Unformatted text preview: LowPower Design and Test
GateLevel Power Optimization
Vishwani D. Agrawal
Auburn University, USA
[email protected] Srivaths Ravi Texas Instruments India
[email protected] Hyderabad, July 3031, 2007 http://www.eng.auburn.edu/~vagrawal/hyd.html Copyright Agrawal & Srivaths, 2007
Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 1 Components of Power Dynamic Signal transitions Logic activity
Glitches Shortcircuit Static Leakage Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 2 Power of a Transition
isc R VDD Dynamic Power
Vo Vi = CLVDD2/2 + Psc CL R
Ground Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 3 Dynamic Power
Each transition of a gate consumes CV 2/2. Methods of power saving: Minimize load capacitances Transistor sizing
Librarybased gate selection Reduce transitions Logic design
Glitch reduction Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 4 Glitch Power Reduction Design a digital circuit for minimum transient energy consumption by eliminating hazards Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 5 Theorem 1 For correct operation with minimum energy consumption, a Boolean gate must produce no more than one event per transition. Output logic state changes
One transition is necessary
Copyright Agrawal & Srivaths, 2007 Output logic state unchanged
No transition is necessary LowPower Design and Test, Lecture 5 6 Event Propagation
Single lumped inertial delay modeled for each gate
PI transitions assumed to occur without time skew
Path P1
1 0 13 P2 0 2 0 Copyright Agrawal & Srivaths, 2007 1 3
2 246 Path P3
5 LowPower Design and Test, Lecture 5 7 Inertial Delay of an Inverter
Vin dHL+dLH d = ────
dHL 2 dLH Vout
time
Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 8 MultiInput Gate
A
DPD: Differential path delay Delay = d C B A DPD B C
Copyright Agrawal & Srivaths, 2007 d d Hazard or glitch
LowPower Design and Test, Lecture 5 9 Balanced Path Delays
A DPD Delay buffer Delay = d C B A
B C
Copyright Agrawal & Srivaths, 2007 d No glitch
LowPower Design and Test, Lecture 5 10 Glitch Filtering by Inertia
A
Delay ≥ DPD C B A DPD B d =DPD C
Copyright Agrawal & Srivaths, 2007 Filtered glitch
LowPower Design and Test, Lecture 5 11 Theorem 2 Given that events occur at the input of a gate with inertial delay d at times, t1 ≤ . . . ≤ tn , the number of events at the gate output cannot exceed
tn – t1
min ( n , 1 + min
d ) tn  t 1 t1
Copyright Agrawal & Srivaths, 2007 t2 t3 tn LowPower Design and Test, Lecture 5 time
time
12 Minimum Transient Design Minimum transient energy condition for a Boolean gate:  t i  tj  < d Where ti and tj are arrival times of input
Where
events and d is the inertial delay of gate Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 13 Balanced Delay Method All input events arrive simultaneously
Overall circuit delay not increased
Delay buffers may have to be inserted 1 1 1 1 1 1 1 3 1
Copyright Agrawal & Srivaths, 2007 1 1 LowPower Design and Test, Lecture 5 No increase in critical path delay 14 Hazard Filter Method Gate delay is made greater than maximum input path delay difference
No delay buffers needed (least transient energy)
Overall circuit delay may increase
1 1 1 1 1
Copyright Agrawal & Srivaths, 2007 1 1 1 1 3 LowPower Design and Test, Lecture 5 15 Designing a GlitchFree Circuit Maintain specified critical path delay.
Glitch suppressed at all gates by Path delay balancing Glitch filtering by increasing inertial delay of gates
A linear program optimally combines all objectives.
Delay = d1
Delay = d2 Copyright Agrawal & Srivaths, 2007 d1 – d2 < D
D LowPower Design and Test, Lecture 5 16 Benchmark Circuits
Normalized Power
Average
Peak Circuit Maxdelay
(gates) No. of
Buffers ALU4 7
15 5
0 0.80
0.79 0.68
0.67 C880 24
48 62
34 0.68
0.68 0.54
0.52 C6288 47
94 294
120 0.40
0.36 0.36
0.34 c7552 43
86 366
111 0.44
0.42 0.34
0.32 Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 17 FourBit ALU
maxdelay Buffers inserted 7
10
12
15 5
2
1
0 Maximum Power Savings (zerobuffer design):
Peak = 33 %, Average = 21 %
Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 18 ALU4: Original and LowPower Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 19 C7552 Circuit: Spice Simulation Power Saving: Average 58%, Peak 68%
Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 20 References
R. Fourer, D. M. Gay and B. W. Kernighan, AMPL: A Modeling R. Fourer, D. M. Gay and B. W. Kernighan, AMPL: A Modeling Language for Mathematical Programming, South San Francisco: The Scientific Press, 1993.
M. Berkelaar and E. Jacobs, “Using Gate Sizing to Reduce Glitch Power,” Proc. ProRISC Workshop, Mierlo, The Netherlands, Nov. 1996, pp. 183188.
