His circuit provides a constant current source as stable as the reference.
I would be surprised if it doesn't start the OPA177 can't drive to ground. It probably sources some current while trying to, if not a bit of pull up on the op-amp output will fix that.
I've not breadboarded it, but I'm pretty confident it will work. It is a constant current circuit. Initially, as the OPA177 output can't go to ground (typ. 2V), we will get an initial current of about 0.6 mA to the zener, through R4. It will start it up and get to about 6.9V. This voltage will be amplified by 1.468 to about 10.13V. Then the current will be (10.13 - 6.9) / 3k11 (R4) = 1.04 mA and will be as stable as the LM399.
Given what you've told me about its startup, then I think I am also convinced it will get enough starting current and will eventually reach regulation. And I understand that the output buffer drops a voltage across the 3k11 and provides the drive current. But I see that design decision has problems that are easily remedied.
1) All of the regulating current for the reference comes from the output of the opamp,
which is also feeding other circuits in your power supply. You should immediately see this is a problem for maintaining the stability of your reference. This would only be acceptable if you are going to put another voltage follower immediately at J2 before it goes anywhere else on to the rest of your circuits. And if so, why not put that buffer on the reference board itself, so that J2 is the output of a real buffer, not the output of your self-referential voltage reference that also provides it's own current source.
2) R4 provides a path for any voltage or current noise from outside your reference board to get in and throw the reference off course.
3) if J2 is feeding outside, and something outside sinks a large current, say an ADC sample and hold event, then it will steal current that is supposed to be for your constant current source to your reference. I don't know how you can call it a constant current source when you are taking that node off board and allowing other circuit nodes to siphon current away from it. That net feeding your LM399 should be stable and quiescent. Yes, I realize the opamp will provide more drive current when needed, but it cannot recover instantaneously, and do you really want the junction at the top of your current source changing that much due to dynamic loads off-board? I would not.
4) I don't like that your reference has no actually set current.. you really don't know what it will be, just trust that it will stop rising in voltage value as the opamp gives it more and more current until it settles.. and yes, I understand at that point it will be stable. But in my opinion I'd like to actually
SET the current to something I specify, and maintain it there.
My design would have a separate op amp for the current source and one more as a buffer. As I said, if your going to the effort of using an LM399, why do something that can mess up your reference?
Actually, I'd guild the lily, and use the second opamp not for merely a current source for the main reference, but as a servo for the LM317 providing your 15V rail. servo the LM317 to stabilize it over time and temperature, and then you can set your 1.5mA current reference with a 5k42 low tempco resistor through the LM399. Use the original opamp as a buffer amplifier where you can dial it up to 10.0000V
Now reading the datasheets, why is the AD706 much better in noise than the OPA177? The typical input voltage noise @ 1kHz BW of the 706 is 15 nV/sqr(Hz) and the 177 is about 8 nV/sqr(Hz), both reading the noise graphs.
Actually, I'm quite familiar with the AD706 so I know it's a good amp and there's something to be said for going with what you know. But I just read the datasheets for the OPA177 too, and I agree, it seems quite a lot better in noise, offset and drift specs, and is designed to replace the AD707, which is an even better amp then the AD706.
The only thing the AD706 has over the OPA177 would seem to be its sub-nanoAmp bias currents, which you don't need to worry about. So your choice of OPA177 will work good here.
Sorry for the long post. I get windy.