the clock is equal to logic 1 The input will influence the outputs only when the clock is active, i.e., CK=0 14

15 The clocked NAND-based SR latch Both the input signals and the CK signal are active high CK=1 S=1, R=0 Q will be set S=0, R=1 Q will be reset CK=0 The latch preserves its state Drawback The transistor count is higher than the active low version shown in Fig

16 Clocked JK latch All simple and clocked SR latch circuits suffer from the common problem Having a not-allowed input combination Their state becomes indeterminate when both inputs S and R are activated at the same time JK latch (JK flip-flop) By adding two feedback lines from the outputs to the inputs (in SR latch) NAND-based JK latch Active high inputs 16

17 All-NAND implementation of the clocked JK latch circuit The J and K inputs in this circuit correspond to the set and reset inputs of the basic SR latch J=1, K=0 set J=0, K=1 reset J=0, K=0 preserves its current state J=1, K=1 the latch simply switches its state due to feedback The JK latch does not have a not-allowed input combination 17

18 NOR-based implementation of the clocked JK latch The AOI-based circuit structure resulted in a relatively low transistor count There is no not-allowed input combination for the JK latch If J=1, K=1 during the active phase of the clock pulse The output of the circuit will oscillate (toggle) continuously until either the clock becomes inactive (goes to zero), or one of the input signal goes to zero To prevent this undesirable timing problem The clock pulse width must be made smaller than the input-to-output propagation delay of the JK latch circuit The clock signal must go low before the output level has an opportunity to switch again Assuming that the clock constrain above is satisfied The output of the JK latch will toggle (change its state) only once for each clock pulse, if both inputs are equal to logic 1 Toggle switch 18

19 Master-slave flip-flop The master-slave flip-flop Most of the timing limitations encountered in the previously examined clocked latch circuits can be prevented by using two latch stages in a cascaded configuration The two cascaded stages are activated with opposite clock phases Operation Clock high The master is activated the inputs J and K entered into the flip-flop the first stage outputs are set according to the primarily inputs Clock goes to zero The master inactive, the slave active The output levels of the flip-flop circuit are determined during this second phase 19

20 Master-slave flip-flop The circuit is never transparent A change occurring in the primarily inputs is never reflected directly to the outputs Because the master and the slave stages are decoupled from each other, the circuits allows for toggling when J=K=1 But it eliminates the possibility of the uncontrolled oscillations since only one stage is active at any given time 0

21 CMOS D-latch and edge-triggered flip-flop Direct CMOS implementations of conventional circuits such as the clocked JK latch or the JK master-slave flipflop tend to require a large number of transistors The simple D-latch circuit Simpler, fewer transistors Operation: When the clock is active the output Q=the input D When the clock goes to zero the output will preserve its state The CK input acts as an enable signal which allows data to be accepted into the D-latch Application Temporary storage of data or as a delay element 1

22 CMOS implementation of the D-latch Circuit diagram Two-inverter loop and two CMOS transmission gate (TG) switches Operation CK high the input signal is accepted (latched) into the circuit CK low this information is preserved as the state of the inverter loop Timing diagram The valid D input must be stable for a short time before (setup time, t setup ) and after (hold time, t hold ) the negative clock transition, during which the input switch opens and the loop switch closes Once the inverter loop is completed by closing the loop switch, the output will preserve its valid level

23 CMOS implementation of the D-latch (version ) Circuit consisting Two tri-state inverters, driven by the clock signal and its inverse Operation CK high The first tri-state inverter accepts the input signal The second tri-state inverter is at its high-impedance state The output Q is following the input signal CK low The input buffer becomes inactive The second tri-state inverter completes the two-inverter loop Preserving its state until the next clock pulse 3

24 CMOS negative edge-triggered master-slave D flip-flop Circuit Cascading two D-latch circuits The first stage (master) is driven by the clock signal Positive level-sensitive The second stage (slave) is driven by the inverted clock signal Negative level-sensitive Operation CK high Master follows D input Slave holds the previous value CK: high low Master cease to sample the input and stores the D value at the time of the clock transition Slave becomes transparent, Q s =Q m The input cannot affect the output because the master stage is disconnected from the D input CK: low high Salve locks in the master latch output Master sampling the input against This circuit is a negative edge-triggered D flip-flop by virtue of the fact that it samples the input at the falling edge of the clock pulse 4

25 Simulated input and output waveforms of CMOS DFF The output of the master stage latches the applied input (D) when the clock signal is 1 The output of the slave stage becomes valid when the clock signal drops to 0 The DFF samples the input at every falling edge of the clock pulse 5

26 Set-up time violation The operation of the DFF circuit can be seriously affected if the master stage experiences a set-up time violation If the input D switches from 0 to 1 immediately before the clock transition occurs Master fail to latch the correct value Slave produces an erroneous output 6

27 Layout of DFF 7

28 NAND3-based positive edge-triggered DFF Initially (S, R, CK, D)=(1, 0, 0, 0) and Q=0 Second phase (S, R, CK, D)=(1, 0, 1, 1) and Q=0 Third phase (S, R, CK, D)=(1, 1, 1, 1) The output of gate switches to 0, which in turn sets the output of the last stage SR latch to 1 The output of DFF switches to 1 at the positive-going edge of the clock signal, CK 8

29 Schmitt trigger circuit A very useful regenerative circuit The schmitt trigger Has an inverter-like voltage transfer characteristic With two different logic threshold voltages For increasing input signal For decreasing input signal Being utilized for the detection of low-to-high and high-to-low switching events in noisy environments 9

30 i) At V V ii) At V iii) At V iv) At V Schmitt trigger circuit- operation (1) in = 0V M1 and M are turn on V V V z = V in in z in DD = V -V T 0,n =. 0V = 3. 5V T, 6 = 3. 5V = 10. V 1 W k' in T 0, L 5 V =. 976 V 1 W k' in L 5 Vz =. V V = V = V M4 and M5 off, M3 off, M6 on saturation 1 W L 6 = < V = 5V ( V V ) = k' ( V V V ) GS, 4 1 W [ ( V V ) V V ] = k' ( V V V ) T 0, 5 GS, 4 z x z y DD M5 starts to turn on, M4 is still off V DD T 0,n L = = 13. > V is being pulled down towar d "0" x region = 5V Assume M4 is off, while both M5 and M6 saturation z continues to decrease. Assume M5 linear, M6 saturation T 0,n At this point, M4 is already on, above assumption x 5 We conclude the upper logic threshold voltage V z = 1, so M4 still off 6 = 1 T 0, 6 DD + th z no longer val id 3. 5V T 0, 6 30

31 i) At V iii) At V iv) At V Schmitt trigger circuit- operation () in = 5.0V M4 and M5 are turn on V 1 W k' L 3 ii) At V = 4. 0V in in in in If M is y ( 0 V V ) the output vol tage = 3. 0V 1 W k' in DD L 1 V =. 0 V = 15. V 1 W k' in L 1 V =. 79V y = 0V M1 and M off, M3 on saturation T,3 V = 15. V M1is at the edge of turning on, M off, M3 saturation 1 W ( V V V ) = k' ( 0 V V ) GS, L = = 0.98 > V 1 W [ ( V V V )( V V ) ( V V ) ] = k' ( 0 V V ) DD T 0,p M is still off at this point still off, M1 linear, x = 0 is still unchanged M1 is on and in saturation region, M3 is also saturation T 0,p y region y M3 saturation DD At this point, M is already turn on T 0,p - We conclude that the lower logic threshold voltage V 3 y y = 1 DD T, 3 the output vol tage th is being pull up to V 1.5V L 3 y T, 3 DD 31

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