V. D. Agrawal, “Low Power Design by Hazard Filtering,” Proc. 10th Int’l Conf. VLSI Design, Jan. 1997, pp. 193197.
V. D. Agrawal, M. L. Bushnell, G. Parthasarathy and R. Ramadoss, “Digital Circuit Design for Minimum Transient Energy and Linear Programming Method,” Proc. 12th Int’l Conf. VLSI Design, Jan. 1999, pp. 434439.
M. Hsiao, E. M. Rudnick and J. H. Patel, “Effects of Delay Model in Peak Power Estimation of VLSI Circuits,” Proc. ICCAD, Nov. 1997, pp. 4551.
T. Raja, V. D. Agrawal and M. L. Bushnell, “Minimum Dynamic Power CMOS Circuit Design by a Reduced Constraint Set Linear Program,” Proc. 16th Int’l Conf. VLSI Design, Jan. 2003, pp. 527532.
T. Raja, V. D. Agrawal and M. L. Bushnell, “Variable Input Delay CMOS Logic for Low Power Design,” Proc. 18th Int’l Conf. VLSI Design, Jan. 2005, pp. 596603. Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 21 Components of Power Dynamic Signal transitions Logic activity
Glitches Shortcircuit Static Leakage Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 22 Subthreshold Conduction
Ids Vgs – Vth
Vds
I0 exp( ───── ) × (1– exp ── )
nVT
VT = 1mA
100μA
10μA
1μA
100nA
10nA
1nA
100pA
10pA Copyright Agrawal & Srivaths, 2007 Subthreshold
region Ids
Saturation region Sunthreshold slope Vth
0 0.3 0.6 0.9 1.2 LowPower Design and Test, Lecture 5 1.5 1.8 V Vgs
23 Thermal Voltage, vT
VT = kT/q = 26 mV, at room temperature.
When Vds is several times greater than VT Ids Copyright Agrawal & Srivaths, 2007 = Vgs – Vth
I0 exp( ───── )
nVT
LowPower Design and Test, Lecture 5 24 Leakage Current Leakage current equals Ids when Vgs= 0
Leakage current, Ids = I0 exp(Vth/nVT)
At cutoff, Vgs = Vth , and Ids = I0 Lowering leakage to 10bI0 Vth = bnVT ln 10 = 1.5b × 26 ln 10 = 90b mV Example: To lower leakage to I0/1,000
Vth = 270 mV Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 25 Threshold Voltage Vth = Vt0 + γ[(Φs+Vsb)½ Φs½] Vt0 is threshold voltage when source is at body potential (0.4 V for 180nm process) Φs = 2VT ln(NA /ni ) is surface potential γ = (2qεsi NA)½tox /εox is body effect coefficient (0.4 to 1.0) NA is doping level = 8×1017 cm3 ni = 1.45×1010 cm3 Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 26 Threshold Voltage, Vsb = 1.1V Thermal voltage, VT = kT/q = 26 mV Φs = 0.93 V εox = 3.9×8.85×1014 F/cm εsi = 11.7×8.85×1014 F/cm tox = 40 Ao γ = 0.6 V½ Vth = Vt0 + γ[(Φs+Vsb)½ Φs½] = 0.68 V Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 27 A Sample Calculation
VDD = 1.2V, 100nm CMOS process Transistor width, W = 0.5μm OFF device (Vgs = Vth) leakage I0 = 20nA/μm, for low threshold transistor
I0 = 3nA/μm, for high threshold transistor 100M transistor chip Power = (100×106/2)(0.5×20×109A)(1.2V) = 600mW for all lowthreshold transistors
Power = (100×106/2)(0.5×3×109A)(1.2V) = 90mW for all highthreshold transistors Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 28 DualThreshold Chip
Lowthreshold only for 20% transistors on critical path. Leakage power = 600×0.2 + 90×0.8
= 120 + 72
= 192 mW Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 29 DualThreshold CMOS Circuit Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 30 DualThreshold Design To maintain performance, all gates on the critical path are assigned low Vth .
Most of the other gates are assigned high Vth . But,
Some gates on noncritical paths may also be assigned low Vth to prevent those paths from becoming critical. Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 31 Integer Linear Programming (ILP) to Minimize Leakage Power Use dualthreshold CMOS process
First, assign all gates low Vth Use an ILP model to find the delay (Tc) of the critical path
Use another ILP model to find the optimal Vth assignment as well as the reduced leakage power for all gates without increasing Tc Further reduction of leakage power possible by letting Tc increase Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 32 ILP Variables For each gate i define two variables. Ti : the longest time at which the output of gate i can produce an event after the occurrence of an input event at a primary input of the circuit. Xi : a variable specifying low or high Vth for gate i ; Xi is an integer [0, 1], 1 gate i is assigned low Vth ,
0 gate i is assigned high Vth .
Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 33 ILP objective function Leakage power: Pleak = Vdd ∑ I leaki
i minimize the sum of all gate leakage currents, given by Min∑ ( X i ⋅ I Li + (1 − X i ) ⋅ I Hi )
i ILi is the leakage current of gate i with low Vth
IHi is the leakage current of gate i with high Vth
Using SPICE simulation results, construct a leakage current look up table, which is indexed by the gate type and the input vector. Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 34 ILP Constraints For each gate (1) Gate i Ti ≥ T j + X i ⋅ D Li + (1 − X i ) ⋅ D Hi Ti output of gate j is fanin of gate i (2) Gate j 0 ≤ Xi ≤1 Tj Max delay constraints for primary outputs (PO) (3) ≤ Tmax Ti Tmax is the maximum delay of the critical path
Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 35 ILP Constraint Example
0 1 2
3 Ti ≥ T j + X i ⋅ DLi + (1 − X i ) ⋅ DHi Assume all primary input (PI) signals on the left arrive at the same time. For gate 2, constraints are T2 ≥ T0 + X 2 ⋅ DL 2 + (1 − X 2 ) ⋅ DH 2 T2 ≥ 0 + X 2 ⋅ DL 2 + (1 − X 2 ) ⋅ DH 2
Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 36 ILP – Constraints (cont.) DHi is the delay of gate i with high Vth
DLi is the delay of gate i with low Vth A second lookup table is constructed and specifies the delay for given gate type and fanout number. Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 37 ILP – Finding Critical Delay
Ti ≤ Tmax T can be specified or be the delay of longest path (Tc).
max To find Tc , we change constraints (2) to an equation, assigning all gates low Vth 0 ≤ Xi ≤1 Xi =1 Maximum Ti in the ILP solution is Tc. If we replace T with Tc , the objective function minimizes leakage power without sacrificing performance. Copyright Agrawal & Srivaths, 2007 max LowPower Design and Test, Lecture 5 38 PowerDelay Tradeoff
1
0.9 N
ormalized Leakage Pow
er 0.8
C
432
0.7
C
880
0.6 C
1908 0.5
0.4
0.3
0.2
0.1
1 1.1 1.2 1.3 1.4 1.5 N
ormalized C
ritical Path D
elay
Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 39 PowerDelay Tradeoff If we gradually increase Tmax from Tc , leakage power is further reduced, because more gates can be assigned high Vth .
But, the reduction trends to become slower.
When Tmax = (130%) Tc , the reduction about levels off because almost all gates are assigned high Vth . Maximum leakage reduction can be 98%. Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 40 Leakage & Dynamic Power Optimization 70nm CMOS c7552 Benchmark Circuit @ 90oC
900
700
600
500
400
300
200
100
0 Leakage power
Dynam ic power
Tot al power Le
ex aka d cee ge
yn d
po am s
we ic
r Micr owat t s 800 Or iginal cir cuit Copyright Agrawal & Srivaths, 2007 Opt im ized
design LowPower Design and Test, Lecture 5 Y. Lu and V. D. Agrawal, “CMOS Leakage and Glitch Minimization for PowerPerformance Tradeoff,” Journal of Low Power Electronics (JOLPE), vol. 2, no. 3, pp. 378387, December 2006. 41 Summary Leakage power is a significant fraction of the total power in nanometer CMOS devices.
Leakage power increases with temperature; can be as much as dynamic power.
Dual threshold design can reduce leakage. Reference: Y. Lu and V. D. Agrawal, “CMOS Leakage and Glitch Minimization for PowerPerformance Tradeoff,” J. Low Power Electronics, Vol. 2, No. 3, pp. 378387, December 2006. Access other paper at http://www.eng.auburn.edu/~vagrawal/TALKS/talks.html Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 42 Problem: Leakage Reduction
Following circuit is designed in 65nm CMOS technology using low threshold transistors. Each gate has a delay of 5ps and a leakage current of 10nA. Given that a gate with high threshold transistors has a delay of 12ps and leakage of 1nA, optimally design the circuit with dualthreshold gates to minimize the leakage current without increasing the critical path delay. What is the percentage reduction in leakage power? What will the leakage power reduction be if a 30% increase in the critical path delay is allowed? Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 43 Solution 1: No Delay Increase Three critical paths are from the first, second and third inputs to the last output, shown by a dashed line arrow. Each has five gates and a delay of 25ps. None of the five gates on the critical path (red arrow) can be assigned a high threshold. Also, the two inverters that are on fourgate long paths cannot be assigned high threshold because then the delay of those paths will become 27ps. The remaining three inverters and the NOR gate can be assigned high threshold. These gates are shaded grey in the circuit.
The reduction in leakage power = 1 – (4×1+7×10)/(11×10) = 32.73%
Critical path delay = 25ps Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 44 Solution 2: 30% Delay Increase Several solutions are possible. Notice that any 3gate path can have 2 high threshold gates. Four and five gate paths can have only one high threshold gate. One solution is shown in the figure below where six high threshold gates are shown with shading and the critical path is shown by a dashed red line arrow.
The reduction in leakage power = 1 – (6×1+5×10)/(11×10) = 49.09%
Critical path delay = 29ps Copyright Agrawal & Srivaths, 2007 LowPower Design and Test, Lecture 5 45 ...
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