While procrastinating and avoiding reality this morning, I made
myself a nice cup of espresso and sat down at my electronics bench
to build an oscillator. Not wanting to waste too much time, I wanted
to make a really simple oscillator. My circuit was a 2N3904 with
the emitter grounded, the collector being pulled up to 3.6 volts
through a 150-ohm resistor, and the collector connected to the base
through 1.6m of RG-58 coaxial cable. The shield of the RG-58 cable
was grounded. The circuit was constructed on a breadboard with
fairly relaxed spacing of components. The power supply was bypassed
between the top of the collector resistor and ground using a 1uF tantalum
capacitor.
The circuit oscillates at 24.4MHz with 760mV peak-to-peak output,
observed with a 10x probe on my scope. Note that the frequency of
oscillation is not only determined by the cable. The delay in the
cable is probably about 7.5ns. If the transistor were operating
as a pure inverter, we could say that 7.5ns is half of the period
of the oscillation, so the period would be 15ns so the system would
oscillate at 67MHz. What is probably actually happening is that
various parasitics are putting a pole in the response of the transistor,
and adding some phase lag. The period of the actual oscillation is
about 40ns. The cable accounts for 7.5ns and the transistor accounts
for the other 32.5ns. It has an extra 12.5ns of delay due to phase
lag. This is 112 degrees of lag. I would measure the phase response
of the amplifier part of this oscillator in isolation but it will be
difficult because it is a self-biased through the coaxial cable.
Getting the same conditions in an open-loop mode will be unlikely.
Also, it shold be pointed out that circuits like this are highly
nonlinear, so linear circuit analysis concepts like impedance are
not really applicable. We could think about the 112 degrees of lag
and speculate on the existence of two poles in the response
of the amplifier, each pole being below 24.4 MHz, but that is really
too much linear circuit analysis for an oscillator.