There's only so much you can say about them using small-signal analysis; oscillations are inherently large-signal phenomena.
You can only analyze circuits with small-signal techniques for stability or not-stability, and if the analysis says not-stability it doesn't immediately imply oscillation.
I'd go so far as to say when a system is oscillating all these small-signal classical-EM and physics derived terms "input impedance", "negative resistance" etc. have no meaning at all
Huh? My calculator makes 4uH 10nF come to 800kHz? For 5MHz at 4uH it needs C=250pF
Are these nH changes in your low-Q uH inductor that you want to track happening fast or slowly? Are you after absolute values or just watching deltas?
piglet
The Barkhausen criterion and the negative resistance view are really just two ways of looking at the problem, completely equivalent.
You have to get rid of this "voltage increasing and the current decreasing" idea. Impedance is a complex function of frequency. If its real part goes negative in some range of frequency, it's completely valid to talk of negative resistance and it will happily supply energy to an LC resonator if it happens to be tuned within that range. This often happens by accident in emitter followers.
It's really trivial to turn my LTspice emitter follower example into a CC Colpitts oscillator. Just replace the AC source by a
200nH coil and increase the series resistor to 500 Ohms or so, to limit the rate of growth of the oscillator amplitude to something reasonable. Note that the equivalent coil Q is really, really bad! Set an initial condition ".ic v(in)=1" to get it going. Do a .tran simulation of the first 50ns or so and you'll see a healthy exponentially growing sinusoid, in spite of the poor Q.Of course, there is nothing in this AC equivalent circuit to limit the amplitude, so it just keeps growing.
Jeroen Belleman
It's a terminology thing. The mechanization of the Barkhausen criteria, namely provide a feedback in phase with the resonance and a multiple of 360 degrees, with power gain avove 1, is in fact negative resistance.
The oscillation criterion that net loop gain be exactly 1 is met by something going nonlinear before it goes nuclear.
The exponential increase in amplitude as oscillations start is a normal function of oscillators. The amplitude increases until the energy delivered to the tank matches the energy lost in the tank.
If the idea of negative resistance were true, there would be nothing to limit the amplitude of oscillations, and no way to control it.
Negative resistance means an increase in voltage causes a decrease in current.
There is no portion of the cycle in a cc Colpitts where this is true. An increase in voltage causes an increase in current. That is positive resistance.
The idea of negative resistance and the Barkhausen criteria being equivalent is false. There is no portion of the oscillator cycle where an increase in voltage causes a decrease in current.
The oscillation amplitude in a cc Colpitts is controlled by the current through the emitter follower. This adjusted by changing the emitter resistor. The amplitude will increase until the energy delivered to the tank matches the loss in the tank. There is no limiting effect where the amplitude is clipped by forward biasing the base-collector junction so it conducts into the VCC supply.
Parasitic oscillations are caused by inductance in the base combined with stray capacitances to form a Colpitts oscillator.
I am including the readme from my Oscillators.zip file. It shows how to design the tank, as well as explicit instruction on how to adjust the amplitude.
----------------------------------------------------------------------
A Brief Survey Of RF Oscillators in LTspice
Steve Wilson
V1.0 Oct 2018
The Colpitts oscillator was invented in 1918 by Edwin Colpitts. It is one of the most vigorous oscillators known, and often finds its way where it is not wanted, such as in parasitic oscillations.
People often have difficulty getting their oscillator to run. Here are a series of working examples that can be used as a template, and to gain further understanding of how the oscillator works.
These examples have been tested in LTspice IV and XVII.
01.ASC Classic Colpitts ~~~~~~~~~~~~~~~~~~~~~~~ This is the simplest and easiest to get working. Here are the steps:Run the LTspice model.
NOTE: In all these oscillators, you should monitor the signal on the base to ensure it doesn't approach VCC, and check the base-emitter voltage at the negative peak to make sure it doesn't exceed the reverse breakdown voltage of the transistor.
02.ASC Colpitts Q=1 ~~~~~~~~~~~~~~~~~~~ Parasitic oscillations are caused by having an inductance in the base of an emitter follower that combines with the base-emitter capacitance and capacitance from the emitter to ground. This forms a a voltage divider made of two capacitors in series across the inductor, which makes a classic Colpitts.The inductance is often very lossy, which gives the circuit a low qualty factor, or Q. This is no problem for a Colpitts. Here is one running with a Q of 1.
