[time-nuts] On low-voltage TAC/TDCs for a GPSDO

[Bruce Griffiths]

J.D. Bakker wrote:
> At 08:30 +1200 14-08-2010, Bruce Griffiths wrote:
>> J.D. Bakker wrote:
>>>> 4) If the ADC(s) have a sufficiently wide full power bandwidth then 
>>>> one could just sample a pair of quadrature phased 250kHz sinewaves.
>>>
>>> As someone who's used to thinking in I/Q I must say I've always 
>>> liked the elegance of this approach. Trouble is that I don't see a 
>>> cheap/easy way to generate quadrature sines with low enough 
>>> distortion/noise.
>> Distortion isnt a great problem if its relatively small and stable as 
>> it can always be measured as part of the calibration process and its 
>> effect may then be compensated in software.
>
> Those are two large "if"s, if you're going for a small/cheap 
> implementation. Fully analog solutions can get messy, phase shifter 
> hybrids are doable but would definitely need to be shielded from 
> drafts and DDSes plus appropriate filters do the job but are still 
> relatively expensive. And then there's motor/generators... Am I 
> missing any method here?
>
> (on a semi-related note: some interesting work on ultralow distortion 
> low frequency oscillators, employing quadrature signals to simplify 
> the AGC, is being done here: 
> <http://www.prodigy-pro.com/diy/index.php?topic=26461.0>)
>
>>> (I'm not sure why I'd want to use a synchronizer in this path. The 
>>> way I see it the TAC operates as a linear phase detector, with the 
>>> GPS PPS and the synthesized PPS as inputs. The microcontroller then 
>>> applies the sawtooth correction to the measured time offset, and 
>>> uses the result in a DPLL. There will, of course, be a synchronizer 
>>> in the input line from the GPS PPS to the microcontroller, but 
>>> that's only used for the FLL and for rough synchronization).
>>
>> Using a synchroniser allows the TAC output range to be combined with 
>> the coarse timestamp derived by sampling a counter clocked by the 
>> same clock as the synchroniser.
>
> I think we're looking at it from two different angles.
>
> What I read from your description is close to the traditional 
> architecture such as used in the HP5335A, with a counter running at 
> the system clock frequency for coarse measurement and a TAC to measure 
> the remainder. What I'm planning to do is more akin a traditional PLL, 
> with the TAC as the Phase Detector. For this to work I assume that a 
> coarse FLL (using a counter) has already brought the oscillator within 
> lock range. Is there any reason that method won't work, or can 
> trivially be made to work better?
>
Having a wide TAC range means that its resolution and noise depends 
critically on that of the ADC.
Since some ADCs embeded within processor dont have true 12 bit 
performance this may limit the TAC resolution/noise to several nanosec 
rather than the desired 1ns or better.
> (The regenerated PPS output will indeed be derived from and 
> synchronous with the VCXO/OCXO. It is also my intention to have the 
> OCXO clock the microcontroller, either directly or through a 
> prescaler, depending on whether the XO runs higher or lower than the 
> max CPU clock).
>
That ensures that all intermod products are harmonically or submultiples 
of the OCXO frequency.
>>>>> - Circuit 3 expands on this approach by having dual ramp 
>>>>> generators, and having the ADC measure the voltage difference 
>>>>> between the two.
>>>>
>>>> Not a good idea, as this requires accurate matching of the gains of 
>>>> the 2 TACs.
>>>
>>> Why?
>>>
>>> At that points they're not TACs yet, just ramp generators. Circuit 3 
>>> uses the difference between these ramps, and I believe it need not 
>>> be constant.
>>>
>>> Assume there's a 1% difference in ramp rates; say C3 charges at 
>>> 1V/us and C4 charges at 1.01V/us. [...]
>>
>> Since NP0/C0G caps are only available in 5% and 10% tolerance at 
>> best, matching gains to 1% will require using selected parts (adjust 
>> current source to compensate) or trimming.
>
> I picked the 1% figure out of the air, simply to have an example for 
> the math. Even so, if required it would be easy to have the 
> microcontroller trim the ramp rates through one of the on-chip DACs. 
> However I don't believe that the ramp rate can't be dealt with in 
> software through calibration.
Software is probably best (if feasible) as this eliminates the parasitic 
capacitances and noise associated with trimmers and DACs.
With a single ADC its not possible to correct the TAC nonlinearity since 
there are a wide range of possible output voltages from the first TAC 
for any given differential input to the ADC.
>
>> Simulation indicates nonlinearity of the order of 1% or so in the 
>> ramp generator. This is largely due to the Early effect and 
>> semiconductor output capacitance modulation.
>
> Yeah, I noticed that. It helps a lot in the four-transistor mirror to 
> have all transistors carry approximately equal amounts of current. 
> Further linearization can be achieved by increasing the current, 
> slowing the ramp rate and picking transistors with lower hFE for a 
> given fT and/or higher VAF. An output resistance of up to 1M can be 
> achieved, but it's the voltage-dependent capacitance that's hurting 
> linearity.
>
Lower hfe requires tighter matching for good tracking.
> (I'm still not set on a given ramp rate, but the more I think about it 
> the more I feel that it makes sense to go lower than the 1V/us I 
> picked earlier. Many of the nonlinearities in the current source, 
> buffer amps and ADC get worse with increasing slew rate, and as long 
> as the total ramp time is << the interval between measurements there 
> should be no major issues there either. Sample clock drift could be an 
> issue, but as the ADC is driven by the OCXO that shouldn't impact 
> matters either).
>
>> The output compliance of your four transistor current mirror is 
>> limited to around 1.3V or so before the onset of saturation or gross 
>> nonlinearity.
>
> It's actually better than that, from what I can see from simulations 
> and measurements. If the transistor currents are close to equal and 
> the ramp rate isn't too high, output current stays within 1% up to 
> ~1V, and the mirror saturates at 0.6-0.7V. This is with common 
> small-signal transistors with an fT of a few hundred MHz.
Really?
There are 2xVbe + 1x diode drop to subtract from 3.3V ie somewhere from 
1.8V -2.4V leaving a ramp amplitude of 1.5V to 1.1V depending on 
temperature and transistor current. 1% nonlinearity isnt that good with 
a 1nF ramp cap one should be able to do much better than that.  
Alternative current source configurations have somewhat higher 
compliance and output resistance. Using a Schottky diode will gain a few 
tenths of a volts at the expense of increased leakage current.
>
>> Unless the transistors are closely thermally coupled some resistance 
>> in the emitters of the CE transistors may be required to avoid 
>> thermal runaway.
>
> While I plan to use some of those newer dual transistors in SOT-23-6 
> to improve thermal coupling, I'll probably add a few VsubT worth of 
> emitter resistance there.
>
> Thanks again,
>
> JDB.
> [I should probably make a sketch of the entire GPSDO and post it]
Yes that would be useful as details can often be important.

Bruce