how to construct a PTAT current source using only the output voltage of the bandgap ? (can't use any of the internal nodes of the bandgap cell. Only it's output.)
1. Tie the reference voltage to the gate and a resistor at the source of the same transistor.
2. Use current mirror, mirror current flowing thru the transistor to where you need the current source.
My train of thought: With reference voltage, I can use that to regulate a drain current. Therefore fixing the drain current and using current mirror i can steer that to where i want.
Level shift your voltage reference output with a bipolar transistor. Then you get
V2=Vref-Vbe, which is a PTAT voltage. Apply this voltage across a resistor. You can have a PTAT current.
BTW: Pay attention to the temperature coefficient of the resistor.