Re: analysis of hartley oscillator


"Ira Rubinson" <irarubinson@xxxxxxxxx> wrote in message
news:e6udnRlHe9dq5jDfRVn-jg@xxxxxxxxxxxxxxx
> Thanks Robert, Roger,
> I'll try implementing some of your suggestions.
> What I meant by analyze is to come up with an equation that will show that
> it indeed oscillates.
> For example, what circuit analysis technique does the simulation program
use
> to derive the equation for the waveform.
> I assume that what I'm looking for will involve kirchoff loops, locus
root,
> small signal parameters etc....
> My problem is that when I read about locus root, it is all math and I
don't
> know how to apply it to this simple circuit.
> When I read about hartley oscillators I usually see "freq =
> 1/(2*pi*sqrt(LC)) which is a little simplistic.
>
> Thanks -Ira

The simulation program does non-linear analysis, so it does not work with
equations you would use for root locus with small signal parameters.
Instead, it tracks the movement of charge at small steps in time, at each
step iterating to get a solution which satisfies the equations describing
each circuit component, including the equations for the non-linear
transistor. If it was linear analysis, you would only see sinewaves.

Again, I recommend Wes Haywards "Introduction to RF Design. He will present
you with equations, but also discusses the result you want to achieve. In
the end, oscillator design means trading off many requirements, noise,
amplitude, power, drift. It turns out that establishing that you have
correct loop gain and phase is the easy part, at least below UHF. Haywood
uses surprisingly simple transistor models which you will find give you a
feel for the issues. He also has a Smith Chart design method for the higher
frequencies. The book has a bit of everything, and will get you going in
the RF world.

If you want to, draw the hybrid pi model of the transistor, add the other
components, then break the loop and calculate gain and phase around the
loop. You will find this analysis in plenty of Uni library textbooks. It
is useless for designing good oscillators at the 3 or 4 MHz where your
oscillator functions, because those equations only tell you that the
oscillator will start, and nothing about its performance.

Feedback phase does not have to be perfectly 180 degrees at resonance,
because oscillation can still occur at a frequency somewhat away from
resonance, where the tuned circuit gives enough phase shift to give make up
the exact 180 degrees. This is why oscillators like yours mostly work, and
why the linear ?will it start? analysis is not much help.

Your oscillator is not a linear device, once it gets started. The
transistor puts spikes of current into the tank circuit and nothing the rest
of the time.

Reduce DC current until you are free of clipping and you will have a decent
oscillator. Apart from avoiding clipping, the other issue is the impedance
presented by the tuned circuit to the transistor base and collector. A
lower impedance presented to the collector lets you run at a higher
collector current, storing more energy in the tank circuit and swamping
thermal and transistor noise. A lower impedance presented to the base is
associated with less feedback, so it can't be too low, but lower means the
base loads the tuned circuit less and allows higher Q, giving a cleaner
sinewave.

L1 and L2 are mutually coupled in a Harley circuit, and since L1=L2 in your
circuit, there is very heavy feedback, meaning your oscillator can't fail to
work. So reduce L1 and increase L2 until it stops oscillating, then back
off. Then bypass R5 with a capacitor and increase R5 until clipping stops.


Roger


.

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