oscillators

1. Avalanche relaxation oscillator biasing resistor

I've tried the circuit in this article. It works very well and I've obtained 2ns clear pulses at 150 V (the main issue was to find the right avalanche voltage, which turned out to be 150-160V for my 2n3904 transistor). While the basic principles of operation in this circuit is clear for me, I...
2. Perturbation on an oscillator

Hi, I am reading the Hajimiri-Lee phase noise model, and got a question on that. If you have an LC tank circuit that is free-running and I inject a current i(t) (dirac current) at instants either t1 or t2 (shown in the figure), depending on when you inject the phase of the output changes (as...
3. I Why high Q factors have low phase noise

If we define Q factor as 2*pi* energy stored/ energy dissipated per cycle, what's the physical insight behind obtaining low phase noise for oscillators when we have high Q factors? (I know the mathematical derivation based on finding the frequency profile of an oscillator (like LC oscillator)...
4. Weak Damping - how to relate the amplitude and phase difference

1. Homework Statement Derive the relationship bewteen x_{max}, A_{+}, A_{-} and \phi 2. Homework Equations x(t) = e^{\gamma t}(A_{+}e^{i \omega_d t} + A_{-}e^{-i \omega_d t}) x(t) = x_{max} e^{\gamma t} cos(\omega_d t + \phi) 3. The Attempt at a Solution I know the e^{\gamma t} cancels and...