Hi I'm a bit confused.
the current source has a emitter resistor Re, If Rc limits the transistor current Rc~= Re,
why is Re required? If Re =1ohm and Rc = 10K, Rc dictates the current Ic.
thanks
If Rc dictates the current then it is not a "transistor current source" anymore. In this circuit you should always have beta*Ib<<Vcc/Rc so that the load current is controlled (i.e. limited) solely by the transistor collector current Ic=beta*Ib and does not depend on Rc.
The Re is not needed in principle here, but if Re=0 then your Ib current (and thus the Ic current Ic=beta*Ib) will vary exponentially with VB=VBE, which is not practical.
With Re, as calculated in the cited ref.
https://www.electronics-notes.com/articles/analogue_circuits/transistor/active-constant-current-source.phpwe have approximately
Ic=(Vb-0.6)/Re which is much more practical and, more important, does not depend on the beta of the transistor.
Compare this with another version where instead of Re you put a resistor Rb in series between the input and the base to control the base current. Then
Ib=(Vb-0.6)/Rb and
Ic= beta*(Vb-0.6)/Rb
so that Ic depends on beta. The role of the emitter resistor Re is to introduce a negative feedback making the final Ic/Vb gain roughly independent of the transistor parameters (look at the calculations: beta appears only in the factor beta/(beta+1) roughly equal to 1). This is the same principle as in the opamp circuits : the gain is determined by the feedback resistor network and to some extent is independent of the open-loop gain of the amplifier.