Colpitts kick-start in LT Spice

You removed my time step. Set it to 1 ms and wait, very patiently, to see a beautiful bizarre startup that doesn't oscillate.

With an unspecified time step, LT Spice LC tank frequencies are not very accurate.

--

John Larkin         Highland Technology, Inc 

lunatic fringe electronics

Doesn't start. 2N7002 models are bad. Here's the error log:

Questionable use of curly braces in ".model sir870adp vdmos(rg=3 vto=2.9 rd=3.2m rs=1.5m rb={m} kp=100 mtriode=1.85 cgdmax=1.4n cgdmin=70p cgs=2.9n cjo=3.6n m=.4 a=.7 vj=.7 lambda=20m is=3p ksubthres=.08 mfg=siliconix vds=

100 ron=5.5m qg=53.5n)" Error: undefined symbol in: "[m]" Circuit: * C:\0DNLOAD\1.ASC

Direct Newton iteration for .op point succeeded.

Date: Tue Nov 12 12:22:34 2019 Total elapsed time: 150.536 seconds.

tnom = 27 temp = 27 method = modified trap totiter = 30000048 traniter = 30000040 tranpoints = 15000021 accept = 15000021 rejected = 0 matrix size = 9 fillins = 2 solver = Normal Matrix Compiler1: off [1.9]/3.8/2.3 Matrix Compiler2: off [2.0]/3.2/22.1

[about a Spice-model of oscillator]

The REAL oscillator has thermal noise to start it. Even a wire has some Johnson noise. SPICE isn't equipped to handle that, in transient analysis.

whit3rd wrote:

JL is using the 2N7002 model, which is defective. If you use the 2N7000 model from PSPICE, it starts fine. LTspice supplies the initial conditions, and it runs from there.

Version 4 SHEET 1 2804 680 WIRE 976 -144 816 -144 WIRE 816 -80 816 -144 WIRE 976 -32 976 -144 WIRE 368 0 320 0 WIRE 640 0 480 0 WIRE 688 0 640 0 WIRE 768 0 688 0 WIRE 368 80 368 0 WIRE 640 80 640 0 WIRE 320 96 320 0 WIRE 480 112 480 0 WIRE 976 128 976 48 WIRE 976 128 896 128 WIRE 896 160 896 128 WIRE 640 192 640 144 WIRE 688 192 640 192 WIRE 816 192 816 16 WIRE 816 192 688 192 WIRE 640 240 640 192 WIRE 816 256 816 192 WIRE 976 256 976 128 WIRE 320 400 320 176 WIRE 480 400 480 192 WIRE 480 400 320 400 WIRE 640 400 640 304 WIRE 640 400 480 400 WIRE 816 400 816 336 WIRE 976 400 976 336 WIRE 976 400 816 400 WIRE 640 432 640 400 FLAG 688 0 OSC FLAG 640 432 0 FLAG 896 160 0 FLAG 688 192 SRC FLAG 368 80 0 SYMBOL ind 464 96 R0 WINDOW 0 54 39 Left 2 WINDOW 3 60 70 Left 2 SYMATTR InstName L1 SYMATTR Value 1 SYMATTR SpiceLine Rser=1m SYMBOL cap 624 80 R0 WINDOW 0 51 20 Left 2 WINDOW 3 59 54 Left 2 SYMATTR InstName C1 SYMATTR Value 1 SYMBOL current 320 176 R180 WINDOW 0 63 41 Left 2 WINDOW 3 -214 220 Left 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName I1 SYMATTR Value PULSE(0 1 100 1m 1m 50m) SYMBOL cap 624 240 R0 WINDOW 0 51 20 Left 2 WINDOW 3 59 54 Left 2 SYMATTR InstName C2 SYMATTR Value 5 SYMBOL nmos 768 -80 R0 WINDOW 0 90 24 Left 2 WINDOW 3 70 58 Left 2 SYMATTR InstName M1 SYMATTR Value 2N7000 SYMBOL res 800 240 R0 WINDOW 0 61 43 Left 2 WINDOW 3 60 78 Left 2 SYMATTR InstName R1 SYMATTR Value 500 SYMBOL voltage 976 -48 R0 WINDOW 0 49 45 Left 2 WINDOW 3 48 80 Left 2 SYMATTR InstName V1 SYMATTR Value 20 SYMBOL voltage 976 240 R0 WINDOW 0 53 37 Left 2 WINDOW 3 57 72 Left 2 SYMATTR InstName V2 SYMATTR Value 20 TEXT 456 -136 Left 2 !.tran 0 20 0 1m TEXT 456 -168 Left 2 ;'2N7000 Colpitts Self-Start TEXT 328 464 Left 2 !* PWRMOS.LIB \n* NOT SPICE 2G.6 Compatible. FOR USE WITH MICROSIM PSPICE\n.model 2n7000 NMOS(Level=3 Gamma=0 Delta=0 Eta=0 Theta=0 Kappa=0.2 Vmax=0 Xj=0 Phi=.6 Kp=1.073u W=.12 L=2u Rs=20m Vto=1.73 Rd=.5489 Rds=48MEG Cgso=73.61p Cgdo=6.487p Cbd=74.46p Mj=.5 Pb=.8 Fc=.5 Rg=

