Differential oscillator operation details

The question is far too loose to get sensible answers.

What are you aiming to? The target may be anything from a two-transistor astable multivibrator to a kilowatt- size inverter and beyond.

Not reference material, but Jim Thompson (RIP) was a fan, and posted some info and LTSpice schematics about 5 years back in response to discussions I started (talking about AGC). Jim's oscillator worked, but his AGC didn't :) I fixed it and built it though.

Have a search in the archives.

Clifford Heath.

The simplest differential oscillator I recall encountering as a young man (about age 20, around the turn of the century) was figure 4 here I guess it was called the "cathode coupled oscillator" back in the day.

I built a transistor version and used the simplest AGC scheme I could think of which was using a current source in the tail and applying the rectified and filtered AGC signal there to control the gain, it seemed to work OK so I'm assuming Jim Thompson's scheme was a bit more sophisticated than that.

On 28/3/19 10:33 am, Clifford Heath wrote:

This isn't JT's circuit, but it's a simple differential oscillator without AGC. Change the transistor to a 2n2222 if you don't have a CA3046 model.

--- Cut Here --- Version 4 SHEET 1 1132 708 WIRE 304 -160 208 -160 WIRE 384 -160 304 -160 WIRE 464 -160 384 -160 WIRE 800 -160 464 -160 WIRE 912 -160 800 -160 WIRE 1040 -160 912 -160 WIRE 384 -128 384 -160 WIRE 800 -128 800 -160 WIRE 912 -128 912 -160 WIRE 304 -112 304 -160 WIRE 304 -32 304 -48 WIRE 384 -32 384 -48 WIRE 384 -32 304 -32 WIRE 560 -32 560 -64 WIRE 560 -32 384 -32 WIRE 656 -32 560 -32 WIRE 800 -32 800 -48 WIRE 800 -32 720 -32 WIRE 560 0 560 -32 WIRE 912 16 912 -48 WIRE 944 16 912 16 WIRE 304 80 304 -32 WIRE 464 80 464 -160 WIRE 912 80 912 16 WIRE 1040 80 1040 -160 WIRE 208 128 208 -160 WIRE 240 128 208 128 WIRE 560 128 560 80 WIRE 560 128 528 128 WIRE 800 128 800 -32 WIRE 848 128 800 128 WIRE 304 192 304 176 WIRE 384 192 304 192 WIRE 464 192 464 176 WIRE 464 192 384 192 WIRE 384 240 384 192 WIRE 912 288 912 176 WIRE 928 288 912 288 WIRE 912 320 912 288 WIRE 800 336 800 128 WIRE 384 432 384 320 WIRE 800 432 800 416 WIRE 800 432 384 432 WIRE 912 432 912 400 WIRE 912 432 800 432 WIRE 1040 432 1040 160 WIRE 1040 432 912 432 WIRE 1040 464 1040 432 FLAG 1040 464 0 FLAG 560 -64 Vtank IOPIN 560 -64 Out FLAG 928 288 Veout IOPIN 928 288 Out FLAG 944 16 Vcout IOPIN 944 16 Out SYMBOL voltage 1040 64 R0 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value 3.4v SYMBOL cap 288 -112 R0 SYMATTR InstName C2 SYMATTR Value 180pF SYMBOL ind 368 -144 R0 SYMATTR InstName L3

