Hi all,
estimating state of charge from a simple voltage measurement is close to impossible. There are too many variables: temperature, load current, and internal resistance to name a few. In the "good old days", tape decks had VU meters. Battery powered ones had a button to switch one of them to a battery meter - not with a voltage scale, but with a sector telling you full or empty - my Marantz CP430 did this. My Sony WM-D6C had four LEDs to show me battery voltage or level. You had to learn to understand what your recorder wanted to tell you - this has not changed in the last 30 or so years
Another point to keep in mind is that current consumption of modern recording devices is not constant over changing supply voltage! Back then only a few parts of a tape deck were supplied with a stabilised voltage - the capstan motor, maybe the bias oscillator or sensitive preamps. The rest was simply powered off the batteries - mostly C or D cells (my marantz used three of the latter). So current drain dropped with dropping voltage.
Not so nowadays: our portable computers we call "decks" or "recorders" often use an elaborate array of high-efficiency switchmode converters to power the different subcircuits. The interesting part is that a DC/DC converter has the astonishing property to present the battery with a partially NEGATIVE input resistance! In simple terms: since the converter tries to keep the input power constant, current rises when voltage drops. I will give you an example:
Assume a recorder with four phantom powered mics, drawing about 3W of power overall. A good, modern, power supply of the switching type has an efficiency of 90%, so the battery has to deliver 3W/0.9 = 3.333W. Battery type is a Lithium polymer cell with 3.7V nominal, voltage goes from 4.2V (full) to 3.2V (empty). Now we can calculate current drawn from the cell:
4.2V: 0.79A
4.0V: 0.83A
3.8V: 0.88A
3.6V: 0.93A
3.4V: 0.98A
3.2V: 1.04A
Those numbers are also valid for the typical USB power bank.
Problem: the internal resistance of most electrochemical systems rises when they get discharged. There is a tipping point when the battery simply cannot sustain the ever rising current demand of the converter - the problem tonedeaf described.
My advice: keep backup batteries handy, use external power (power banks with as much capacity as possible), check your rechargeables often (there are chargers that can check capacity - since they discharge to a certain switchoff voltage, high internal resistance also shows as low capacity). Keep battery contacts clean, wipe with denatured alcohol: this keeps contact resistance and power loss down. If you record outdoors in cold climate: keep your rechargeables warm - put them in your pocket.
Greetings,
Rainer