546.2 Is=10f N=1 Rb=1m) [Transient Analysis] { Npanes: 1 { traces: 1 {524291,0,"V(osc)"} X: (' ',0,0,2,20) Y[0]: ('p',0,-1e-009,2e-010,1e-009) Y[1]: ('_',0,1e+308,0,-1e+308) Volts: ('p',0,0,1,-1e-009,2e-010,1e-009) Log: 0 0 0 GridStyle: 1 } }

Why?

What kind of not accurate? Frequency, voltage, etc? Please specify. And how do you know about very accurate? Have you built them to verify?

I showed you that your own model self-starts in LTSpice without a kickstart. You said it never would, but it does. You never mentioned accuracy. Build one and bench test it. Report back here with your results. Be honest and don't change the stream in the middle of a horse.

Frequency.

Built? I compare the LT spice frequency to the calculated value. Even bare LCs are a bit wrong at the default settings.

The issue isn't bench testing, it is the hazards of LT Spice, and the general weirdness of numerical simulation of physical systems.

It used to be that LT Spice wouldn't allow you to run if one end of a capacitor was open, or if you have two caps in series. Now it does.

--

John Larkin         Highland Technology, Inc 
picosecond timing   precision measurement  

jlarkin att highlandtechnology dott com 
http://www.highlandtechnology.com

I have both simulated and built quite a few oscillators using LTSpice, allowing them to start by amplifying the noise in the models. Anything reasonable seems to start in LTSpice and in real life, once you get the gain and phase right. I've never used a kick-start in any case.

John Larkin wrote:

If you are referring to the test you did on July, 2015, you compared the amplitudes of a shocked LC circuit and a generated sine wave.

you ignored the fact that the inductor ESR defaults to 1 milliohm unless you specify otherwise.

As you ran the sym, the LC amplitude decayed.

You took the difference in amplitudes between the LC and generated sine waves and found a difference. How you translated that into a percentage frequency error I'll never know.

Also, you have to set an appropriate timestep. If you don't specify any timestep, the sym produces garbage.

Here is your statement from July, 2015:

This is in "SPICE tarnsient analysis of oscillators - sampling time"

$20wilson$20larkin$20lc$20accuracy%7Csort:date/sci.electronics.design/4cScUlUOldk/3zQjf2pFAwAJ

I posted a LTspice file with an appropriate inductor ESR and timestep that showed the frequency error is in the parts per billion. It is difficult to measure. And you still go around spouting false information.

LTspice can give very accurate answers if you give it correct data. GIGO.

Here is the sym:

Version 4 SHEET 1 880 680 WIRE 224 -192 64 -192 WIRE 416 -192 224 -192 WIRE 480 -192 416 -192 WIRE 64 -112 64 -192 WIRE 416 -32 336 -32 WIRE 480 -32 416 -32 WIRE 336 -16 336 -32 WIRE 224 0 224 -192 WIRE 288 0 224 0 WIRE 64 16 64 -32 WIRE 288 48 224 48 WIRE 224 112 224 48 WIRE 224 112 64 112 WIRE 320 112 224 112 WIRE 416 112 320 112 WIRE 480 112 416 112 WIRE 64 160 64 112 WIRE 320 160 320 112 WIRE 224 176 224 112 WIRE 64 288 64 240 WIRE 224 288 224 240 WIRE 320 288 320 240 FLAG 224 288 0 FLAG 320 288 0 FLAG 64 288 0 FLAG 64 16 0 FLAG 336 64 0 FLAG 416 -32 DIFF FLAG 416 -192 IDEAL FLAG 416 112 LC SYMBOL ind 304 144 R0 WINDOW 0 46 29 Left 2 WINDOW 3 50 62 Left 2 SYMATTR InstName L1 SYMATTR Value 0.1591549430918953357688837634 SYMATTR SpiceLine Rser=1u Cpar=1p SYMBOL cap 208 176 R0 WINDOW 0 24 -3 Left 2 WINDOW 3 -84 189 Left 2 SYMATTR InstName C1 SYMATTR Value 0.1591549430918953357688837634 SYMATTR SpiceLine Rser=1n Lser=1p SYMBOL current 64 160 R0 WINDOW 0 -70 50 Left 2 WINDOW 3 -165 99 Left 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName I1 SYMATTR Value PULSE(1 0 0.5) SYMBOL voltage 64 -128 R0 WINDOW 0 -109 61 Left 2 WINDOW 3 -188 104 Left 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value SINE(0 1 1 0.5) SYMBOL e 336 -32 R0 WINDOW 0 60 40 Left 2 WINDOW 3 53 74 Left 2 SYMATTR InstName E1 SYMATTR Value -1 TEXT 16 -232 Left 2 !.tran 0 1000 0 100u TEXT 16 -264 Left 2 ;'LTSpice Compare LC Frequencies Larkin July 2015 TEXT 592 -232 Left 2 !.options numdgt=15 TEXT 264 -168 Left 2 ;Can't tell if frequency is changing or\ntank amplitude is dropping. A frequency\ndifference will case a linear ramp. Exponential\ndecay due to Q will cause an exponential rise.

