Wes Hayward's book "Radio Frequency Design" has a pretty good section on analysis of the various LC oscillator topologies on pages 265-290, and how to plot the gain and phase angle as a function of emitter current.
The book is very math-heavy in general, it's like the anti-AoE.
There's also apparently a variation on the Colpitts where the crystal is inserted in the feedback path instead of parallel to the capacitors, to resonate at the series resonant frequency. I may try that one as well.
Spice has made all sorts of math unnecessary. Math tends to sputter out when things get nonlinear anyhow.
-- John Larkin Highland Technology, Inc lunatic fringe electronics jlarkin att highlandtechnology dott com http://www.highlandtechnology.com
To satisfy the Barkhausen requirements, shouldn't you model the startup condition as a linear amplifier and a frequency selective feedback network ?
Inject some low level white noise (thermal noise) into the amplifier input and for each cycle around the feedback loop, the amplitude at the peak frequency will grow, while the relative noise bandwidth decreases drastically and soon or later you will have a single spectral line. Finally the amplifier runs in a saturated state with constant amplitude output.
The amplifier should initially be biased into Class-A so that it will amplify the weak thermal noise, but of course, when the maximum amplitude has been reached during startup, it can/will run in Class-C. If the oscillator is initially biased into Class-C, it is not capable of amplifying the weak thermal noise and you need some external kick-start, e.g. rapidly applying the power supply voltage. This also explains why some oscillators starts nicely, when battery power is applied, but fails to start when connected to a mains power supply, which takes a while to start when the storage capacitors are slowly charging, after plugging it into mains socket.
Sure. That's why I suggested using a much smaller current step omce the sim looks OK, to check for startup problems.
If the initial transient dies away rather than continuing, the gain is too low.
Thing is, being an iterative ODE solver, SPICE uses all sorts of heuristics and fairly coarse convergence checks that make it flaky and unreliable for very small signals. You have to supply an initial amplitude big enough to not get ignored if you want reliable (simulated) startup.
When not using ALC, it's a good idea to arrange the bias so that amplitude limiting happens due to cutoff, which is clean and fast, rather than satura tion, which is neither.
Cheers
Phil Hobbs
Trying to start a (simulated) oscillator with external transient either relies on: a.) the transient puts the amplifier momentarily from Class-C to Class-A and amplifies everything during startup
b.) the startup transient contains so steep waveforms containing frequencies in the feedback filter bandwidth that then can be amplified
In case b.) the amplifier gain would have to be as high as 100 dB, if you have a crystal in the feedback path :-)
Have you tried to "unwind" the startup with a number of cascaded stages ?
You would require a noise source (say a resistor at room temperature generating -174 dBm/Hz noise temperature) followed by your amplification stage (transistor with fT limitations) followed by your oscillator feedback frequency response. Instead of using feedback, connect the output of the filter to the next identical amplifier/filter stages.
With 20 dB stages, you would need 10-30 stages, until the amplifier stages are overdriven.
That is an other kettle of worms how to handle the steady state situation (phase noise etc.)
Of course, this simulation doesn't solve the other Barkhausen criterion regarding the phase shift in the feedback loop. If for some reason (a resonator on the collector side in frequency multipliers) causes a negative feedback phase on the resonator frequency, the oscillator doesn't oscillate.
As the old practical wisdom goes, amplifiers oscillate, oscillators don't oscillate :-)
Sure. The amplifier has to be in normal class-A bias with adequate gain to begin with. It's all the ABSTOL and RELTOL and VOLTTOL and convergence hacks and stuff, related to SPICE being an iterative solver, that makes starting up from roundoff noise flaky.
A real oscillator just needs a loop gain larger than 1.0, because it builds up exponentially from noise. A SPICE oscillator does too, but it takes awhile and doesn't always succeed unless you get it out of the mud to start with.
There's nothing wrong with using a (sufficiently small) transient to get it going. All you care about for startup purposes is the gain in the small signal regime, not necessarily at 0.000000000000000000... volts.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
It had better be Class A at startup, or you're guaranteed a lot of midnight phone calls. Have you ever shipped an oscillator that wasn't Class A in quiescent conditions?
