# F14 Memory Circuits. Lars Ohlsson

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1 Lars Ohlsson F14 Memory Circuits Outline Combinatorial vs. sequential logic circuits Analogue multivibrator circuits Noise in digital circuits CMOS latch CMOS SR flip flop 6T SRAM cell 1T DRAM cell Memory column-row-block organisation Memory peripheral circuits Sense amplifiers, (address decoders, clocks, etc.) Reading Guide Problems Sedra/Smith 7ed int Chapter 14.4 (bistable multivibrators) Chapter memory cells (Chapter (address decoders, ROM, image sensor)) P17.2, 17.4, 17.15, Sedra/Smith 7ed int 1

2 Combinatorial vs. Sequential Logic Circuits Digital systems require logic gates and memory circuits Perform logic operations and save the result Store input data until needed in an operation Combinatorial logic circuits (logic gates) Given a specific input, output is always the same Sequential logic circuits (memory circuits) Given a specific input, output may depend on history 2

3 Analogue Multivibrator Circuits Bistable, a.k.a. latch Retains its state until change is triggered A circuit with two stable operating points, e.g. an op amp with positive feedback (Astable, a.k.a. function generator) Switches states periodically Self-triggered bistable multivibrator utilising an additional feedback circuit with delay (Monostable, a.k.a. pulse generator) Switches state momentarily when triggered A circuit with one stable state and one quasi-stable state that initiates self-triggering at predefined delay Bistable circuits exhibit memory functionality, but analogue versions are large and power hungry. 3

4 Bistable Multivibrator Operation Trigger input applied to either of grounds in bistable multivibrator circuit Toggling output from high to low, using trigger at inverting input v + = βv O, v O = A v + v L ± v = v I < v +, v + = βv O = βa v + v βl + v I > βl + v + v < 0 v O = L v + = βl Trigger input point determines if characteristic is inverting or non-inverting. 4

5 Noise Sources Power supply noise due to switching logic gates, output stages, etc. Thermal noise(/ hot electron noise) Carrier energy fluctuations due to temperature(/ apparent temperature) S Shot noise v,thermal ω = v2 ഥi 2 Δf = 4kTR S v,thermal ω = Δf = 4kTG Carrier fluctuations due to MOSFET gate tunnelling ഥi 2 S Burst noise i,shot ω = Δf = 2qI G Carrier fluctuations due to MOSFET channel interaction with a trap with a time constant ഥi 2 S i,burst ω = Δf = k I D Burst 1 + ωτ 2 Flicker noise Carrier fluctuations due to MOSFET channel interaction with multiple traps with evenly distributed time constants ഥi 2 S i,flicker ω = Δf = k I D Flicker f 5

6 Basic CMOS Latch Latch (bistable multivibrator) circuit Retains its own output signal by means of positive feedback Basic CMOS latch Two inverters in positive feedback loop Inverted output fed back to input of the same inverter Three possible operating points Low/ high Midpoint High/ low W X = Y Z Latch provides volatile memory, requiring power supply for data storage, at minimal static power. 6

7 Basic Latch Operation Three possible operating points A: Low/ high B: Midpoint (unstable) C: High/ low Operation at slight offset above(/ below) B will initiate regenerative latch process towards A(/ C) Inverter butterfly diagram can be used to illustrate operation points and noise margins 7

8 Two inverters in a loop yields latched output, but what about three inverters? 8

9 ҧ Two Input NOR Gate (recap) Logic (boolean) NOT-OR compound function Inputs, A, B A, B 0, 1 Output, Y Y = A + B = CMOS NOR gate PUN, Y = ҧ A തB One series branch with all inputs PDN, തY = A + B 1, A = 0, B = 0 A തB = ቊ 0, otherwise One parallel branch for each input A B Y = A + B Inclusive OR function, dissimilar from exclusive XOR function. 9

10 Set/ Reset (SR) Flip Flop SR flip flop: latch with trigger inputs Two NOR gates in latch configuration allow set/ reset trigger operations Storage mode R and S low, i.e. തR ҧ S, preserves latched output Q n+1 = NOR തR, Q n = Q n, Q n+1 = NOR ҧ S, Q n = Q n Set operation R low, S high yields Q forced high Q n+1 = NOR S, Q n = 0 Q n+1 = 1 Reset operation R high, S low yields Q forced low Q n+1 = NOR R, Q n = 0 R S Q n+1 Q n Q n Q n Not used Not used Complementary SR flip flop using NAND gates is also possible, etc. 10

11 Clocked SR Flip Flop Inverter latch with clocked set/ reset inputs Clock, φ, form AND functions with respective trigger inputs, S and R Trigger inputs ignored when clock is low, തφ Clock and trigger inputs use NMOS transistors only Requirements for set operation Q5-Q6 sink enough current to pull തQ below threshold of Q3-Q4 inverter Set signal remains high long enough to cause regeneration to take over the switching process Requirements for reset (parallels set due to symmetry) Q7-Q8 sink Q below threshold Q1-Q2 inverter Reset signal remains high Superior functionality at same transistor count as SR flip flop: clock low enforces storage mode. 11

12 Set Operation on Clocked SR Flip Flop: Part I Set operation on clocked SR flip flop in reset storage mode v φ = V DD, v S = V DD, v R = 0 V Q n = 0, Q n = 1, φs തR = 1 Q n+1 = 1, Q n+1 = 0 Part I: Q5-Q6 must pull Q n+1 down past midpoint v Q = 0, v തQ < V DD 2 I D2 < I D5 = I D6 ቚ I Deq 1 2 I D2 = I Deq = i Dx V GS = V DD, V DS = V DD 2 i Dx = k x W V L DD V tx 1 x 2 W > 2 k p L 5,6 Part II: and hold at least until latch responds k n V DD 2 W L 2 V DD 2 w L 5,6 Reset operation parallels that of set operation. 12

