When is a Butler not a Butler ?

[Ken Smith]

It doesn't work that way. The right-hand current source is smaller
than the left, so what is limited is drive current into a tank with
limited (and known) Q.

So what is lowering the gain? If the gain doesn't decrease, the signal
will continue to build up.

 

[Tim Williams]

So what is lowering the gain? If the gain doesn't decrease, the signal
will continue to build up.

Sounds like it's set exactly right...

I think you're making an error along the lines of Tesla: resonances aren't
unlimited. Jim said the Q is known and the drive is known, so you get a
voltage divider between the Thevenin output impedance of the amplifier and
the resistive loss component in the tank. For constant current drive it's
even simpler, V = I*R.

Such a circuit could be hard to start, but a hysteretic drive should do it
quite nicely. Although, gain is then very large (indeed, greater than
infinity, so to speak, due to the positive feedback in excess of the open
loop gain), so it must be limited by the driver stage. In that case, the
output impedance (to the tank) is limiting it, with much harmonic content of
course, which is mostly attenuated, depending on Q.

Tim

 

[Ken Smith]

Sounds like it's set exactly right...

I think you're making an error along the lines of Tesla: resonances aren't
unlimited. Jim said the Q is known and the drive is known, so you get a
voltage divider between the Thevenin output impedance of the amplifier and
the resistive loss component in the tank. For constant current drive it's
even simpler, V = I*R.

No, if there is an error, that one isn't it.

Consider the general case of an oscillator consisting of an amplifier and
a tuned element:

In order for oscillations to build up, you need a gain around the loop
that is greater than unity. In order for them to remain stable, you need
the gain around the loop to be exactly unity. Something must reduce the
gain.

In most oscillators, the signal builds up until something goes nonlinear.
In some there is an AGC action that is nearly linear as far as the RF is
concerned. This is usually done by having the RF amplitude much smaller
than the bias variations used to control the gain.

Such a circuit could be hard to start, but a hysteretic drive should do it
quite nicely.

Hysteretic drive is by its nature non-linear. It is one of the sort of
nonlinearities that are used to set oscillator amplitude. In this case it
is one that is mostly used in RC oscillators because it also remembers the
past.

 

[Tim Williams]

Hysteretic drive is by its nature non-linear.

Well then there you go, I think.

Tim