DC Single Supply to DC Dual Supply Conversion

There are several method to do. One is to use oscillator (that uses a transformer) to convert DC into AC then this AC is fed to a centertapped transformer. So when we'll be having another center tapped transformer we can use bridge rectifier and capacitors to take the Dual output.

There is also another method using a Timer IC that is 555 timer.
Circuit diagram taken from datasheet is given below also available on google.

The first method can provide lot of more power while the second arrangement is for low power applications. Also the voltage is limited to 15v. But at least 15v is enough to power op-amps and several other applications.

Now generating -ve voltage can also be done using any operational amplifier with some specifications like a TDA2030 which is dual voltage operated Integrated Chip used for the HIFI audio amplification. Given below is the circuit for TDA2030 dual voltage supply from single voltage source.

The pin 1 is the non-inverting input and so, when we see the feedback (shown by a green trace) between pin 2 & 4 we can easily recognize that it is in the voltage follower mode. The resistors 2.2k are used to keep the same voltage on the GND (from input) or -Vout. So, the voltage follower in this case turns the level of the output pin 4 as 0 which become refernce node for output GND.

Given below is the pinout configuration of TDA2030. 

The other amp ic's can be used for this purpose. But again this method is for the low power amplification the output of the input voltage will never be the same in this case but it will be divided as there is a voltage divider section in the circuit shown above.

The Vout=Vin/2 like if the input voltage was 9v then output will be 4.5v dual.

All of the above circuits are efficient and they do work and tested practically by me. Because i believe that everything a human design doesn't mean that it will always work.