Transient Simulation of Dynamic-Comparator Noise

This project includes a Verilog-A test block for measuring noise and offset of a comparator. Designed at the Institute of Microelectronics, Ulm University, Ulm, Germany by Joschua Conrad under the supervision of Prof. Maurits Ortmanns. Published at NEWCAS 2024. When using the code or concepts shown here for your own work, please cite the published paper:

bibtex @inproceedings{Conrad_Confidence_Boosting_2024, author = {Conrad, Joschua and Kauffman, John and Wilherlmstätter, Simon and Asthana, Rohan and Belagiannis, Vasileios and Ortmanns, Maurits}, title = {Confidence Estimation and Boosting for Dynamic-Comparator Transient-Noise Analysis}, booktitle = {2024 22nd IEEE International New Circuits and Systems Conference {(NEWCAS)}}, date = {2024-06-16}, eventtitle = {2024 22nd IEEE International New Circuits and Systems Conference {(NEWCAS)}}, publisher = {IEEE}, location = {Sherbrooke, CA}, pages={1-5}, doi={10.1109/NewCAS58973.2024.10666354}, url={https://ieeexplore.ieee.org/document/10666354}, }

Also please acknowledge LICENSE.

Test Procedure

The test block can provide a test-voltage $v_{t}$ to the comparator, simulate a number of decisions and read its output. The following comparator properties can be found:

• Plain comparator offset without any noise by utilizing a binary search (BS) algoithm. This needs only about 20 decisions and simulates very fast.

• Unknown noise and unknown offset by using the proposed confidence boosting and a mix of binary-search and deterministic convergence to find a test-voltage $v_{t}$, which ensures a known share of decisions being flipped by noise. This simulation takes more time, but the confidence into the predicted sum of noise and offset is known without any assumptions or limitations regarding noise or offset.

• Unknown noise without any offset can be tested with the same algorithm, but deterministic convergence is then even faster, as it does not need to predict offset from simulation history.

• Lastly, the test block provides an input ramp with known bounds around the comparator's trip-point. This is handy for anaylzing e.g. metastability.

The following table lists the simulation procedure depending on whether the comparator is noisy or has offset.

| | w/ Offset | w/o Offset | |----|-----------|------------| |w/ Noise|Confidence-Boosted Convergence with offset guessed from simulation history|Confidence-Boosted Convergence with more educated guess $v_{o}=0$| w/o Noise|Rapid Binary-Search Convergence|Simulate input-ramp only|

How to Use

It is assumed, that Cadence Virtuoso Analog Design Environment is used.

1. Download all files.

2. Create a new cell(view) from the code.

   1. Create empty Verilog-A cell and view
   2. Copy-paste the provided code from veriloga.va.
   3. Check and Save.
   4. Create a symbol view from Verilog-A view.

3. Place the block

   1. Place the schematic symbol next to the comparator in a schematic.
   2. Connect clock, reset and supply.
   3. STIM connects to the input of your comparator. COMP to the output of the comparator. Use baluns, if the comparator has differential terminals.
   4. Parameterize the block. The CDF parameters should be editable on the placed instance. See parameter description.

   - Make sure to set *SNCDFI_TABLE_PATH* to an absolute path.

   - Set *HAS_NOISE* and *HAS_OFFSET* to variables controlled from ADE.
     This allows to first simulate just the offset without any noise and
     then just the noise on the same testbench schematic.

   - *DECISIONS_PER_ITER* (K), *CONFIDENCE_SAMPLE_RANGE* (r) and
     *EXPECTED_FLIP_NUMBER* (M) should always be set. Choose values from
     the manuscript Table I.

   - *Threshold* and *Trf* should be set according to level and speed of
     your logic signals. Good guesses are half the supply voltage for
     *Threshold* and about 1/100 of the clock period for *Trf*.  

1. Simulate

   1. Make sure, that the sncdfi file is inside a directory where the simulator finds it. This can be your project directory. See also sncdfi.