No, you misunderstand what I'm proposing. If you put a current source in parallel with the inductor, then at t=0 the full current is going through the crystal inductance. When you turn that off, the crystal rings strongly at its series resonance. A microamp of crystal current in a watch crystal is probably full amplitude, or nearly.
No. What would I learn from that?
But they wouldn't be indentical. The phases would be independent, so there would be nothing to enforce the oscillation criterion. All you'd get would be filtered white noise, whereas a good oscillator has a much, much narrower line width than the crystal.
20 dB is too much stage gain for a good oscillator anyway--the resonator amplitude will be too small.Phase noise is the main reason you do it. If the amplifier is nonlinear, all of its baseband crap and 1/f noise gets intermodulated with the output signal.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
Oscillator and high frequency amplifier design are special cases, where grinding out the math is important. Even in a classical Colpitts, the choice of collector current, tank impedance, the ratio of the tank caps, and the size of the emitter and base coupling caps have a lot of influence on frequency stability and phase noise.
That's a 5-D search space, so getting it right can take awhile numerically, and you can never really be sure you're not on a local optimum.
You only have to do it once for each topology, then you just use Mathcad or Mathematica or something to apply it to the case at hand.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
I like the standard Colpitts, because you can take the output right from the crystal, which gives you a nice wave shape for the second stage, and less broadband noise. Also capacitors are more stable than inductors, and you can't pull the oscillator off the crystal resonance the way you can with a separate tank.
One good use of inductors is as overtone selectors: you resonate one of the tank caps so that it looks like the right size capacitor at only one of the overtones. Parzen's crystal oscillator book is a good read on that sort of thing.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
My favorite crystal oscillator structure...
No fiddle, no fuss, no critical matching... always works.
First used it to get to 144MHz (2m) by X3 (transistor), X3 (varactor), from 16MHz crystal for my first (and last ;-) 2m rig... when in my mid '20's. ...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |
I love to cook with wine. Sometimes I even put it in the food.
On 7/25/2015 9:56 AM, bitrex wrote:
See if this works for you
Version 4 SHEET 1 1560 740 WIRE 176 -192 -1056 -192 WIRE 416 -144 -816 -144 WIRE 784 -144 416 -144 WIRE -1056 -112 -1056 -192 WIRE 784 -112 784 -144 WIRE 416 -80 416 -144 WIRE 784 -16 784 -32 WIRE -816 16 -816 -144 WIRE -528 16 -624 16 WIRE -368 16 -448 16 WIRE -224 16 -304 16 WIRE -64 16 -144 16 WIRE 176 64 176 -192 WIRE 416 64 416 0 WIRE 416 64 176 64 WIRE -816 144 -816 96 WIRE -624 144 -624 16 WIRE -624 144 -816 144 WIRE -816 160 -816 144 WIRE 416 160 416 64 WIRE -1056 208 -1056 -48 WIRE -960 208 -1056 208 WIRE -880 208 -960 208 WIRE -624 208 -624 144 WIRE -352 208 -624 208 WIRE -64 208 -64 16 WIRE -64 208 -288 208 WIRE 176 208 -64 208 WIRE 272 208 176 208 WIRE 352 208 272 208 WIRE -880 224 -880 208 WIRE -864 224 -880 224 WIRE 352 224 352 208 WIRE 368 224 352 224 WIRE -960 240 -960 208 WIRE 272 240 272 208 WIRE -1056 320 -1056 208 WIRE 176 320 176 208 WIRE 416 320 416 256 WIRE -816 368 -816 256 WIRE 416 464 416 400 WIRE 416 464 336 464 WIRE -1056 480 -1056 400 WIRE -960 480 -960 304 WIRE -960 480 -1056 480 WIRE 176 480 176 400 WIRE 272 480 272 304 WIRE 272 480 176 480 WIRE 336 496 336 464 WIRE 416 496 416 464 WIRE 176 512 176 480 WIRE -1056 528 -1056 480 WIRE -816 544 -816 448 WIRE 336 624 336 560 WIRE 416 624 416 576 WIRE 416 624 336 624 WIRE 416 672 416 624 FLAG 416 672 0 