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standard deviation of the mismatch for two devices (Read 148 times)
polyam
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standard deviation of the mismatch for two devices
Jan 09th, 2023, 12:28pm
 
Hi,

According to Pelgram's rule the standard deviation of the mismatch for two devices is calculated by Delta_Vth = Avth / sqrt(WL). Obviously W and L is the device size and Avth is a technology dependent constant. Could you please anyone help me how to find/calculate/simulate that constant for a given MOS process?

Thanks
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smlogan
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Re:  standard deviation of the mismatch for two devices
Reply #1 - Jan 14th, 2023, 11:02am
 
Dear polyam,

> Could you please anyone help me how to find/calculate/simulate that constant
> for a given MOS process?


The constant has been documented in various forms in a number of papers. Marcel Pelgrom (note spelling) and others (see references 1,2) have devised a term "matching energy" defined as Cox*AVT^2 that has been documented to show how the term varies with process node. You might examine the figures in either of these two references to better understand the magnitude of the AVT^2 term. If you are getting models for simulation from a foundry that include mismatch parameters, you can probably simulate the mismatch for devices with different W/L to emprically estimate its value for that process.

Shawn

[1]. P. R. Kinget, "Device Mismatch: An Analog Design Perspective," 2007 IEEE International Symposium on Circuits and Systems, New Orleans, LA, USA, 2007, pp. 1245-1248, doi: 10.1109/ISCAS.2007.378336.
[2.] M. J. M. Pelgrom, H. P. Tuinhout and M. Vertregt, "Transistor matching in analog CMOS applications," International Electron Devices Meeting 1998. Technical Digest (Cat. No.98CH36217), San Francisco, CA, USA, 1998, pp. 915-918, doi: 10.1109/IEDM.1998.746503.
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Shawn
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A Kumar R
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Re:  standard deviation of the mismatch for two devices
Reply #2 - Jan 16th, 2023, 1:19am
 
Hi Polyam,

usually PDK document contains a plot of Vth mismatch voltage vs. 1/sqrt(WL), can we find this constant from the plot?.

Thanks.
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andyjackcao
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Re:  standard deviation of the mismatch for two devices
Reply #3 - Jun 3rd, 2023, 6:31am
 
enjoy it
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my mail is andyjackcao@sina.com;
I am focus on analog IC,that is wonderful!
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andyjackcao
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Re:  standard deviation of the mismatch for two devices
Reply #4 - Jun 3rd, 2023, 6:33am
 
the other paper
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my mail is andyjackcao@sina.com;
I am focus on analog IC,that is wonderful!
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jerry lang
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Re:  standard deviation of the mismatch for two devices
Reply #5 - Jul 22nd, 2023, 4:17am
 
To calculate the standard deviation of the mismatch for two devices, you would typically follow these steps:

Collect Data: Obtain measurements or data points from both devices under the same conditions or tests.

Calculate the Differences: For each corresponding data point from the two devices, calculate the difference between them. If Device A has measurements A1, A2, ..., An, and Device B has measurements B1, B2, ..., Bn, then the differences would be D1 = A1 - B1, D2 = A2 - B2, ..., Dn = An - Bn.

Calculate the Mean: Find the average of all the differences calculated in step 2. This is done by summing all the differences and dividing by the number of data points (n).

Calculate Variance: For each difference, subtract the mean (calculated in step 3) and square the result. Then, find the average of these squared differences.
spinning the wheel to solve the problem
Calculate Standard Deviation: The standard deviation is the square root of the variance calculated in step 4.

The formula for the sample standard deviation (used when dealing with a subset of data) is:
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