How do I find the gain of this colpitts oscillator?

Discussion in 'General Electronics Chat' started by bciaren, Sep 25, 2013.

  1. bciaren

    Thread Starter New Member

    May 18, 2013
    3
    0
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Where did you obtain that circuit reference? I would think 5MHz is beyond the LM741's capabilities. As shown the amplifier section has a gain magnitude of unity. Normally one anticipates slightly above unity loop gain to ensure sustained oscillation.
     
    bciaren likes this.
  3. bciaren

    Thread Starter New Member

    May 18, 2013
    3
    0
    It's just a theoretical question my professor proposed. Right now, I'm attempting nodal analysis to get an equation and play with the values in the hopes of producing a Vo / Vi. .. .
     
  4. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    I see. Presumably you realize you open the loop to deduce the open loop gain function. The ideal RC Colpitts network simply provides the pure 180 degree phase shift at resonant frequency.
     
    bciaren likes this.
  5. bciaren

    Thread Starter New Member

    May 18, 2013
    3
    0
    Please elaborate. We just finished a chapter that showed us how to handle circuits with an AC voltage that previously had a DC voltage source. The end of the chapter provided a section titled "applications" and demonstrated a colpitts oscillator. It asked the reader to design a colpitts oscillator at 50kHz.

    This was simple as it's the exact same thing as before!

    my Ceq = 10nF
    C1 = C2 = 20nF
    L = 10.13mH
    Ri = Rf = 20k

    Now based on memory, to acquire gain from a standard (inverter?) op amp it's Av = - Rf / Ri (could have that backwards). So this is a unity condition.. My question is, how does one produce a gain greater than 1 with a colpitts? I don't have a clue on whether or not there is a standard formula for gain with this oscillator. . so I'm deriving one! *(or at least trying)

    I'm attacking this problem by using nodal analysis and obtaining an expression that equals Vout / Vin. The problem I'm coming across is, the expression is REALLY long, and I have no idea if it's correct (especially since it's now 1:30AM haha). The following link contains the expression I came up with after nodal analysis . . .

    http://i359.photobucket.com/albums/oo39/r19ecua/nodal.jpg

    Here's the equation I started with:
    Vin / (1/jwC1) = ((Vin - Vout)/ (R1 + R2)) + (Vin - Vout) / jwL + Vout / (1/jwC2)

    Whether or not I got this correctly, am I looking in the right direction here? Or am I just completely lost with this topic? If I am, please set me in the proper direction :)
     
  6. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Go to bed. It's too late in the night to be worrying about this.
     
  7. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    As I indicated earlier the analysis must be done in open loop. In other words you have to "break" the feedback path at some point and then perform the analysis to find the voltage transfer function through the entire path between the ends of the break point, having regard to the proper signal flow.

    The analysis of the Colpitts feedback network is probably better understood using a particular topology transformation (Delta-Wye). The matter of the open loop analysis is further complicated in that the inverting operational amplifier input resistance is directly related to the associated input gain control resistance (Ri). This resistance will shift the operating frequency off the "ideal" value due to its loading effect on the resonant network.

    I'm not sure what level your understanding is in regard to such matters & I suspect you are perhaps expected to make one or more simplifying assumptions. My advice would be therefore to refer back to your professor in regard to how he (or she) expects you to solve the problem.
     
Loading...