Measuring transistor beta (hFE) - Ib anomalies explanation needed
It is not clear why the experimenter expects \$I_B\$ to be constant in the face of changing transistors, including substitutions of Darlingtons for regular NPN's.

We can assume that the voltage source is ideal (valid: since these results are from a simulation), then the magnitude of \$I_C\$ does not disturb the voltage. (Indeed in the circuit on the right, we have the simulated transistor cheerfully passing 39000 Amperes, yet the source delivers!)

Even two different diodes will not pass exactly the same current if they are hooked up to the same voltage source and same resistor, because they have different curves.

In the case of a Darlington versus NPN base junction, we are looking at two diodes versus one. Plus, the Darlington may incorporate an internal bypass resistor.

The base current can be approximated using simple diode arithmetic: subtract the forward \$V_{BE}\$ drop from 5V, and divide that by the 100 ohm base resistance:


Regular NPN: \$(5 - 0.7)/100 = 0.043\$
Darlington: \$(5 - 1.4)/100 = 0.036\$.


If we use the exact \$V_{BE}\$ figures given in the diagram, we get the exact \$I_B\$ current values:


Regular NPN: \$(5 - 0.72945)/100 = 0.0427055\approx 0.0427\$
Darlington: \$(5 - 1.01)/100 = 0.0399\$.


The base current is simply that: application of Ohm's Law to the base resistor, subject to to voltage which remains when \$V_{BE}\$ is subtracted from 5V.

It is not a variation of base current with \$beta\$. That is to say, of course it varies with beta, but beta is perhaps not the relevant parameter to choose as an independent variable for understanding the variation.  \$beta\$ is a high level summary of the characteristics of a transistor, connected with the simplified model.

If you wish to hold \$I_B\$ absolutely constant, then you have to drive the base with a current source. (Your circuit simulation software surely has an ideal current source component that you can immediately plant into the circuit.)

Take the most sensitive transistor that you want to measure, and choose the base current so that this transistor is just barely saturated.  Less sensitive transistors will then derate the collector current from there. Include a collector resistor to protect the transistors, and as a basis for measuring current.