Of all the stepping up circuits, one pair of selected resistors plus a precision op-amp provide the simplest ways.
However, there are three issues with this scheme namely drift, tempco and difficult to adjust to 10V.
Often people say 'matched pair' to describe the requirement, meaning R1/R2 have the same drift and tempco thus will keep the ratio constant so will be the output. While techniques or selection associated with matched pair are not easily accessible, separate resistors of good quality will also make the day. Consider this: two very good resistors, very low aging rate and very low tempco, they form a natural match.
Drift of resistors is factor we can hardly control, and I never heard of any feasible way to direct compensate for the drift, so we will pass that.
However, we can do much better on tempco compensation and value adjustment.
The first problem usually encountered is not the selection, purchase, or assemble the resistors, rather, it is the calculation!
It's not difficult though, to calculate step up or resistors required, making parallel, but anyone considered how to calculate the combined TCR when series or parallel connected? Any quantitative ideas on how a component affect the output? How sensitive a resistor contribute to the output?
It does not matter anymore, I have a spread sheet specifically designed for this purpose.
There are two compensations involved:
- Compensation for output value to exact 10V. This can be done by adding either Ra or Rb in the resistor string. sometimes Ra and Rb can be added at the same time because of the availability of the resistors. Adding both has also the advantage of very fine adjustment of the 10V by parallel others resistors of larger value onto them.
- Compensation for tempco. This can be achieved simply by adding a copper resistor. Copper has a very large tempco of about 4250ppm/K, and copper wire is very stable against time, only a small value compensate a lot. If the 10V has positive tempco, add copper resistor at the lower part as Rc2. If the 10V has negative tempco, add copper resistor at the upper part as Rc1. Copper resistor can be easily made from a piece of enameled wire(of about 0.15mm) wrapped around a coax resistor(of a large value).
By using the spread sheet, the life will be much easier. It also serve the purpose of documentation on how you calculated. I've been using it for sometimes myself, now I made some remarks and clean up. Here are the steps:
1. Leave room for compensation resistor Ra, Rb, Rc1, Rc2 when making the PCB. Suggest also make a parallel resistor for Ra and Rb. Main resistor pair R1/R2 can be selected using the spread sheet as well. Better to make the output as close to 10V as possible without using any compensation resistor. Large compensation resistor of Ra and Rb requires more for stability.
2. Assemble your reference and 7V to 10V step up, short Ra, Rb, Rc1 and RC2 first, make measurements of the output for voltage and tempco.
If your reference happened to be output at exact 10V and tempco is zero, then you can forget about the rest of this. If, however, your circuit turn out to be not very idea, the spread sheet will help.
3. Open the spread sheet. There are two tables of similar function for manual and semi-auto adjustment, recommend to use semi-auto first.
4. Type in the data in light green area of the left section. If you don't know the exact value of R1 and R2, just enter the nominal value, and make slight alterations to let the yellowish-background voltage be the value you measured. Similarly, if you don't know the exact tempco of R1 and R2, just make up something and let the yellowish background tempco be the value you measure.
5. Now one of the Ra or Rb is calculated on the right hand section, and the purple cell will be 10V exact.
6. There will be a suggested value of either Rc1 or Rc2, enter it in the corresponding green cell, the purple tempco will be close to zero. If not, there will be a new suggested value and you need to type in again. Note that there is no need to be perfect on this, just compensate to within 0.01ppm will do, the reality will be slightly different.
7. There is also a 'sensitivity' column, telling you how sensitive the compensation resistor to the 10V output. This mean: how many ppm the 10V will change if the compensation resistor changed by 100ppm. This will help when choose the proper type.
8. When you've familiar the process, you can go manual. You can do both Ra and Rb at the same time, also the tempco for Ra/Rb can be entered.
9. Once you've done in the spread sheet, you can prepare the compensation resistor. Better to use a slightly larger value than said, to create slight over -compensation. Be sure to measure those compensation resistor before put them on.
10. Test the circuit again, if Ra or Rb over compensated, parallel a resistor to adjust. If Rc1 or Rc2 is over-compensated, cut the copper wire a bit.
(bookmarked, downloaded) 