It is probably a good idea to add a resistor to the base in every circuit that could potentially form a parasitic. The resistor could range from 5 Ohms to perhaps 50 ohms. You will quickly find the correct value for a particular transistor and circuit arrangement.
03.ASC 5 MHz Clapp ~~~~~~~~~~~~~~~~~~ One problem with the Colpitts is the difficulty of adjusting the frequency to a desired value. The Clapp oscillator puts a small capacitor, C3, in series with the inductor, which gives the oscillator a limited tuning range.This changes the design procedure, which follows:
CT = (32e-12 * 320e-12) / (32e-12 + 320e-12) = 29.09 pf
CX * CT / (CX - CT) = 470 * 320 / (470 - 320) = 1002pf
XC = 1 / (2 * pi * fo * CT) = 1 / (2 * pi * 5e6 * 29.09e-12) = 1,094.19Ohms
L = XC / (2 * pi * fo) = 1094 / (2 * pi * 5e6) = 34.82uH
Adjust the emitter resistor, R1, for the desired operating point.
04.ASC JFET 155MHz Clapp Osc ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Some people think JFETs are only good for low fequency audio. Here's one running quite well at 155 MHz. 05.ASC 10MHz Slow Start Xtal Osc 94 seconds ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ High Q oscillators take a long time to start up and settle. This is a typical result. It requires 94 seconds to stabilize.This means it is virtually imposssible to view the actual waveforms at various points in the oscillator in order to optimize them.
06.ASC 10MHz Fast Start Xtal Osc 0.030 seconds ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Various methods have been proposed to speed up the process. One method is to perturb the oscillator so it starts oscillating faster. However, it is difficult to inject enough energy into the tank to make much difference, and it still takes a long time to settle.Here is a method I developed a long time ago to greatly speed the process.
It uses the .IC command to initialize a current into the inductor that is equal to the peak current after the oscillator has stabilized.
Note you cannot simply initialize the inductor with a current. This generates a very large current in the tank and doesn't start the oscillator properly. This is shown later in 11.ASC.
The solution is to use the equivalent resistance in the crystal. A voltage is established across the inductor and resistor to set the desired current. This reduces the startup time from 94 seconds to 0.030 seconds, which is an improvement of a factor of 3,133.
Now you can examine the oscillator waveforms in detail and make whatever optimizations you desire.
07.ASC 10MHz Low Noise Oscillator ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The speedup even works in complicated feedback circuits that can take a while to stabilize. Here is a circuit by Bruce Griffith that stabilizes the operating point to reduce low frequency noise. 08.ASC Pierce crystal oscillator with B-source ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The speedup technique even works for Pierce oscillators. Here is a circuit with a bit lower Q but still takes 14 seconds to stabilize.It is impractical to make detailed observations of the waveforms to see what can be done to optimize the oscillator.
09.ASC Fast Start Pierce crystal oscillator ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The Fast Start method is applied to the Pierce oscillator. The total elapsed time is 0.010 seconds, an improvement of a factor of 1,400. 10.ASC Pierce oscillator with Current Pulse ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Some have tried to speed up a crystal oscillator by injecting a pulse of current into the inductor after the analysis has started.This does not work. I have not been able to produce the desired current by making any change to the injected pulse.
11.ASC Pierce oscillator with Initial Condition ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Using the .IC command to inject a current into the inductor prior to the analysis does not work.In this case, it produces a current of 2e17 Amps in the inductor.
The Fast Start method is the only one that starts the analysis with the desired current.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Change Log ~~~~~~~~~~
V1.0 Initial Release Oct 2018
Barkhausen describes the conditions necessary for oscillations to start.
There is nothing in Barkhausen that shows negative resistance in the oscillator.
Power gain is supplied by the active circuit - the emitter follower in a cc Dolpitts, and amplifier in a Pierce.
Oscillations increase until the energy delivered to the tank matches the energy lost in the tank. This is controlled in a cc Colpitts by adjusting the emitter resistor, which changes the emitter current, which changes the energy delivered to the tank.
If the idea of negative resistance were true, there would be no way to limit the amplitude of oscillations, and no way to control it.
Please see the readme in my Oscillators.zip
I posted it earlier to Jeroen.
Isn't that what I wrote, just a few lines higher?
