But there is a catch, that I first heard of from Bob Pease: the higher the beta, the lower the output impedance. It can be seen in this datasheet: the 547A has 55.5k typical output impedance, the 547B 33.3k, and the 547C 16.6k, and it could go as low as 9k!. This can be very important when building current sources/sinks, active loads, etc.
Only relevant to pure current mirrors without degeneration.
Tim
Sorry for going a bit off topic, but honestly, I'm confused beacuse this beta thing has been bothering me for a time. Do you mean that there is a workaround for low rout, or that it's not relevant for current sinks and active loads? I've gone back to basics to see if I got this wrong, redoing example 2 here:
http://leachlegacy.ece.gatech.edu/ece3050/notes/ISources/isources.pdf [There is an errata in the exercise: they changed m for n]. I attach the python code I used:
beta = 100.0 # Current gain.
Va = 75.0 # Early voltage.
Vbe = 0.65 # Base-emitter voltage.
Vce = 8.00 # Collector-emitter voltage.
rx = 40.0 # Base spreading resistance.
Ic = 1.5e-3 # Collector current.
Vcc = 15.0 # High rail.
Vdd = -15.0 # Low rail.
n = 2.0 # Emitter resistor Vbe multiplier.
m = 10.0 # Stiff current multiplier at the base.
Vt = 300.0*1.3806e-23/1.6022e-19 # Thermal voltage.
alpha = beta/(1+beta)
Re = (beta*n*Vbe)/((1+beta)*Ic)
R1 = beta*(Vcc-Vdd-(n+1)*Vbe)/((m+1)*Ic)
R2 = (beta*(n+1)*Vbe)/(m*Ic)
r0 = (Va + Vce)/Ic
rep = (R1*R2/(R1+R2) + rx)/(1+beta) + alpha*Vt/Ic
rout = (r0 + rep*Re/(rep+Re))/(1.0 - (alpha*Re)/((rep+Re)))
print "beta ", beta
print "va ", Va
print "Vt ", Vt
print "Re ", Re
print "R1 ", R1
print "R2 ", R2
print "r0 ", r0
print "rep ", rep
print "Output resistance: ", rout
For the same circuit, if beta=100, Va=75, the resistance of the sink is 379k, in agreement with the exercise. Now take beta=200, Va=75/2=37.5. The resistance drops to 215k. Even if beta=400, Va=37.5, the resistance is still 218k. Beta does not compensate for Va drop. If we go to the extreme, beta=600, Va=12.5, resistance drops to 100k. At least we can say that high beta parts underperform in this role. Isn't it just the same with a common emitter with active load: will a piece with 15k-9k output impedance give the same gain than a piece with 50k?
Found Pease's article warning about high beta:
http://www.electronicdesign.com/power/whats-all-vsubbesub-stuff-anyhow-part-2 .
Edit: Aha, I found it! What was spoiling the resistance of the current source was not the Va, but the choice of resistors R1 and R2. For high beta you need a much stiffer current at the base divider, m=100 or so. I think I'll need to think this over, much deeper.

Thanks!