I have made a remote arduino two weeks ago:An Pro Mini with ATmega328P at 8MHz, the voltage regulator removed. That should run at 2.5V to 5.5V.An DHT22 which needs at least 3.3V.An cheap 433MHz transmitter of 3V to 12V, but at 3V it has almost no power.Using the VirtualWire, and Narcoleptic libraries.With three NiMH AAA batteries.I did a test with 3.0V and it was still working well. My DHT22 failed 1 in 10 times, but then I just don't transmit the data.Everything depends on your Bluetooth module.The ATmega328P can do 2.5 to 5.5V at 8MHz.
When the ATmega328P is used with low voltages, the clock speed must be low. An 8MHz ATmega328P is still compatible with one of the official supported Arduino boards, but with lower clock speeds you have to make your own bootloader and add you own board definition.The specifications for the HM-11 are not always the same. Some say 2.5 to 3.7V. Some modules have a voltage regulator on board so the module will work at 5V as well.A Li-ion battery is 3.0 to 4.2V.I think you need some kind of buck-boost converter. For example this one : https://www.sparkfun.com/products/11231
I am working on a project which has atmega328p and HM-11 Bluetooth module. Bluetooth module requires 3.3 volts and likewise atmega328p also requires constant voltage for proper functioning, am I right ?
Umm, exactly no!These are digital devices - they deal in binary values - HIGH or LOW, but as long as these are adequately distinguished, the exact voltage level is not critical.The Bluetooth module does not want to see too much voltage, but can tolerate a reasonably lesser voltage. You need the ATmega328 to be clocked at 8 MHz to operate at these low voltages.Just use a single lithium cell which holds a very steady voltage by itself - much more practical than alkaline dry cells. This is how mobile phones operate, and the electronics is designed around them. They do not use buck-boost converters! If the Bluetooth module is absolutely not specified to tolerate 4V in standby, then you may have to remove the Li-po battery to charge it.
What is the relationship between charging and 4 volts input to Bluetooth module?