jFET load line arithmetic

Discussion in 'General Electronics Chat' started by tindel, Nov 8, 2015.

  1. tindel

    Thread Starter Active Member

    Sep 16, 2012
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    I am working on a RF(ish) receiver that uses a common source jFET input stage. The design will eventually be open source and I am planning on releasing detailed design information here in the completed projects section once I'm done. I am currently writing a report on how to design a CS input stage, and this has left me needing to be able to solve the following equation for Vgs... but I'm stuck - I don't even know where to look to try to solve this equation. You might notice that this equation is derived from the equation of the load line and the equation of the transconductance equal to each other.

    upload_2015-11-8_11-0-56.png

    Note that sf is the 'squared factor' which is usually 2 - but does vary with transistor and I have accounted for this in my calculations. I could use the quadratic equation... Approximating the value by setting this value to 2, but this doesn't do me any good because there is no 'a' - not that I can readily identify anyway. I would also prefer to not assume a squared factor of 2.

    Any help pointing me in the right direction would be helpful.
     
  2. Jony130

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    Feb 17, 2009
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    Last edited: Nov 8, 2015
  3. tindel

    Thread Starter Active Member

    Sep 16, 2012
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    Yes - I am biasing up the gate voltage to obtain less delta_I between transistor variance. That is where that term comes from.
    upload_2015-11-8_12-13-37.png

    I guess I should clarify. I know the square factor - I have calculated it from data in the datasheet. I guess I'm asking how to solve this equation when the value is not 2. I've realized however that I'm not sure how to solve the equation if it was 2.
     
  4. Papabravo

    Expert

    Feb 24, 2006
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    Take the logarithm of both sides and solve the resulting equation.
     
  5. Jony130

    AAC Fanatic!

    Feb 17, 2009
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    For this case you have the equation in this pdf on page 5
    http://cecs.wright.edu/~dkender/bme3512/BiasingFETs.pdf

    Also I do not understand why you need to know Vgs ?? All you need is Rs.
    So the equation for Rs looks like this
    1.PNG
     
    Last edited: Nov 9, 2015
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