second ibias circuit 22 ext where the current ibias ext is referenced to an external resistor the operation of the multiplication circuitry 18 can best be described mathematically by the following loop equation where v be3 is a voltage measured across the base to emitter of the transistor q 3 v be4 is a voltage measured across the base to emitter of the transistor q 4 v be5 is a voltage measured across the base to emitter of the transistor q 5 and v be6 is a voltage measured across the base to emitter of the transistor q 6 by replacing the base emitter voltages with the forward biased diode current equation the above loop equation becomes v t ln ue8a0 iptat int i s v t ln ue8a0 ibias int i s v t ln ue8a0 ibias ext i s v t ln ue8a0 iptat ext i s 0 after simplification the loop equation becomes ln ue8a0 iptat int ibias ext iptat ext ibias int 0 which further simplifies to iptat ext iptat int ibias ext ibias int in operation the multiplication circuitry 18 produces the current iptat ext defined as a current proportional to absolute temperature generated based on an external resistor more importantly the multiplication circuitry 18 generates the currents iptat ext and ibias ext referenced to only one external resistor thereby accurately producing these currents using a minimal number of external connections and minimizing the cost of manufacturing the circuit fig6 illustrates a practical implementation of the multiplication circuitry 18 wherein additional circuitry is used to bias the transistors q 3 q 4 q 5 and q 6 in this implementation biasing of transistors q 5 and q 06 is accomplished by diode connecting each of the transistors q 5 and q 6.