FLAG 784 -16 0 FLAG -816 544 0 FLAG -1056 528 0 FLAG 176 512 0 SYMBOL ind -240 32 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 5 56 VBottom 2 SYMATTR InstName Lm SYMATTR Value 1701.17Hy SYMBOL res -544 32 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 0 56 VBottom 2 SYMATTR InstName Rs SYMATTR Value 15k SYMBOL cap -368 32 R270 WINDOW 0 32 32 VTop 2 WINDOW 3 0 32 VBottom 2 SYMATTR InstName Cm SYMATTR Value 1.489fF SYMBOL cap -352 224 R270 WINDOW 0 32 32 VTop 2 WINDOW 3 0 32 VBottom 2 SYMATTR InstName Cs SYMATTR Value 1.743pF SYMBOL voltage 784 -128 R0 WINDOW 123 24 132 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value 9 SYMBOL res 400 -96 R0 SYMATTR InstName R1 SYMATTR Value 2.2k SYMBOL njf 368 160 R0 SYMATTR InstName J1 SYMATTR Value U309 SYMBOL res 400 480 R0 SYMATTR InstName R2 SYMATTR Value 680 SYMBOL cap 320 496 R0 SYMATTR InstName C2 SYMATTR Value .01u SYMBOL res 160 304 R0 SYMATTR InstName R3 SYMATTR Value 10meg SYMBOL cap -1072 -112 R0 SYMATTR InstName C4 SYMATTR Value .01u SYMBOL diode 256 240 R0 SYMATTR InstName D1 SYMATTR Value 1N4148 SYMBOL njf -864 160 R0 SYMATTR InstName J2 SYMATTR Value U309 SYMBOL res -832 352 R0 SYMATTR InstName R4 SYMATTR Value 1.8k SYMBOL res -1072 304 R0 SYMATTR InstName R5 SYMATTR Value 10meg SYMBOL diode -976 240 R0 SYMATTR InstName D2 SYMATTR Value 1N4148 SYMBOL res -832 0 R0 SYMATTR InstName R6 SYMATTR Value 1.8k SYMBOL res 400 304 R0 SYMATTR InstName R7 SYMATTR Value 470 TEXT -392 -128 Left 2 ;Crystal TEXT 1200 200 Left 2 !.tran 0 2 1.9 startup RECTANGLE Normal -48 320 -656 -96 2
I tend not to put DC on crystals, though modern ones may be less sensitive.
One thing that series resonant oscillators are especially good for is ring-down calibrators for logarithmic amplitude detectors (DLVAs). Exponential envelope decay -> linear ramp output (ideally).
Running at series resonance maximizes the initial amplitude of the envelope when the oscillator switches off. One of those will calibrate an SA615 good to at least 12 bits, usually more.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
No DC there... each end of the XTAL is 1*Vbe down from rail
...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |
I love to cook with wine. Sometimes I even put it in the food.
I can usually find a paper or a book, where someone has done the math for me. It's amazing how little serious math I need to do electronic design; not much past algebra. The only really hairy stuff that we do is digital filter design, in FPGAs, and quantization issues make accurate analytical solutions impossible, so we wind up simulating the final filters anyhow.
-- John Larkin Highland Technology, Inc lunatic fringe electronics jlarkin att highlandtechnology dott com http://www.highlandtechnology.com
That is essentially the "two transistor Butler" topology. I think I've seen it with an inductor across the crystal to null out the parallel capacitance. For high precision, you have to keep the xtal current low, which is a compromise.
-- John Larkin Highland Technology, Inc lunatic fringe electronics jlarkin att highlandtechnology dott com http://www.highlandtechnology.com
I have seen oscillator designs with some kick-start pulse delivered through a diode or some kind of power on reset type circuit that slams on the Vcc when a sufficient voltage has been stabilized from the mains PSU, simulating the turn on transient from battery powered devices :-)
At least it would educational to those that haven't thought about oscillators as amplifiers with positive frequency selective feedback.
Yes, I pointed out that in my follow-up message.
Ah, right, quite so. You IC guys and your weird-ass biasing schemes. ;)
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
The parallel inductor is very helpful if you want to run at a high overtone.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
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