Here is the PLT file:

[Transient Analysis] { Npanes: 3 Active Pane: 1 { traces: 1 {524292,0,"V(ideal)"} X: ('K',3,2304,3,2334) Y[0]: (' ',1,-1,0.2,1) Y[1]: ('_',0,1e+308,0,-1e+308) Volts: (' ',0,0,1,-1,0.2,1) Log: 0 0 0 GridStyle: 1 }, { traces: 1 {268959746,0,"V(lc)"} X: ('K',3,2304,3,2334)

Y[1]: ('_',0,1e+308,0,-1e+308)

Log: 0 0 0 GridStyle: 1 }, { traces: 1 {268959747,0,"V(diff)"} X: ('K',3,2304,3,2334) Y[0]: (' ',0,-100,20,100) Y[1]: ('_',0,1e+308,0,-1e+308) Volts: (' ',0,0,0,-100,20,100) Log: 0 0 0 GridStyle: 1 } }

Steve Wilson wrote:

Rats. Line wrap kills the file. Here is the fixed version:

Version 4 SHEET 1 880 680 WIRE 224 -192 64 -192 WIRE 416 -192 224 -192 WIRE 480 -192 416 -192 WIRE 64 -112 64 -192 WIRE 416 -32 336 -32 WIRE 480 -32 416 -32 WIRE 336 -16 336 -32 WIRE 224 0 224 -192 WIRE 288 0 224 0 WIRE 64 16 64 -32 WIRE 288 48 224 48 WIRE 224 112 224 48 WIRE 224 112 64 112 WIRE 320 112 224 112 WIRE 416 112 320 112 WIRE 480 112 416 112 WIRE 64 160 64 112 WIRE 320 160 320 112 WIRE 224 176 224 112 WIRE 64 288 64 240 WIRE 224 288 224 240 WIRE 320 288 320 240 FLAG 224 288 0 FLAG 320 288 0 FLAG 64 288 0 FLAG 64 16 0 FLAG 336 64 0 FLAG 416 -32 DIFF FLAG 416 -192 IDEAL FLAG 416 112 LC SYMBOL ind 304 144 R0 WINDOW 0 46 29 Left 2 WINDOW 3 50 62 Left 2 SYMATTR InstName L1 SYMATTR Value 0.1591549430918953357688837634 SYMATTR SpiceLine Rser=1u Cpar=1p SYMBOL cap 208 176 R0 WINDOW 0 24 -3 Left 2 WINDOW 3 -84 189 Left 2 SYMATTR InstName C1 SYMATTR Value 0.1591549430918953357688837634 SYMATTR SpiceLine Rser=1n Lser=1p SYMBOL current 64 160 R0 WINDOW 0 -70 50 Left 2 WINDOW 3 -165 99 Left 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName I1 SYMATTR Value PULSE(1 0 0.5) SYMBOL voltage 64 -128 R0 WINDOW 0 -109 61 Left 2 WINDOW 3 -188 104 Left 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value SINE(0 1 1 0.5) SYMBOL e 336 -32 R0 WINDOW 0 60 40 Left 2 WINDOW 3 53 74 Left 2 SYMATTR InstName E1 SYMATTR Value -1 TEXT 16 -232 Left 2 !.tran 0 1000 0 100u TEXT 16 -264 Left 2 ;'LTSpice Compare LC Frequencies Larkin July 2015 TEXT 592 -232 Left 2 !.options numdgt=15

High-Q oscillators, especially crystal oscillators, can take thousands or millions of cycles to settle. And need a small time step to model accurately. That can make a run take hours.

