The output current flowing across the collector of Q1 and positive supply terminal, is very close to emitter current:
where β is the current gain of Q1. The V-I characteristic of the converter is drawn in Fig. 2.
For the 2N3904 transistor, β ≈ 230; thus the collector current is about 0.44% lower than its emitter current. To lower this error, you could use a Darlington pair, or a cascade of two bipolar transistors, in place of Q1. The input voltage, V IN, can be derived either from potentiometer P1 or an external source.
If you choose, for example V DB = 0.1×V REF, V DB = V ED you get from Equation 1 that R D = 9R E. A theoretical dependence of output current on input voltage is depicted in Fig. 2.
Experimentally, V REF = 0.19645V and full-scale emitter voltage VED = 0.19660V have been measured. The V DB has been determined by detecting an abrupt change at the output of IC2a of either zero-to-positive, or positive-to-zero voltage transitions, and by measuring the VIN value