Such a system requires merely a cheap analog quartz clock, a constant current sink and a threshold switch to turn off the clock when the battery is discharged. The circuit in Figure 3 is fairly obvious - the ADR291 voltage reference and R2 & R3 provide 1V at node 1 when the battery is charged. This voltage is the voltage reference for a constant current sink comprising op-amp A, T1 and R1. The bias current of an AD822 is sufficiently small that its loading of the voltage divider is insignificant.
Figure 3: Battery capacity measurement circuit
For my purposes (2400-4000mAH Li-Ion cells) 500mA was a suitable discharge current but larger cells may need higher currents and smaller ones less. Somewhere between the 4-hour and the 10-hour rate is usually suitable for measuring and comparing capacities. T1 and T2 need low threshold voltages (<1.4V) and T1 and R1 must dissipate whatever power is necessary to handle the highest expected current. The voltage across R1 is always 1V during discharge and the current is adjusted by setting R1:-
I = 1V/R1 Equation 1
The dissipation in the resistor is therefore:-
V2/R1 = 1/R1 Equation 2
The dissipation in the transistor is the product of the current and the maximum voltage across it, Vbat. Maximum transistor dissipation is therefore:-
(V bat - 1V)((1V)2/R1) Equation