SYMBOL npn 240 80 R0 SYMATTR InstName Q1 SYMATTR Value CA3046 SYMBOL npn 528 80 M0 SYMATTR InstName Q2 SYMATTR Value CA3046 SYMBOL npn 848 80 R0 SYMATTR InstName Q4 SYMATTR Value CA3046 SYMBOL res 896 304 R0 SYMATTR InstName R8 SYMATTR Value 220 SYMBOL res 784 -144 R0 SYMATTR InstName R4 SYMATTR Value 33k SYMBOL cap 720 -48 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C3 SYMATTR Value 22pF SYMBOL res 784 320 R0 SYMATTR InstName R6 SYMATTR Value 47k SYMBOL res 896 -144 R0 SYMATTR InstName R10 SYMATTR Value 330 SYMBOL res 368 224 R0 SYMATTR InstName R1 SYMATTR Value 2.2k SYMBOL res 544 -16 R0 SYMATTR InstName R2 SYMATTR Value 10k TEXT 208 512 Left 2 !.tran 0 50uS 0 1nS TEXT 200 464 Left 2 !.INC "..\\Lib\\Transistors\\ca3000.lib"

I have SPICE simulated CMOS differential oscillators with frequencies going upto 1000 MHz, using both Level 3 CMOS and BSIM 4.6 libraries from UC Berkeley. However, I have so after reading up some journal papers and experimentation. I am looking for simple, intuitive description of how they work. For example, a feedback oscillator has an amplifier and resonator/frequency selector. Like that.

This type of thing?

From here,

Sorry long links.

It would be nice if you attached links etc. (This is a basic discussion of cross coupled oscillators

George H.

There are problem with long links. Sometimes the reader won't include the entire url. It stops at the first line break.

There are different attempts to get the reader to continue, such as surrounding the url with various termintators such as "", , etc. Most of the time these don't work.

However if you can shorten the link so it occupies a single line, it helps the reader get the proper url.

For example, you can use

becomes

becomes

Much easier to work with.

Right, I was being as lazy as the OP.

GH

Yeah that's what a differential oscillator is too. but electronic oscillators in general don't have a simple or intuitive set of equations that govern their behavior they're intrinsically large-signal phenomenon, not LTI, so many of the tools you'd use for analyzing LTI circuits are useless. You can use math to answer some basic questions as to whether a given configuration is stable, or not, from looking at the small-signal characteristics and something like the Barkhausen criteria.

Sometimes the feedback network is complex enough that Barkhausen can't be applied directly you'd apply something like Routh-Hurwitz:

You'd analyze stability or lack thereof in a positive feedback circuit same as any other feedback loop you break the loop and look at the input to output transfer function and apply your mathematical tests of choice to determine probable instability and the oscillation frequency. there are well-known small signal models for CMOS differential pairs, and frequency selective tanks, and all that stuff.

I can't remember if it's applied to the differential oscillator topology specifically but Wes Hayward's "Introduction to Radio Frequency Design" has a chapter on high-frequency oscillator design and does some quantitative analysis of them of that type.

But I don't believe there's any general test that can prove _instability_ you can only prove stability. Most circuits which are not stable will oscillate, but there are probably edge cases.

Unfortunately, H-L are using their "ISF" theory in the analysis. This theory is proven false, as explained here:

With full mathematical details of the proof of failure of the H-L approach in the cited link:

I do have a somewhat interesting analysis on a diff osc though... :-)

-- Kevin Aylward

What is hard to understand? Instead of a single-ended amp, they're built around a diff-amp, with appropriate feedback phasing. Run the sim I posted.

Clifford Heath.

Aren't differentials bang-bang oscillators? That was always my impression.

George H.

There should be a comma between 'differentials' and 'bang-bang'. GH

Thanks, I have looked at each of these references myself - in fact I do have a copy of Hajimiri-Lee paper pn my home PC.

The cross-coupled pair is just a negative resistance. It's i-v curve is something like this:

^i | * *******| * * *-------*-----> v * *******

Place a parallel LC across it and the negative conductance cancels out the tank's losses and it starts oscillating. Of course the nonlinearities play a significant role, but the basics are these.

Any oscillator can be analyzed as a negative-resistance + resonator or unit-gain feedback loop. Some structures are more intuitive from one point of view others from the other. The cross-coupled oscillator is intuitive from the negative-resistance pov.

Pere

I don't have the CA3046 model so I replaced them with the 2N2222 as you suggested. The simulation does not oscillate.

