From Maxim Integrated Application Note 4003:
A series reference design is fairly easy. Just make sure the input voltage and power dissipation are within the maximums specified for the IC:
P_SER = (VSUP – VREF )IL + (VSUP × IQ )
For a series reference, the worst-case power dissipation occurs for maximum power-supply voltage and maximum load:
WC_P_SER = (VMAX – VREF )ILMAX + (VMAX × IQ )
where:
P_SER = power in series reference
VSUP = power-supply voltage
VREF = reference output voltage
IL = load current
IQ = reference quiescent current
WC_P_SER = worst-case power in series reference
VMAX = maximum power-supply voltage
ILMAX = maximum load current
This is the second fundamental on references leading up to our Ask the Experts session on Wednesday, May 21, at 1:00 p.m. EDT (10:00 a.m. PDT). You can sign in using this link on May 21, and you can even enter questions ahead of time.
WC_P_SER = (VMAX – VREF )ILMAX + (VMAX × IQ )
A solution to minimize the WC_P_SER is to have a very low series resistance, then the difference VMAX – VREF will be minimum and, at the same time, by providing a good shutdown procedure to minimize the quescient current of the reference.
Worst case circuit analysis is one of interesting area including power dissipation. Junction temperature factor such as Tj might be included in the equation. A few components are sensitive to temperature. Equation would be nonlinear differential formulation.
@DaeJ: the junction temperature plays a role in the power dissipation of the single component of the IC, for the Voltage Reference the balance of power supplied and absorbed is the best way to evaluate the efficiency. The worst case is the most interesting case, as you correctly said.