Determining signal (internal) resistance and bypass/coupling capacitance values for JFET circuit

Discussion in 'Homework Help' started by bdn1790, Jan 10, 2019.

  1. bdn1790

    Thread Starter New Member

    Dec 31, 2018
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    A basic common-source potential divider JFET circuit is given with existing values, and with me calculating them with the help of another user in this forum:

    ImgrImage.png

    V_{DD} = 20V (Power Supply)
    I_{DSS} = 10mA
    I_{DQ} = 3mA
    V_G = 1.728V
    V_{GSQ} = -1.357V
    V_{GS(OFF)} = -3V
    V_{DS} = 7V
    g_m = 3.51mS
    R_S = 1028\Omega
    R_D = 3305\Omega
    R_1 = 1585450\Omega
    R_2 = 150k\Omega
    R_L = 10k\Omega
    r_d = \infty (negligible)

    [​IMG]

    My objective now is to find the bypass/coupling capacitance values (C1/Cs/C2) and the signal (internal) resistance using a low-frequency small signal analysis so that I can find the cutoff frequencies:f_{L_{C_{i}}}, f_{L_{C_{o}}}, f_{L_{C_{s}}}

    f_{L_{C_{i}}} = Lower cut-off frequency at capacitor Ci = \frac{1}{2\pi(R_{sig}+(R_1||R_2))C_i}

    f_{L_{C_{o}}} = Lower cut-off frequency at capacitor Co = \frac{1}{2\pi(R_D+R_L)C_o}

    f_{L_{C_{s}}} = Lower cut-off frequency at capacitor Cs = \frac{1}{2\pi(R_{eq})C_s}, where R_{eq} = R_S || \frac{1}{g_m}

    I can find the equivalent resistance from the bypass capacitor Cs at the source resistance Rs using the above formula, but then what to do next? I do not have the values of Rsig (signal resistance) and the capacitance values. The solutions I have tried are:

    1. I attempted to use this online resource in finding Rsig. Though, my assignment question did not provide the value of Vsig so I am unable to use the equations provided in that resource.

    2. I am unable to use the internal/stray capacitance that become available at high frequency, because I am supposed to solve this at low frequency.

    3. Although I can find the voltage gain at midrange frequency, I fail to see how it can help me in finding the aforementioned values unless I am missing out on something.

    Pointing me in the right direction would be very helpful. Thanks!

    Mod edit: added image from link.
     
    Last edited: Jan 15, 2019 at 1:42 PM
  2. dl324

    AAC Fanatic!

    Mar 30, 2015
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    Schematic referenced:
    [​IMG]

    Is this school work?
     
  3. bdn1790

    Thread Starter New Member

    Dec 31, 2018
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    Yes, university assignment.
     
  4. dl324

    AAC Fanatic!

    Mar 30, 2015
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    You need to post your work so members can see where you're having difficulty and can offer guidance.
     
  5. Jony130

    AAC Fanatic!

    Feb 17, 2009
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    OMG, electronic is not the math classes. Such precision in the calculation is pointless. It is impossible to buy 1028.255451Ω ohms resistor.
    And most resistors we are using will have 5% tolerances.

    Did you ever heard about E24 series?

    And F_LG and others are equal to what?

    Next, you need to find the equivalent resistance "seen" from the capacitor's terminal (from the capacitors point of view).
     
  6. bdn1790

    Thread Starter New Member

    Dec 31, 2018
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    I apologize for giving the exact resistance values. I have updated the thread with more information, hopefully that can better help you understand what my problem is. I have also updated the thread with the formula for the equivalent resistance. I can also find the value of the equivalent resistance. But what to do from there? Do I have to analyze the small-signal circuit using KVL at the capacitance, or?
     
  7. Jony130

    AAC Fanatic!

    Feb 17, 2009
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    If in your technical requirement do not specify the lower cutoff frequency. You can choose it yourself between 10Hz...500Hz.
    Or simply write that the capacitor reactance Xc should be equal or lower than the equivalent resistance seen by the capacitor at the lowest frequency you care about. Xc ≤ Req. As for the Rsig if not specified simply assume Rsig = 0Ω.
     
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