Needed a solar powersupply for an ESP8266-01. As the ESP8266-01 needs 3.3 Volt, a LiPo cell seemed a good choice for a battery. However, fully loaded these give 4.2 Volt, which is too much for the ESP8266. In order to get to 3.3Volt a Lowdrop (LDO) regulator is necessary.
As the ESP8266 does require a hefty current when it is transmitting, the regulator needs to give some 500mA.
Possibilities are the SPX3819 (500mA, dropvoltage 340mV, maxinput 20V) (found on the Lolin NodeMCU-ESP12E) and the AP2112 (600mA, dropvoltage 250mV, maxinput 6V) ( found on the Adafruit Huzzah). As the maxinput will be 4.2Volt, I have chosen the AP2112. The HT7333, that is recommended for e.g. the backside of the ESP8266-12 adapter plate has a drop voltage of 100mV. However, that is measured at 40mA and the datasheet gives no info on the dropvoltage at higher currents, so I would steer clear of that one for battery power.
Other possible options are the RT9013 (That is for instance found on the Wemos D1 mini) and the XC6203
The LiPo battery is being charged by a small TP4056 module. These have a maxinput of 8 Volt, hence a 6 Volt solarpanel will do nicely.
Capacity of the LiPo and the Solarpanel depend on the current needed. If you put the esp8266 to sleep in between transmission it can last long on a battery, especially if it is charged throughout the day.