Colipitts oscillator LC Tank with PNP transistor - Page 1
Forum section: electronics / projects

author: macck
author_rank: Contributor
timestamp: November 12, 2017, 07:40:04 pm
content: Hello everyone,I have some problems with understanding common-base PNP BJT Colpitts oscillator.Circut is simple in elements, potentiometric biased PNP, with inductor hooked between collector-ground, capacitor between emitter-collector and also emitter-ground capacitor of simillar capacitance.I get general idea of what we have to fullfil to get oscillating circut, but i feel sort of locked in figuring this one out. It may be due to my lack of experience with oscillators/amplifiers. I have this working in LTSpice, also on my bench. I bellive that someone could explain this circut to me easeliy, why, for the sake of theroy this is working.Thank you for your time.

author: orolo
author_rank: Frequent Contributor
timestamp: November 12, 2017, 10:52:26 pm
content: A few days ago I built an NPN Colpitts common base at 27MHz, so details are fresh in mind. I think you need either a choke or a resistor (or both, the resistor if alone with a bigger value than the impedance of the caps at the working frequency) from emitter to Vcc for this circuit to work reliably. The schematic, I think, is:It doesn't matter if the emitter cap goes to ground or Vcc. To the right is the small signal equivalent at a given frequency, with the trick of using variable \$s = I\omega\$ to get rid of imaginary numbers. The choke creates voltage node w, which otherwise would not exist. If the transistor is biased right, the base resistance \$r_{\pi}\$ is big enough relative to the impedance of C1 to be ignored (otherwise the calculation gets a bit more involved, but remains similar).The trick is computing the input impedance seen by the inductor, that is, Z = v/i. This impedance will have a negative resistance arising from the capactiors and the transconductance of the transistor, that will allow the circuit to start oscillating.From the nodes in the above circuit, you have three equations:\$v - w \ = \ -\frac{1}{sC_2}\, j\$\$i \ = \ j - g_{m}w \$\$w \ = \ -\frac{1}{sC_1}\, i\$Use the third equation to eliminate w in the first two:\$v + \frac{1}{sC_1}i \ = \ -\frac{1}{sC_2}\, j\$\$i \ = \ j + g_m\frac{1}{sC_1}\, i\$From the second equation, you have: \$j \ = \ \left(1 - g_m\frac{1}{sC_1}\right)\, i\$. Use this to eliminate j from the first equation:\$ v + \frac{1}{sC_1}\,i \ = \ -\frac{1}{sC_2}\,i + g_m\frac{1}{s^2C_1C_2}\,i\$In other words, remembering that \$s = I\omega\$, so \$s^2 = -\omega^2\$:\$Z \ = \ \frac{v}{i} \ = \ -\frac{1}{sC_1} - \frac{1}{sC_2} - \frac{g_m}{\omega^2C_1C_2}\$The first two terms in the impedance seen by the inductor are the two capacitors acting in parallel. The third term is a negative real resistance.If at your working frequency the impedance of the inductor cancels the impedances of the capacitors, the resulting LC tank will have a negative resistance that will allow it to start oscillating, assuming its parasitics are lower than the negative resistance.This computation is very useful because it gives you the conditions for the oscillator to start up, and the resonant frequency. However, once the Colpitts oscillator is in full swing, this model is no longer adequate. If you run your Spice simulation of the large signal Colpitts, you will see it's very nonlinear, with strong short bursts of current each cycle.Edit: from being used to compute with the imaginary unit put in, I took the capacitor impedances as negative. They should be positive. The final result doesn't change, however.