   2. Setup the simulation.

      1. Choose a simulator understanding Verilog-A, e.g. Spectre.
      2. Use a TRAN simulation. Possibly run two: a noisy and a non-noisy one to find the sum of offset and noise and just the offset. Make sure to run the exact same netlist (beside test block parameters) to ensure that all devices use the same Monte-Carlo sequence in the two (noisy, non-noisy) simulations.
      3. If automatic simulation stopping is enabled (default), choose a huge simulation time. The test block will stop simulation as soon as the $v_{t}$ search converged.
      4. In the settings, go to Outputs -> Save All and enable saveahdlvars.
      5. Add Verilog-A variables as output. If the test-block instance is named ISTIM, one can add the variable finalvt by adding the output expression getData("ISTIM:finalvt" ?result "tran"). The results browser can be used after a simulation to find these expressions. Add the following outputs.

      | Variable | Meaning | | -------- | -------- | | finalvt | The final test voltage $v{t}$ after convergence, which is the noise amplitude standard deviation $\sigma{n}$ minus the offset $v_{o}$. | | convergencegood | 1, if the algorithm convergence worked. | | flippeddecisionsdebug | How many decisions flipped during the last iteration. Over iterations, this approaches M and one can observe convergence here. | | totaliters | Total number of done iterations, where each one simulated K samples. | | badrampsamples | Refers to the input-ramp test. This many decisions did not have the desired value (due to noise, metastability, ...) |

      It is also recommended to create one output endtime with expression xmax(xval(anyoutput) -1), as that finds the end-time of the simulation. anyoutput is any named output expression. With value(anyotheroutput endtime), one can then evaluate the values of outputs at the end of simulation, as for e.g. finalvt that is the one time where the variable has its final value.

Block Interface

This describes parameters and ports of the block.

Parameters

First, common parameters are introduced.

| Parameter | Meaning | Allowed Values | Default | |-----------|---------|----------------|---------| |HASOFFSET|If set, it is assumed that the comparator has offset. So the offset is estimated by binary-search for non-noisy comparators. For noisy comparators, a confidence-boosted convergence for $v{t}$ is always needed, but the offset $v{o}$ does not need to be estimated from simulation history for comparators not having an offset.|bool|Comparator has offset.| |HASNOISE|If set, it is assumed that the comparator has noise. The confidence-boosted convergence is used then. Otherwise, only a simple binary-search offset estimation or even just the ramp-shaped stimulus is applied.|bool|Comparator has noise.| |DECISIONSPERITER|Number of simulated decisions per iteration. Manuscript calls this K.|integer larger than 1|Defaults from Table I for $c=0.9$ and $a=0.1$.| |EXPECTEDFLIPNUMBER|Targeted number of noise-flipped decisions per iteration. Manuscript calls this M.|integer larger than 0|Defaults from Table I for $c=0.9$ and $a=0.1$.| |CONFIDENCESAMPLERANGE|Tolerated range expressed in number of samples around K. Manuscript calls this r.|integer larger than or equal to 0|Defaults from Table I for $c=0.9$ and $a=0.1$.| |DEBUG|Whether to print debug messages about convergence.|bool|Print messages.| |FIRSTVTFACTOR|Relative magnitude of first applied binary-search stimulus. Large values increase the number of iterations. Small values set a starting binary-search stimulus, where exactly half the decisions are flipped by noise. There is then no information about noise in the decision counts. Deterministic convergence cannot start with that. So the binary-search convergence continues, decreases the stimulus magnitude and makes the problem even worse. Increase this value, if very large offset or noise prevents convergence. Note that offset-only binary-search convergence ignores this parameter value and uses one being as large as possible, as simulation time is anhow short.|float larger than 0 up to 0.5|First $v{t}$ is 1/100 of half the dynamic range. In all experiments, this was good enough to make it into deterministic convergence, which can then find any $v{t}$.| |RAMPLOWERBOUND|First collected ramp stimulus sample.|real value between -1 and 1, where -1 descibes to use $-\frac{VDD-VSS}{2}$, where STIM outputs VSS if VCM is $\frac{VDD-VSS}{2}$. 0 causes STIM to output VCM|-1, which starts the ramp at VSS, if VCM is mid-rail.| |RAMPUPPERBOUND|Last collected ramp stimulus sample.|real value between -1 and 1, where +1 descibes to use $+\frac{VDD-VSS}{2}$, where STIM outputs VDD if VCM is $\frac{VDD-VSS}{2}$. 0 causes STIM to output VCM|+1, which ends the ramp at VDD, if VCM is mid-rail.| |RAMPSTEPS|How many decisions to collect along the ramp. Endpoints are included. Odd values tend to include $v{t}=0$.|integer larger than 1|10 samples.| |SNCDFITABLEPATH|The path to the sncdfi table described in sncdfi.|Any string. Prefer absolute paths.|File sncdfi_table.csv in simulator working directory.|

