You got this all wrong my friend. First of all, 12vdc is the nominal voltage, meaning average power required. A 12vdc Battery does not output 12vdc, it can output 14.5 VDC fully charged for example (depending on the battery type, it can go as high as 16.5 VDC) and the voltage drops during discharge. Once the external power drops below 10vdc, the Pocket camera gives a low voltage warning, and shuts down when the battery can not linger provide the minimum power requirements. Leaving a battery in the camera whilst the external power is applied, the camera will take part of that power input to charge up, and maintain the internal battery charge. So leaving a battery in the camera will reduce the run time of the external battery.
BMD says the voltage requirements are:
Our recommended input levels are as follows:
Internal battery connection - 6.2V to 10VDC max
DC input - 10.8Vto 20VDC maxGo below these requirements and the camera will shut down. Exceed these requirements and component damage may result. But these are the voltage requirements for the camera’s DC-DC power supply, which in turns converts the voltage to what the camera requires, different, as internal components run at different voltages, anywhere from 3.2 VDC to 6 VDC for example (not actual requirements). USB power used to supply around 5 vdc, while the newer USB ports (post 2007) can supply up to 12 VDC, which is what the new iPhones run on. But this does not mean the device runs on 5 or 12 VDC, only that it’s power supply requires this nominal voltage to run properly.
The actual voltage requirements inside the Pocket 4K, or any camera, is not s simple single voltage, the camera’s DC-DC power supply takes the input voltage and converts it to what each component needs. The camera is a mini computer, which has one or more circuit power requirements, the LCD screen a different voltage, whilst the cooling system may need a different voltage yet. You are correct, that each time a voltage source is converted up (has more loss) or down, there is power loss cure to the conversion. But their is no single “magical” voltage level you could feed the camera to reduce this conversion process, any power applied to either the external or internal battery requires conversion to the varied voltage levels required internally.
Will a BMD Camera run on less voltage? Sometimes, but it is not a good practice to do so. I would use BMD’s recommendations and not try to second guess what the camera actually needs. I would suggest you re-read Dmitry’s and the BMD responses posted in this discussion.
Cheers