I like to force initial conditions close to what the steady-state values will be. It starts instantly. Then I can zoom up on what it's doing and see if the amplitude is increasing or decreasing.

--

John Larkin         Highland Technology, Inc 
picosecond timing   precision measurement  

jlarkin att highlandtechnology dott com 
http://www.highlandtechnology.com

You set the time step to 100u. That makes it more accurate.

My Colpitts frequency changes most of a per cent when I set a max time step low, compared to the LT Spice default. Run time goes way, way up.

--

John Larkin         Highland Technology, Inc 
picosecond timing   precision measurement  

jlarkin att highlandtechnology dott com 
http://www.highlandtechnology.com

I prove this wrong in a separate post. But you have to be sure to use the correct model.

I take that to mean letting it run for many cycles then looking at the envelope to see if it is constant. Then adjust the initial conditions as appropriate.

You don't have to do that. There's a better way.

I show how to do this in oscillators.zip

You start the oscillator and let it run for an appropriate length of time, then measure the peak voltage across the crystal ESR. Convert that to the voltage required to produce that current, and set the initial conditions to produce that voltage across the inductor and ESR resistor. This produces a current in the inductor that matches the value measured after many cycles.

The result is the oscillator starts and settles within a few cycles, at exactly the correct amplitude.

Even complex stabilization methods, such as suggested by Bruce Griffiths, settle extremely quickly. I also show this in Oscillators.zip

It's a technique I have used for decades, and often posted to SED.

An extension of this technique is suggested by Kevin Aylward of Superspice:

He starts by looking at the formula Q = XL / R

He reasons you can make a high Q oscillator run faster by lowering the Q. Then you have to increase C by the same amount to maintain the same frequency. He cautions to not try to go beyond a factor of 100.

His suggestion does indeed work. But it changes the frequency slightly, which may be important in some applications.

Each setting of initial conditions can be run for just a few cycles to see if the amplitude is increasing or decreasing. Zoom the heck up on the peaks. Then tweak the conditions and try again. It converges fast.

Got to be careful about bias, which can involve long time constants.

That's the problem. The appropriate screen time may be hours. Maybe days with a good time step.

Why not just measure the voltage and current of all the crystal elements? It has shunt and series paths, so the current through the series resistance is only part of the story.

It only settles at its normal rate, which might be a million cycles.

An XO must be analyzed in time domain to estimate the voltages and currents. It's basically impossible to do PPM or PPB frequency analysis in time domain. Best switch to frequency domain for that.

--

John Larkin         Highland Technology, Inc 
picosecond timing   precision measurement  

jlarkin att highlandtechnology dott com 
http://www.highlandtechnology.com

Not enough to go from a few percent to parts-per-billion. That's 7 orders of magnitude.

You did not know the inductor ESR defaults to 1 milliohm. This caused the amplitude to decay. You measured the difference in amplitudes, which cannot distinguish between a frequency or amplitude change. You assumed the error was caused by a frequency difference when it was actually amplitude decay.

You would have seen this if you had overlapped the IDEAL and LC waveforms. It stands out like a sore thumb.

If you set the inductor ESR to 1u, the curves overlap exactly even after

1,000 cycles. It is extremely difficult to measure the error.

Reduce the time step until the runtime increases, then back off. I do this in Oscillators.zip and get very reasonable run times, except when showing the startup and settle times in crystal oscillators.

That's trial and error and guesswork. You can spend a lot of time trying to get close.

LTspice settles the bias conditions for you.

I have never seen more than a few minutes. Your time step is way too small.

The ESR is the one you are interested in. It gives the exact value needed to start the oscillator and settle in a few cycles, maybe one or two.

I don't think you are paying attention. I stated a few cycles. If your trial and error technique works, why do you reject mine?

Nonsense. Let the oscillator run for 1,000 or 10,000 cycles, then measure the frequency and divide by the number of cycles.

You can use Keven's method to speed things up, although I have never run into an occasion that really needs it.

I don't think frequency domain can get down to ppb. You are dealing with a response curve at the peak, which is quite flat on these scales.

Steve Wilson wrote:

Vig, April 2012, Page 81, shows the maximum Q of a crystal:

The maximum Q of a resonator can be expressed as:

Qmax = 1/(2*pi*F*t)

For 10 MHz, Qmax = 1/(2*pi*1e7*1e-14) = 1,591,549 where F is the frequency in Hz, and t is an empirically determined "motional time constant" in seconds, which varies with the angles of cut and the mode of vibration. For example, t = 1 x 10 -14 s for the AT-cut's c-mode (Qmax= 3.2 million at 5 MHz), t = 9.9 x 10 -15 s for the SC-cut's c-mode, and t = 4.9 x 10 -15 s for the BT-cut's b-mode.

