Hey this isn't assigned homework but I figured this would be the best forum to post on given the simplicity of the circuit. I think the main problem is in the amplifying portion of the circuit.

I started by choosing the collpits oscillator parameters based on what components I had on hand

\( L = 100\mu H \)
\[ C_1 = 4.7\mu F \]
\[ C_2 = 47\mu F \]

using both the capacitance in series formula, and the tank circuit resonant formula I found the resonant frequency

\[ C_t = \frac{C_1*C_2}{C_1+C_2} = \frac{4.7\mu F * 47\mu F}{4.7\mu F + 47\mu F} = 4. \bar{27} \]
\[ F_r = \frac{1}{2\pi \sqrt{LC_t}} = \frac{1}{2\pi \sqrt{100\mu H*4.27\mu F}} = 7696Hz \approx 7.7kHz \]

for the amplifyer I chose a common emmitter amplifyer and layed out some parameter that just sorta felt right( I guessed)

\( I_C = 2mA \)
\( V_{CC} = 12V \)
\[ V_{Re} = 1V \]
\( \beta = 100 \)

using these numbers I can find the voltage at quintessence, the base current, and the emmitter current.

\[ V_Q = \frac{V_{CC}-V_{Re}}{2} = \frac{12-1}{2} = 5.5V \]
\[ I_B = I_C/\beta = 2mA/100 = 20\mu A \]
\[ I_E = I_B+I_C= 20\mu A +2mA = 2.02mA \]

I read somewhere that the current through R2 should be ten times that of the base so thats what I did

\[ I_{R2} = I_B*10 = 20\mu A*10 = 100\mu A \]

and since R2 is across the base and ground we can solve for base using the saturation voltage and the voltage across Re

\[ R_2 = \frac{V_{sat}+V_{Re}}{I_{R2}} = \frac{.6+1}{200\mu A} = 8k\Omega \]

since the current through R2 and base flow through R1 the the current through R1 should be 11 time the current through base. now we can solve for R1, RL and Re

\[ R_1 = \frac{V_{CC}-V_b}{I_B*11} = \frac{12-1.6}{220\mu A} = 47272.\bar{72} \Omega \]
\[ R_L = \frac{V_Q}{I_C}=5.5/2mA = 2750\Omega \]
\[ R_e = \frac {V_{Re}}{I_E}= \frac{1V}{2.02mA} = 495 \]

which gives us the final values of

\[ R_L = 2750\Omega \]
\[ R_e = 495\Omega \]
\[ R_1 = 47273\Omega \]
\[ R_2 = 8k\Omega \]

the problem being when I build the circuit IRL it simply doesn't oscillate. however the LT Spice simulation does oscillate.

I've attached the schematic below please note that C1, C2, and C4 are electrolytic capacitors IRL and that some of the resistor values are not spot on IRL.

 

the problem being when I build the circuit IRL it simply doesn't oscillate. however the LT Spice simulation does oscillate.

Phase shift is more or less fine but loop gain is way below 1. I don't see how it would be possible to get any sign of life from the oscillator in simulation or real life. The amplifier is heavily loaded down by C1. C2, being 10 x C1, is only adding to the overall attenuation. The amplifier cannot recover the loss. Decrease C1/C2 by an order of magnitude (try also C1 = C2) and adjust L1 accordingly.

 

Hey this isn't assigned homework but I figured this would be the best forum to post on given the simplicity of the circuit. I think the main problem is in the amplifying portion of the circuit.

I started by choosing the collpits oscillator parameters based on what components I had on hand

\( L = 100\mu H \)
\[ C_1 = 4.7\mu F \]
\[ C_2 = 47\mu F \]

using both the capacitance in series formula, and the tank circuit resonant formula I found the resonant frequency

\[ C_t = \frac{C_1*C_2}{C_1+C_2} = \frac{4.7\mu F * 47\mu F}{4.7\mu F + 47\mu F} = 4. \bar{27} \]
\[ F_r = \frac{1}{2\pi \sqrt{LC_t}} = \frac{1}{2\pi \sqrt{100\mu H*4.27\mu F}} = 7696Hz \approx 7.7kHz \]

for the amplifyer I chose a common emmitter amplifyer and layed out some parameter that just sorta felt right( I guessed)

\( I_C = 2mA \)
\( V_{CC} = 12V \)
\[ V_{Re} = 1V \]
\( \beta = 100 \)

using these numbers I can find the voltage at quintessence, the base current, and the emmitter current.

\[ V_Q = \frac{V_{CC}-V_{Re}}{2} = \frac{12-1}{2} = 5.5V \]
\[ I_B = I_C/\beta = 2mA/100 = 20\mu A \]
\[ I_E = I_B+I_C= 20\mu A +2mA = 2.02mA \]

I read somewhere that the current through R2 should be ten times that of the base so thats what I did

\[ I_{R2} = I_B*10 = 20\mu A*10 = 100\mu A \]

and since R2 is across the base and ground we can solve for base using the saturation voltage and the voltage across Re

\[ R_2 = \frac{V_{sat}+V_{Re}}{I_{R2}} = \frac{.6+1}{200\mu A} = 8k\Omega \]

since the current through R2 and base flow through R1 the the current through R1 should be 11 time the current through base. now we can solve for R1, RL and Re

\[ R_1 = \frac{V_{CC}-V_b}{I_B*11} = \frac{12-1.6}{220\mu A} = 47272.\bar{72} \Omega \]
\[ R_L = \frac{V_Q}{I_C}=5.5/2mA = 2750\Omega \]
\[ R_e = \frac {V_{Re}}{I_E}= \frac{1V}{2.02mA} = 495 \]

which gives us the final values of

\[ R_L = 2750\Omega \]
\[ R_e = 495\Omega \]
\[ R_1 = 47273\Omega \]
\[ R_2 = 8k\Omega \]

the problem being when I build the circuit IRL it simply doesn't oscillate. however the LT Spice simulation does oscillate.

I've attached the schematic below please note that C1, C2, and C4 are electrolytic capacitors IRL and that some of the resistor values are not spot on IRL.

Hi,

Without going into it too deep just yet, what is the series resistance for the inductor?
If that is too high and/or the driving impedance is too high you may end up with no solution to the resonant frequency.
A suggestion would be to measure the series resistance of the inductor and include that in the simulation. If the simulation does not oscillate after that, then you know what is wrong.
Some of the little inductors have a series resistance higher than we might think at first. The collector resistor is also kind of high. Those two may be working against any oscillation.
Again this is after a quick look so there may be other issues.

Also, the series R of the inductor combined with the driving point resistance could change the resonate frequency from that obtained from the simpler calculation. The full calculation would be a bit more complicated.

 

Hello again,

I took another quick look at this and it seems that there has to be a certain relationship between the driving point impedance (call it Zdp for now) and the inductor series resistance RL. An approximation might be Zdp<RL or maybe Zdp<K*RL, something like that. If that relationship is not satisfied, there will be no solution to the resonant peak which means the circuit is overdamped which means no sinusoidal terms. We could come up with a more exact expression but it only has to involve those two resistances.

 

All you calculations are correct - however, you started with a certain gain of the CE-stage (by choosing a certain DC operational point).
The gain is A=-gm*Rc/(1+gm*Re) with gm=Ic/26mV. With your values we have app. A=-2,5.

My question: How did your calaculations consider that the loop gain must be somewhat larger than unity at the selected frequency? I suppose you know how the loop gain is determined?
As a first step, you can increase the gain with an the emitter capacitor in parallel to the emitter resistor (or a part of it) with a capacitor Ce.