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Old 3rd Aug 2020, 12:46 am   #1
Chris55000
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Default "Resistance–Capacitance Oscillators" by P.G.M. Dawe, 1947

Hi!

Does anybody know where I can find, or might be able to furnish me with a copy of, the article written by P.G.M. Dawe in 1947, called "Resistance–Capacitance Oscillators" please?

This article, published in "Engineering," October 1947, deals with the transient start–up, as opposed to the steady–state, behaviour of the three or four–stage RC Phase Shift Oscillator.

Chris Williams
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Old 3rd Aug 2020, 1:19 am   #2
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Default Re: "Resistance–Capacitance Oscillators" by P.G.M. Dawe, 1947

Nothing here, but the IET or IEEE will have it if you're a member, but it'll cost!

The Dawe of Dawe instruments, I think.

It's a subject very amenable to noise analysis. Oscillators start-up based on the power-up transient is a bit iffy and prediction of whether something will start is not reliable. The noise approach seems to give reliable results.

Rather amusingly, you can open the loop of an oscillator and cut and paste many hundreds of replica stages in series as an 'unrolled' model of the oscillatory loop. Domestic PCs have the power to simulate this with non-linear models so gain stabilisation is represented and a noise source per stage. LT spice works nicely. And it's free. By probing down the chain, you can examine the early stages of start-up spread in space rather than in time.

With all the millions of words written on the subject of oscillator frequency stability, there is so little on amplitude control, and little on start-up processes.

The simplified equations governing oscillator startup are chaotic and all those Mandelbrot patterns came out of them.

David
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Old 3rd Aug 2020, 7:15 am   #3
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Default Re: "Resistance–Capacitance Oscillators" by P.G.M. Dawe, 1947

There is a reference in WW to Dawe and Gladwin:
https://worldradiohistory.com/hd2/ID...-Page-0177.pdf

The referenced magazine is:
https://worldradiohistory.com/UK/Exp...er-1947-04.pdf

The correspondence indicates a follow up article, although I haven't come across any such article.

The maths is a bit on the Heaviside (dad joke as my kids would say).
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Old 3rd Aug 2020, 8:47 am   #4
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Default Re: "Resistance–Capacitance Oscillators" by P.G.M. Dawe, 1947

I've just lost myself in that second reference for a good hour!

Even the adverts are wonderful.

Dawe talks of negative resistance being created. He talks of aperiodic damping, meaning only on-axis values of poles. Of course, when the amplifier comes into play, root-locus moves those passive, on-axis poles into the complex positions essential to an oscillator.

He doesn't go into the need for a mechanism to servo-control the gain to maintain the poles precisely on the j-omega axis in order to maintain constant amplitude of oscillation. Without this, oscillation will either stop, or will increase into clipping.

For the phase shift oscillator to work, the amplifier is inverting and so the network must provide 180 degrees of phase shift. Theoretically an RC stage can provide 90 degrees but it only gets asymptotically there as its attenuation approaches infinity. So two meshes would almost do. But oscillators aren't fooled by approximations, the phase line really has to cross a total of 360 degrees while there is still loop gain. Asymptotic approach is close, but no cigar. Besides that, infinite attenuation is a bit of a problem. The amplifier will have its own poles which will eventually push the phase shift over the line, but the gain requirement is troublesome.

So a two-mesh phase shift network isn't good.

Three meshes allows 60 degrees per mesh and lets some signal through. This will work.
Four meshes means 45 degrees and 6dB loss per mesh. This is getting comfortable.

Now, as the delay down the phase shift network is 180 degrees it shouldn't come as any surprise that when the input to the network is swinging positive, the output is swinging negative. It is after all a historical artefact of the last time the valve drove the input negative, simply having been delayed.

This is a lot easier to visualise with the lag format phase shifter. Viewing the lead format shifter may make you have to think of negative time, or the output coming out before the input went in


It's fun to hit RC oscillators with Leeson's equation, considering that their 'resonator' has to have an open-loop Q less than unity.

David
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