13 Set Operation on Clocked SR Flip Flop: Part II Set operation on clocked SR flip flop in reset storage mode v φ = V DD, v S = V DD, v R = 0 V Q n = 0, Q n = 1, φs തR = 1 Q n+1 = 1, Q n+1 = 0 Part I: Q5-Q6 must pull Q n+1 down past midpoint Part II: and hold at least until latch responds Flip v Q = 0, flop v തQ 0, v തQ = V DD V DD 2 t PHL Qeq Q2 = CV DD 2I PHL v Q = V DD V DD 2 t PLH Q3 Q4 = CV DD 2I PLH T min = t PHL Qeq Q2 + t PLH Q3 Q4 I PHL I PLH i Deq ቚ = 1 t=0 2 k n i D4 ቚ = 1 t=tphl 2 k p W L eq V DD V tn 2 W L 4 V DD V tp 2 Reset operation parallels that of set operation. 13

14 BREAK 14

15 6T Static Random Access Memory (SRAM) Cell Simplified implementation of the CMOS clocked SR flip flop CMOS inverter latch Q1-Q2 and Q3-Q4 Set/ reset and output are all provided through clocked access transistors (cf. pass transistor logic) Q5 and Q6 Storage mode, തφ Reset operation, φ ҧ SR Set operation, φs തR Read operation, φ Must be controlled to not accidentally set or reset the 6T cell This is the industry standard volatile static memory cell. 15

16 1T Dynamic RAM (DRAM) Cell One single access transistor Storage capacitor Logic 0: not charged Logic 1: charged Read operation exchanges charges with bit line Leakage demands periodic refresh Word line boost required to charge storage capacitor to full supply voltage v OV = v W v CS V tn v w = V DD + V tn 1T is dynamic, requiring periodic refresh on millisecond time scale. 16

17 Memory Chip Column-Row-Block Organisation Memory organisation needed to (time/ energy) efficiently read or write data in a controlled fashion Matrix minimizes bit and word line RC time constant Bits stored in columns Words in rows (across columns) Several blocks required for large memories Memory peripheral circuits Row and column address decoders, built from combinatorial logic circuits Precharge and equalisation for differential bit line preconditioning Sense amplifiers read data from memory cells Drivers write data into memory cells 17

18 6T SRAM Cells in a Memory Block Row address lets row decoder activate all access transistors in a specific row Column address lets column decoder operate on a pair of complementary bit lines Read to or write from I/O data bus Memory cycle time is on nanosecond time scale, limited by word line RC and sense response. 18

19 6T SRAM Cell Operation Conditions Read and write functionality through access transistors Read operation must not shift the logic level more than a threshold voltage from stored value Write operation must toggle the logic level to within a threshold voltage of new value 19

20 6T SRAM Cell: Reading a Stored Logic 1 Initial data and bit lines precharged to supply voltage V Qn = 0 V, V Qn = V DD, v തB ቚ = V DD, t=0 v B ቚ = V DD t=0 Non-destructive read 1 operation v തQ < V Qn + V tn = V tn VതQ V DD V tn = Τ W L 5 Τ W L 1 I 5 = 1 2 k n I 1 = k n W L 5 V DD VതQ V tn 2 W L 1 V DD V tn 1 2 V തQ VതQ WΤL a:5 < WΤL n:1 1 V tn V DD V tn 2 1 ΔQ = I 5 Δt = C തBΔV v തB = V DD ΔV ΔV = I 5Δt C തB Δt = C തBΔV I 5 C തB C തQ Read must not shift data more than a threshold voltage. 20

21 6T SRAM Cell: Writing a Logic 0 Over a Logic 1 Initial data and bit lines precharged to new data V Qn = 0 V, V Qn = V DD, v തB ቚ = V DD, t=0 Successful 1 through 0 toggling v Q < V Qn+1 + V tn = V tn V Q V DD V tn = k p WΤL 4 k n WΤL 6 I 4 = 1 2 k p I 6 = k n v B ቚ = 0 V t=0 W L 4 V DD V tp 2 W L 6 V DD V tn 1 2 V Q V Q k n = 4k p WΤL p:4 < k n WΤ 1 1 L a:6 k p V tx V DD V tx 2 ΔQ = I 6 Δt = C Q ΔV v Q = V DD ΔV ΔV = I 6Δt C Q Δt = C QΔV I 6 C B C Q Write must toggle data to within a threshold voltage. 21

22 How to boost small differential signal from memory cell to logic levels?? 22

23 Clocked Latch as a Differential Sense Amplifier Latch with clocked bias between bit lines First, bit lines are precharged/ equalised Then, word line with addressed memory cell is activated Finally, sense amplifier is activated, latching the detected difference towards full logic levels v B ቚ V DD 0<vB <V DD 2 ± ΔV exp G m t C B = V DD 2 ± ΔV exp g mn + g mp t C B Exponential time response, set by latch transistors and bit line parasitics. 23

24 Dummy Cells for Differential DRAM Operation DRAM cells yield single ended output, not compatible with differential sense amplifier/ driver Dummy cells at memory block edge used to simulate differential characteristics 24

25 MOS Differential Amplifier as a Sense Amplifier MOS differential pair w/ current mirror load Sufficient differential input switches bias current, I, to one branch ΔV > 2V OV = k n Current mirror forces current to/ from output, charging/ discharging its voltage to either logic level within Δt Δt = CV DD I Increased speed costs static power dissipation P = V DD I 2I W L 1,2 25

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