They are still the usual non-linear limiting, linear amp, not a relaxation oscillator.

A major reason they are pretty much the default oscillator of choice in ASICs is because, compared to the standard Colpitts, the loop gain is much higher, which means that they can run at a higher frequencies.

For high stability one is still relegated to single ended xtal oscillators, usually Pierce/Colpitts.

-- Kevin Aylward

On 29/3/19 11:49 pm, John S wrote:

I tried 2N3904 and it works, just a little slower starting. Try this.

Clifford Heath

--- Cut Here --- Version 4 SHEET 1 1132 708 WIRE 304 -160 208 -160 WIRE 384 -160 304 -160 WIRE 464 -160 384 -160 WIRE 800 -160 464 -160 WIRE 912 -160 800 -160 WIRE 1040 -160 912 -160 WIRE 384 -128 384 -160 WIRE 800 -128 800 -160 WIRE 912 -128 912 -160 WIRE 304 -112 304 -160 WIRE 304 -32 304 -48 WIRE 384 -32 384 -48 WIRE 384 -32 304 -32 WIRE 560 -32 560 -64 WIRE 560 -32 384 -32 WIRE 656 -32 560 -32 WIRE 800 -32 800 -48 WIRE 800 -32 720 -32 WIRE 560 0 560 -32 WIRE 912 16 912 -48 WIRE 944 16 912 16 WIRE 304 80 304 -32 WIRE 464 80 464 -160 WIRE 912 80 912 16 WIRE 1040 80 1040 -160 WIRE 208 128 208 -160 WIRE 240 128 208 128 WIRE 560 128 560 80 WIRE 560 128 528 128 WIRE 800 128 800 -32 WIRE 848 128 800 128 WIRE 304 192 304 176 WIRE 384 192 304 192 WIRE 464 192 464 176 WIRE 464 192 384 192 WIRE 384 240 384 192 WIRE 912 288 912 176 WIRE 928 288 912 288 WIRE 912 320 912 288 WIRE 800 336 800 128 WIRE 384 432 384 320 WIRE 800 432 800 416 WIRE 800 432 384 432 WIRE 912 432 912 400 WIRE 912 432 800 432 WIRE 1040 432 1040 160 WIRE 1040 432 912 432 WIRE 1040 464 1040 432 FLAG 1040 464 0 FLAG 560 -64 Vtank IOPIN 560 -64 Out FLAG 928 288 Veout IOPIN 928 288 Out FLAG 944 16 Vcout IOPIN 944 16 Out SYMBOL voltage 1040 64 R0 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value 3.4v SYMBOL cap 288 -112 R0 SYMATTR InstName C2 SYMATTR Value 180pF SYMBOL ind 368 -144 R0 SYMATTR InstName L3

SYMBOL npn 240 80 R0 SYMATTR InstName Q1 SYMATTR Value 2N3904 SYMBOL npn 528 80 M0 SYMATTR InstName Q2 SYMATTR Value 2N3904 SYMBOL npn 848 80 R0 SYMATTR InstName Q4 SYMATTR Value 2N3904 SYMBOL res 896 304 R0 SYMATTR InstName R8 SYMATTR Value 220 SYMBOL res 784 -144 R0 SYMATTR InstName R4 SYMATTR Value 33k SYMBOL cap 720 -48 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C3 SYMATTR Value 22pF SYMBOL res 784 320 R0 SYMATTR InstName R6 SYMATTR Value 47k SYMBOL res 896 -144 R0 SYMATTR InstName R10 SYMATTR Value 330 SYMBOL res 368 224 R0 SYMATTR InstName R1 SYMATTR Value 2.2k SYMBOL res 544 -16 R0 SYMATTR InstName R2 SYMATTR Value 10k TEXT 208 512 Left 2 !.tran 0 100uS 0 1nS

Does not sing. Are you sure about the leftmost base connection?

--

-TV