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7.3: Circuits and Techniques for High-Resolution Measurement of On-Chip Power Supply Noise

7.3: Circuits and Techniques for High-Resolution Measurement of On-Chip Power Supply Noise. Elad Alon, Vladimir Stojanovi ć , and Mark Horowitz Stanford University Rambus Inc. Motivation and Challenges. Scaling leads to drastic reduction in required supply grid impedance

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7.3: Circuits and Techniques for High-Resolution Measurement of On-Chip Power Supply Noise

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  1. 7.3: Circuits and Techniques for High-Resolution Measurement of On-Chip Power Supply Noise Elad Alon, Vladimir Stojanović, and Mark Horowitz Stanford University Rambus Inc.

  2. Motivation and Challenges • Scaling leads to drastic reduction in required supply grid impedance • Supply noise a concern even for digital circuits • CAD tools to quantify supply noise exist • But haven’t been verified • Measuring supply noise is challenging • 20 GS/s, 8-bit ADC’s aren’t cheap 1mΩ(!)

  3. Measurement Approaches • Sub-sampling oscilloscope • Measure repetitive waveforms • Collect probability distribution of noise • Can’t measure noise dynamics • Need distribution and spectrum to characterize effects of noise on circuits. • Measure autocorrelation to find spectrum of supply noise • Extension of sub-sampling technique • Only need 2 low rate samplers

  4. Outline • Random Noise and Autocorrelation • Measurement Circuits • Measurement Results • Measurement Validation • Conclusions

  5. Random Supply Noise • Supply noise is basically deterministic • But extremely complicated to calculate • “Noise” is a label for a random process • Characterized by its frequency spectrum • Which can be found through autocorrelation

  6. Autocorrelation • Autocorrelation measures how correlated a process is with a delayed version of itself • For a stationary (time-invariant) process: • R() = E[V(t-/2)·V(t+/2)] R(τ) • Example: zero-mean white noise • Each time sample independent • Therefore autocorrelation is σ2 δ() σ2 τ

  7. Power Spectral Density • Power Spectral Density (PSD) is the Fourier transform of R White Noise PSD R(τ) ω τ Low-pass Filtered White Noise R(τ) PSD ω τ

  8. Measuring Autocorrelation • Autocorrelation is an average property • Don’t need to know V for all t • Just need pairs of samples • Nyquist frequency set by minimum  • Not by sampling rate V   Tsamp

  9. Outline • Random Noise and Autocorrelation • Measurement Circuits • Measurement Results • Measurement Validation • Conclusions

  10. Measurement System Block Diagram

  11. Sampler Implementation

  12. Sampling switch • PMOS switch to achieve bandwidth • Separate, higher supply • VddQ = 1.3 V • Noise on VddQ couples to sample node through switch parasitics • VddQ heavily decoupled to Vss

  13. VCO-based ADC • VCO converts V to f • Count clock edges to estimate f • Measures average VCO frequency • Filters high frequency noise

  14. VCO-based ADC cont’d • Simple, cheap ADC • High resolution • 1 LSB = 1/(TwinKVCO) • Random VCO phase dithers count by 1 • Increases resolution with averaging • Bad accuracy • But don’t care since we’re calibrating

  15. Outline • Random Noise and Autocorrelation • Measurement Circuits • Measurement Results • Measurement Validation • Conclusions

  16. Chip Details • 0.13 m tech. with four 1-10 Gb/s serial links1 • Can measure digital (Vdd) and analog (VddA) supplies • Noise generators for validation ASIC Link C Link D Link B Link A Measurement Circuits 1 See papers 21.3 and 21.4 for more information on these links

  17. ADC Calibration Curves • Kvco  2.6 GHz/V • With 1 s conversion: • 1 LSB = 385 V

  18. Measured Supply Noise:Deterministic Variations • All 4 links running at 4 Gb/s, 231 PRBS data • Check for deterministic waveform • ~20mV peak-to-peak noise on Vdd and VddA

  19. Measured Supply Noise:Stationary PSD • 3 frequencies from deterministic noise: • 200 MHz - ASIC core • 400 MHz - ref clock & some link logic • 4 GHz - tail current modulation

  20. Measured Supply Noise:Stationary PSD • Random noise appears mostly white • Saw periodic variations in the supply • Could random noise vary as well?

  21. Outline • Random Noise and Autocorrelation • Measurement Circuits • Measurement Results • Measurement Validation • Conclusions

  22. Are we measuring true supply noise? • We used a separate supply VddQ • Sensitive to low frequency VddQ noise • Is VddQ quiet at low frequencies? • We assumed the noise was stationary • Noise might vary with time • How do we measure varying noise?

  23. Is VddQ really quiet? • Key accuracy concern: • Is VddQ really quiet at low frequencies? • Validation method: • Take 2 waveform measurements • First one with noise averaged out • Second one with noise un-averaged • Compare the 2 measured waveforms

  24. Generating Vdd and VddQ Noise • On-chip noise generators inject square-wave currents onto grid • Current causes on-chip Vss to rise relative to board Vss • If VddQ uncoupled to on-chip Vss: • On-chip VddQ has “half” of Vdd signal

  25. Effect of VddQ Noise on Measurement • Vmeasured(t) = Vdd(t) + avg(VddQ(t->t+Twin)) • If Twin = noise pulse-width: • Noise adds triangle wave to measurement • Height of triangle indicative of VddQ noise

  26. Measured VddQ Noise • Twin = 500 ns • Inject noise onto VddA at 4 MHz and at 1 MHz • Height of “triangle” for 1 MHz noise is negligible. • VddQ noise is minimal.

  27. Is Supply Noise Stationary? • Chip clocks may modulate noise. • Number of transitions random, timing periodic. Clock Chip Current • Modulation is repetitive • Supply noise is cyclostationary. • At same time point in each cycle, noise statistics are the same.

  28. Cyclostationary Noise Clock Vdd   t t • Cyclostationary: R, PSD different at each t. • Keep track of t when measuring R. • Can measure average (stationarized) PSD. • By randomly choosing t. • This is the noise many applications care about.

  29. Measured Cyclostationary Noise Example • Measure PSD of random noise at two different times to see example behavior • Reduce link data-rate to 2 Gb/s to make cyclostationarity more apparent • Most digital logic quiet at end of the cycle.

  30. Measured Supply Noise:Cyclostationary PSDs • Measurement verifies cyclostationary behavior • 1 GHz noise at t2, but not at t1 • Link clock is 1 GHz for this data-rate • Link relatively quiet at t1, active at t2

  31. Conclusions • Noise spectrum is relatively easy to measure • Just need 2 low-rate samplers • VCO provides cheap, high-resolution ADC • Supply noise is not stationary • But often only interested in time average noise • Can measure cyclostationary statistics too • Measurement circuits can validate CAD tools • Designers can check circuits with verified noise

  32. Acknowledgements • This work was funded by C2S2, the MARCO Focus Center for Circuit & System Solutions • V. Abramzon and B. Nezamfar at Stanford University • Rambus RaSer X design team

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