How to simplify behavior of a field-effect transistor

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Discussion Overview

The discussion revolves around the governing equations for field-effect transistors (FETs), comparing them to bipolar junction transistors (BJTs). Participants explore the relationships between gate voltage and source-to-drain current, as well as the implications of different types of FETs, such as MOSFETs and JFETs. The conversation includes inquiries about linear approximations and the use of datasheets for practical applications.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether there are simple governing equations for FETs similar to those for BJTs, suggesting a linear relationship between source-to-drain current and gate voltage.
  • Another participant notes that the current is typically represented by the square of the gate voltage, adjusted for the gate threshold voltage.
  • A participant provides a specific equation for the input-output relationship of FETs, including the concept of transconductance.
  • There is mention of the limitations of datasheet curves, indicating that they usually apply at a single VDS value and may provide multiple curves for different conditions.
  • Corrections are made regarding earlier formulas, emphasizing the need for squaring terms in the equations presented.

Areas of Agreement / Disagreement

Participants express varying views on the governing equations for FETs, with some proposing specific models while others highlight the complexity and variability depending on the type of FET. Corrections and refinements to earlier claims indicate ongoing uncertainty and discussion.

Contextual Notes

Some participants acknowledge the limitations of their earlier statements and the need for more precise equations, particularly regarding the squaring of terms in the equations. There is also a recognition that the behavior of FETs can differ significantly based on their type and operating conditions.

Who May Find This Useful

This discussion may be useful for students and professionals interested in the theoretical and practical aspects of field-effect transistors, particularly those comparing FETs to BJTs or seeking to understand the implications of datasheet specifications.

SupernerdSven
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Are there simple governing equations for FETs like there are for BJTs, and if so, what are they? For example, in the BJT case we have
IC = β×IB
IE + IC + IB

I'm sure it depends on the type - MOSFET, JFET, etc. - so anything anyone could contribute would be helpful. From what I understand, the source-to-drain current is proportional to the gate voltage, so if it's linear it would be something like
IDS = β×VG

From what I've seen Googling IV curves, that's fairly close up until saturation. Am I off base here, or am I on the right track?
 
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SupernerdSven said:
Are there simple governing equations for FETs like there are for BJTs, and if so, what are they? For example, in the BJT case we have
IC = β×IB
IE + IC + IB

I'm sure it depends on the type - MOSFET, JFET, etc. - so anything anyone could contribute would be helpful. From what I understand, the source-to-drain current is proportional to the gate voltage, so if it's linear it would be something like
IDS = β×VG

From what I've seen Googling IV curves, that's fairly close up until saturation. Am I off base here, or am I on the right track?

(a) BJT
The second equation should be: IE=IB+IC.
More than that, for the BJT you forgot the control function IC=Io*[exp(VBE/Vt)-1].
This equation is important because the slope of this function gives the transconductance g=IC/Vt.

(b) FET
Here, the input-output relationship (control function) is ID=ID,max*[1-(VGS/VP)²]
with VP: pinch-off or threshold voltage, respectively.
Again, the transconductance is the slope of this function: g=2*SQRT(ID*ID,max)/|VP| .
 
Or you just look up the characteristics in a data sheet:
IDVGS.jpg
 
the datasheet curve only works at one VDS value, usually they give you multiple curves
 
Thanks, everyone!
Baluncore: Wow, I must have missed that. Thanks for pointing it out!
LvW: Whoops, sorry about the typo. Yes, we only used the linear approximation in the class I took - we didn't need anything finer at the time. I appreciate your contribution!
Svein and donpacino: Thanks for pointing those out! Since I didn't feel that I knew enough about how I could use one, I hadn't looked into the datasheets much, but now I know what to expect.
 
donpacino said:
the datasheet curve only works at one VDS value, usually they give you multiple curves
Yes, but when I tried to copy from a real datasheet it was "protected". So for a real datasheet, search at On Semiconductor or Texas Instruments.
 
Sorry, I have to correct one of my formulas (post 3). The expression in the outer brackets [... ] must be sqared:
correct: ID=ID,max*[1-(VGS/VP)]²
 

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