I give up. This is a waste of time.
Jeroen Belleman
That was in your simulation. In a real oscillator, the amplitude of oscillations increases until the energy delivered to the tank matches the energy lost.
In a cc Colpitts, the energy delivered to the tank is controlled by the emitter current, which is adjusted by changing the emitter resistor.
This proves the idea of negative resistance is false.
You cannot provide an example of negative resistance in a real oscillator, or how to control the amplitude of oscillation. Until yo do, your theories don't match reality.
AS JL said, I think you're just having a terminology disagreement. All the oscillators I've built grow until the amplitude hits the power rails.. or is limited by some other non-linear element that is in the loop/ circuit. (Famously a light bulb in the HP200)
George h.
Terminology disagreement - nonsense. There is no such thing as negative resistance in an oscillator. The amplitude would increase without limit until the oscillator railed. This would increase the noise, which is critical in precision oscillators.
Crystal oscillators requires a carefully controlled amplitude. If it is too small, the oscillator may not start. Too high and the crystal may fracture.
You cannot control the amplitude if the oscillator runs on negative resistance.
If your oscillators hit the power rails, you could also be exceeding the reverse breakdown voltage in the b-e junction. This is not good.
Hitting the rails is simply sloppy design when the amplitude is so easy to control.
Try some of the oscillators in my article at
On Aug 29, 2019, snipped-for-privacy@highlandsniptechnology.com wrote (in article):
I do have a question. One can build an oscillator using an EFDA amplifier and a length of optical fiber in a ring connecting input to output. Where is the negative resistance here?
same:.
Joe Gwinn
I think Steve is stuck thinking of negative resistance in the time domain, i.e.
dI_1/dV_1 = -R.
In the frequency domain, an input impedance like that gives an S11 greater than unity at all frequencies.
But in a real oscillator, S11 only has to have a negative real part near the frequency of the resonator--since only that frequency band is relevant, it's at least as good as having a negative input resistance at all frequencies. In fact it's generally better, since the (slow) bias network doesn't have to cope with the negative resistance at all.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
It's not a 1-port electrical resonator, so I don't know.
The oscillator responds on a cycle-by-cycle basis to the input signal. See "A General Theory of Phase Noise in Electrical Oscillators", Ali Hajimiri and Thomas H. Lee:
You are thinking of a 1-port device reflecting energy back to the source.
A real oscillator has two ports. For example, in a cc Colpitts, you can say the base is the input and the emitter is the output.
The negative resistance is measured by inserting a resistor at the base. It is the value needed to shut down oscillations.
However, if the oscillator ran on negative resistance, it would be impossible to control the amplitude of oscillations. They would increase until the oscillator railed.
Railing the oscillator increases the noise, which is bad in precision oscillators.
Crystal oscillators must have careful control of the amplitude. If it is too low, the crystal may not start. If it is too high, the crystal may fracture.
It is easy to control the amplitude of oscillation in a cc Colpitts. The emitter resistor controls the emitter current and thus the energy delivered to the tank. You set the current by changing the value of the emitter resistor so that the energy delivered to the tank equals the energy lost in the tank. This also works the same way with crystal oscillators.
This satisfies the Barkhausen criteria by setting the loop gain to unity.
Again, you cannot do this if the oscillator ran on negative resistance. It has no concept of amplitude.
So the concepts of negative resistance and Barkhausen criteria are not equivalent, and are not two ways of saying the same thing.
Negative resistance in oscillators does not exist.
Right, SOMEBODY forgot the two pi while writing that
Not much faster than 10s of Hz. And absolute values in this case but it's an inductive transducer would like to know how much it is strained compared to its relaxed state, so absolute accuracy with respect to some standard is less important than precision/repeatability.
Indeed. He also seems to have trouble distinguishing between linearized AC-equivalent models and actual circuits. I suppose it will sink in, eventually.
Jeroen Belleman
I thought you were out.
I have been running SPICE since the DOS days in the 1980's. It's a pretty good tool if you know its limits and stay within them.
Your models do not reflect reality. They are useless as an analysis tool. They give no valid predictions of performance. I won't waste my time on them anymore.
Piping in to serve insults is very juvenile. Fortunately, there is a solution. Since your theories and comments serve no useful purpose -
Plonk
There is no excuse for railing an oscillator.
Post one of your designs and I'll fix it for you.
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