The following parameters are not recommened to be changed.

| Parameter | Meaning | Default | |-----------|---------|---------| |NUMEXTRAITERS|How many deterministic convergence cylces to proceed after a first one was successfull. This increases confidence.|Add one additional convergence iteration. If that is done, the whole history is filled with results from deterministic convergene and it is ensured, that the first deterministic convergence was not reached "by chance".| |MAXITERS|Maximum number of iterations to simulate, after which the simulation is aborted even if no convergence was reached. This is implemented to prevent a simulation from hanging.|30 iterations, which caused no aborted simulations in the experiments.| |EXPECTEDFLIPRATIO|The manuscript calls this $sncdf(m)$. Change this when changing the assumed noise distribution. Needs to be given, as only sncdfi is implemented in Verilog-A.|sncdf(-1) for white noise and a gaussian distribution.| |DISTRIBUTIONMOVE|Where to move the noise distribution. The manuscript calls this $m$.|A value of 1 ensures, that $-v{t}$ is the sum of $-\sigma{n}$ and $v{o}$.| |OFFSETDETECTION_BITS|How many binary-search iterations to run in a non-noisy offset estimation.|20 iterations still run very fast, as one iteration in offset-only estimation has only a single simulated decision. Still, 20 iterations provide an accuracy in the range of $\frac{VDD-VSS}{2^{20}}$.|

Ports

| Port | Meaning | |------|---------| |CLK|Clock port. When this crosses Threshold, the comparator decision is watched and remembered and a new $v{t}$ is generated.| |RST|Clock synchronous reset. This can interrupt and reset the whole test routine. A more common use-case is to delay the begin of the test routine to do some settling/initialization of the comparator.| |VDD|Upper supply rail. Defines the full-scale of $v{t}$ for binary-search convergence and for applying the ramp stimulus.| |VSS|Lower supply rail. This is the 0 logic level. VDD and all voltage inputs use this as a reference.| |VCM|Common-mode of STIM.| |STIM|$v{t}$ is output here. Connect to comparator input. Use balun if needed. If $v{t}=0$, this will output VCM.| |COMP|Comparator decision is read here. Connect to comparator output. Use balun if needed. If STIM is larger than VCM, the decisions COMP should tend towards 1.| |PWRMEASn|Is VDD most of the time and only VSS during ramp-shaped stimulus. Can be used to window a power-measurement block to average power consumption during ramp stimulus.|

sncdfi

The confidence derivation needs to know the stochastic properties of the underlying random noise process. This is done by providing the inverse cumulative noise density function. Such functions are not available in Verilog-A and are hence represented as table models. The support values for the table are stored in sncdfi_table.csv. This table is computed from a standard normal cumulative density function inverse (sncdfi).

The table can quickly be re-created. Use python, numpy and scipy and the following code to re-create the table in your current working directory. python import scipy as sp import pathlib as pl import numpy as np NUM_POINTS = 10_0001 EBS = 1. / NUM_POINTS outpath = pl.Path() / "sncdfi_table.csv" xdat = np.linspace(start=EBS, stop=(1.-EBS), num=NUM_POINTS) ydat = sp.special.ndtri(xdat) combined = np.stack((xdat, ydat), axis=-1) np.savetxt(outpath, combined) An odd number of points is recommended, as that also evaluates the function at exactly 0.5. The outer bounds 0 and 1 are excluded with a numerical precision EBS relative to the exported number of points, as the function is undefined at these points.

Tested Versions

The block was tested with Cadence Virtuoso IC6.1.8 and Spectre 21.1.0.

Why no Maestro View, Symbol View, or Testbench Schematic is Provided

In order to not violate any NDA regarding a PDK or Virtuoso itself, no binary files are provided, as only textual files can be screened for inclusion of sensitive information. Hence, no full cell or cellview is provided with the files uploaded here. Instead, this document provides all information to create the needed cells and cell-views.

Acknowledgment

This work was funded by the German National Science Foundation (DFG) under grant number BE 7212/7-1 | OR 245/19-1.