# How do I find the gain of this colpitts oscillator?

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

May 18, 2013
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2. ### t_n_k AAC Fanatic!

Mar 6, 2009
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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.

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3. ### bciaren Thread Starter New Member

May 18, 2013
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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
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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.

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5. ### bciaren Thread Starter New Member

May 18, 2013
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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

Mar 6, 2009
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