A comparison between different logic synthesis techniques from the digital switching noise viewpoint G. Boselli, V. Ciriani, V. Liberali G. Trucco Dept. of Information Technologies Verona, 21 June 2007 Terza giornata nazionale di sintesi logica

Introduction Mixed-signal integrated systems Careful modeling of crosstalk between analog and digital sections Disturbances injected by digital circuits can degrade overall system performance Digital switching Deterministic process, depending on circuit parameters and input signals Huge number of logic blocks  cognitively stochastic process Digital switching currents as stationary shot noise process Amplitude distribution Power spectral density

Digital switching current Proposed model valid under some hypotheses: Transition activity of a logic gate independent of the activity of other gates In fact, gate inputs are driven by other gate outputs A large system contains a huge number of gates  each gate depends on a small number of neighboring cells Logic transitions uniformely distributed in time Correct for asynchronous digital systems Synchronous system: transistion activity correlated with clock  more complex analysis All logic transitions require the same time  all current pulses have the same finite time duration

Stochastic model of digital switching noise (1) Consider: Asynchronous digital network Identical logic cells driving equal capacitive loads Switching instants of input signals applied to gates independent and randomly distributed in uniform manner Digital switching noise as shot noise process Switching instants of input signals as Poisson points

Stochastic model of digital switching noise (2) Input transition of logic gates as Dirac impulses Train of impulses, taken at random instants X(t): stochastic process representing the input transition of logic gates Logic gates all equal (same I DD and I SS current absorption)  convolution between train of impulses X(t) and current absorbed by single logic gate h(t) = total current absorbed by the entire circuit I(t)

Amplitude distribution of switching noise Represented by the Probability Density Function (pdf, f(x)) of the stochastic process I(t) Calculated from the pdf of the single current pulse Arbitrary time instant t 1 pdf of the total current at time t 1 depends on the number of Poisson impulses falling in the interval and the pdf of the single current pulse f H (x) where

Power spectral density of switching noise Power Spectral Density (psd) of switching current: where is the psd of logic transition impulses X(t) H(f) is the Fourier transform of the impulse response h(t) h(t): current pulse, approximated with a triangular pulse  the charge Q transferred during the complete switching of a logic gate is equal to the area under the curve

Normalized power of switching current As a result of few calculations, we obtain Term : dc component of digital switching power Term : ac component of the power More general expression: : “pulse shape” factor, depending on the single current pulse waveform in time domain. whose normalized power is

Model validation clip.pla: digital combinatory circuit included in the IWLS’93 benchmarks synthesized using equal-delay gates in a 180-nm CMOS technology: inverter, 2-input NAND and NOR gates. network made of about 130 logic gates. inputs are driven with random digital signals; at any time, only one bit can change its logic value. Transistor-level simulation with SPECTRE values of the i DD current, sampled at 1-ps intervals, were stored for post-processing. Two different average values of input transition rates, giving a low-density and a high-density switching activity. the number of logic transitions at high-density transition is approximately ten times larger than the low-density transition.

Model validation: amplitude distribution Current waveforms exhibit triangular pulses Simulated circuit gates with different capacitive loads  different current peaks (generalized Poisson process). Amplitude density constant for intermediate values of current For low current values the amplitude density is larger to account for pulse tails. Peak values of the single current pulse assumed to be uniformly distributed between i 2 and i 3. Amplitude density of the single switching current pulse. Digital switching currents (low density of logic transitions).

Amplitude distribution: results Simulated pdf of the i DD switching current (low and high density of logic transitions) Theoretical pdf of the i DD switching current (low and high density of logic transitions)

Model validation: power spectral density Simulated psd of the i DD switching current (low and high density of logic transitions) Theoretical psd of the i DD switching current (low and high density of logic transitions)

IDEA To analyze different logic synthesis techniques from digital switching noise viewpoint To apply the developed methodology to the same logic function, synthesized with different techniques CLIP benchmark circuit: Sop: ~ 770 MOS transistors Xor: ~ 400 MOS transistors 6 transistors 16 transistors

SOP subcircuits NAND NORINVERTER

XOR circuit ABY 00B 01B 10A 110 XOR asymmetric circuit just in one case the output is connected to a supply node In the other three cases XOR works as transfer gate Differences which depends on what input signal switches

Power dissipation fewer MOS transistor= lower digital switching noise? MOS transistor: Static power dissipation Dynamic power dissipation It is important the number and the distribution of input signal commutation Input files Switching at random instants At any time just one input signal can commutate

Currents SOP XOR

PDF SOPXOR

PSD SOP XOR

Conclusion Digital switching noise as stochastic process Faster estimation of digital switching noise, described by few parameters Digital switching current as shot noise process Amplitude density and power spectral density of switching currents derived Circuit synthesized with XOR gates exhibits lower switching activity Future development Analysis for pseudo-synchronous circuits Methodology to optimize the number and distribution of the commutations of logic gates