The ASC file below shows a 10MHz crystal oscillator.

The Q of the crystal is Q = XL/R = 2 * pi * 1e7 * 25e-3 / 1 = 1,570,796, which is close to the maximum of 1,591,549.

The total elapsed time is 161.732 seconds, or about 2.68 minutes.

If you are getting a run time of hours or days, you are doing something wrong.

Here is the crystal oscillator:

Version 4 SHEET 1 880 680 WIRE 208 48 16 48 WIRE 304 48 208 48 WIRE 336 48 304 48 WIRE -480 64 -496 64 WIRE -352 64 -400 64 WIRE 336 64 336 48 WIRE 16 80 16 48 WIRE -496 128 -496 64 WIRE -432 128 -496 128 WIRE -352 128 -352 64 WIRE -352 128 -368 128 WIRE -160 128 -352 128 WIRE -144 128 -160 128 WIRE 208 160 208 48 WIRE 336 160 336 144 WIRE -544 208 -592 208 WIRE -496 208 -496 128 WIRE -496 208 -544 208 WIRE -480 208 -496 208 WIRE -368 208 -400 208 WIRE -256 208 -288 208 WIRE -240 208 -256 208 WIRE -144 208 -144 128 WIRE -144 208 -176 208 WIRE -128 208 -144 208 WIRE -48 208 -64 208 WIRE 16 208 16 160 WIRE 16 208 -48 208 WIRE 96 208 16 208 WIRE 144 208 96 208 WIRE -592 240 -592 208 WIRE 16 240 16 208 WIRE -496 256 -496 208 WIRE -48 256 -48 208 WIRE 16 320 16 304 WIRE 112 320 16 320 WIRE 208 320 208 256 WIRE 208 320 112 320 WIRE -592 336 -592 320 WIRE -496 336 -496 320 WIRE 16 336 16 320 WIRE 208 336 208 320 WIRE -48 352 -48 336 WIRE 16 416 16 400 WIRE 208 432 208 416 FLAG 16 416 0 FLAG 96 208 Q1B FLAG 112 320 Q1E FLAG -160 128 R7C7 FLAG 304 48 Vcc FLAG -592 336 0 FLAG -496 336 0 FLAG 208 432 0 FLAG 336 160 0 FLAG -544 208 Vout FLAG -256 208 L1C1 FLAG -48 352 0 SYMBOL npn 144 160 R0 WINDOW 3 57 69 Left 2 SYMATTR Value 2N3904 SYMATTR InstName Q1 SYMBOL res 0 64 R0 SYMATTR InstName R2 SYMATTR Value 10k SYMBOL res 192 320 R0 SYMATTR InstName R3 SYMATTR Value 2k SYMBOL voltage 336 48 R0 WINDOW 123 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value 5 SYMATTR SpiceLine Rser=0.1 SYMBOL cap 0 336 R0 SYMATTR InstName C2 SYMATTR Value 390p SYMBOL cap 0 240 R0 WINDOW 3 25 49 Left 2 SYMATTR Value 100p SYMATTR InstName C4 SYMBOL cap -512 256 R0 SYMATTR InstName C5 SYMATTR Value 33p SYMBOL res -608 224 R0 SYMATTR InstName R5 SYMATTR Value 100k SYMBOL cap -64 192 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C7 SYMATTR Value 1n SYMBOL res -384 48 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R7 SYMATTR Value 1E7 SYMBOL cap -176 192 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C1 SYMATTR Value 0.01p SYMBOL ind -384 224 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 5 56 VBottom 2 SYMATTR InstName L1 SYMATTR Value 25m SYMATTR SpiceLine Rser=0 SYMBOL res -384 192 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R8 SYMATTR Value 1 SYMBOL cap -368 112 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C8 SYMATTR Value 5p SYMBOL res -32 240 M0 SYMATTR InstName R1 SYMATTR Value 10k TEXT -264 -56 Left 2 !.tran 0 50m 0 10n TEXT -264 -88 Left 2 ;'10MHz Xtal Osc

I get 90 seconds :-)

Thanks. I have an older computer for legacy and compatibility reasons, and I'm only running 1 CPU out of a possible 4 in Virtualbox. Your computer is about twice as fast. That's a good number, which means everybody should get better results than I do. That should make them glee with joy.

I have uploaded an illustration of how to measure 8 parts-per-billion in LTspice. You can download it at

This turned out to be one of the most difficult articles I have uploaded to google drive. Please let me know if you have trouble following it.