Q. Impedance Calculation Formula for TIA

Discussion in 'Homebrew and Kit Projects' started by VK4HAT, Jun 26, 2018.

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  1. VK4HAT

    VK4HAT XML Subscriber QRZ Page

    Anyone up on their Termination Insensitive Amps? R3,4 and 6 set the input impedance to Q1 at 50R. What is the actual equation used to derive that?

    I have tried following the Wes Hayward rabbit hole of PDF's all over the internet that quote missing information from other PDF's and cannot make sense of what information i have found.

    Anyone know the formula or if there is an online calculator, I want to change the input impedance to 200R, so i can forgo winding a transformer.

  2. SM0AOM

    SM0AOM Ham Member QRZ Page

    The design equations and their derivation are found in this document:


    By changing R3 and R6 to 1000 and 56 ohms respectively,
    you will get an input impedance of about 200 ohms, but at some expense of transducer gain and bandwidth.
    R4 is unchanged, as it has influence on the DC operating point of the transistor.

    You will have to check for yourself if the resulting bandwidth will be sufficient for your application.

    VK4HAT likes this.
  3. VK4HAT

    VK4HAT XML Subscriber QRZ Page

    Thanks for the actual values i need. I read that paper twice earlier today and it makes no sense to me. In the first sentence he introduces a value Gm but no way to derive it, or where it comes from. The assumption is made the reader already knows what this is as all the following equasions rely on this value, but i dont know. No offense to Wes Hayward, he is a very clever man but he is painful to read if you are a layman without 30 years as an rf engineer.

    Can you explain how you arrived at those values?
  4. SM0AOM

    SM0AOM Ham Member QRZ Page

    This is explained in the second section: "Adding emitter degeneration"

    The new parameter Gm was introduced as the limit value of 1/(1/gm+Rd)
    when gm is very large.

    This is a quite crude approximation, but sufficiently good for our purposes.

    The actual relation I used,
    implemented as an Excel spreadsheet is:

    Zin = (Rl+Rf)/((Rl*1/Rd)+1)

    here Rl is the 330 ohm or R4
    Rf the 1000 ohm or R3
    and Gm = 1/Rd (R6) or 1/56

    I then shuffled around some resistor values in a range that felt reasonable, knowing that for good RF wideband performance the resistor values should not be made too large, until Zin came out as about 200 ohms.

    It is here my soon 40 years of analogue circuit and RF engineering experience enters...

    VK4HAT and AB3TQ like this.
  5. VK4HAT

    VK4HAT XML Subscriber QRZ Page

    Thank you very much, that is clear, concise and everything i was looking for.
  6. K6BSU

    K6BSU Ham Member QRZ Page

    I looked at this circuit for a long time, trying to understand why an emitter follower drives yet another emitter follower. Seems like just one would be sufficient. Since there is no overall feedback, Q4 has no influence on input Z. Should work however.
  7. AC0OB

    AC0OB Subscriber QRZ Page

    It is somewhat of a "Darlingtonesque" arrangement.

  8. K6BSU

    K6BSU Ham Member QRZ Page

    Maybe if two is good, then three would be better?
  9. VK4HAT

    VK4HAT XML Subscriber QRZ Page

  10. N1OOQ

    N1OOQ Ham Member QRZ Page

    Cool. :cool:
    Doing something interesting with it?

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