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I understand some formulas for determining whether a NMOS transistor is activeis VGS > Vth and if its in saturation you take the drain-to-source voltage VDS => VGS - Vth

But how does the substrate voltage play a part in determining this behavior? For example the image below

enter image description here

If I were to change the substrate voltage from 0 to 5V. Could I turn ON/OFF the transistor and affect the region of operation?

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    \$\begingroup\$ You can find a lot about that using the search terms 'body effect' and 'back biasing'. I found This very good: people.ece.umn.edu/~kia/Courses/EE5323/Slides/Lect_05_MOS2.pdf \$\endgroup\$ – Oldfart May 30 '18 at 14:21
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    \$\begingroup\$ It's sometimes called a "back gate", which might help with your searches. \$\endgroup\$ – Spehro Pefhany May 30 '18 at 14:22
  • \$\begingroup\$ Some opamp circuits do use the Body(s) as input(s) to the opamp. \$\endgroup\$ – analogsystemsrf May 31 '18 at 3:58
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No, you can't increase the substrate voltage to 5V...that would cause the substrate-to-source PN junction to become forward biased.

However, you can change the substrate-to-source voltage and thereby change the transistor's threshold voltage...this is called the "body effect". Making the substrate more negative with respect to the source will increase the transistor's threshold voltage. MOS circuits usually do not allow the substrate voltage to be higher than the source voltage, so the lowest transistor threshold voltage would occur when the source and substrate are tied together.

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