What is the role of R4 in the constant current source circuit

A base stopper resistor is a series base resistor used to reduce or prevent ringing and/or oscillation.
The term is a colloquialism. You can call it a damping resistor in that it could reduce the Q of the ringing.

The need for such a resistor depends on the parts, construction, and circuit in which the current source is used.
You could breadboard the current source, and see how the base resistor's presence and value affects the output.
 
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A base stopper resistor is a series base resistor used to reduce or prevent ringing and/or oscillation.
The term is a colloquialism. You can call it a damping resistor in that it could reduce the Q of the ringing.

The need for such a resistor depends on the parts, construction, and circuit in which the current source is used.
You could breadboard the current source, and see how the base resistor's presence and value affects the output.
Thank you for your reply.
I built a circuit with a bread board for testing
 
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Q1 and Q2 are connected in a negative feedback loop, which like all NFB loops, might possibly oscillate. Resistor R4 works with the collector-to-base capacitance of Q1 to provide dominant pole (Miller) compensation, which stabilizes the loop and prevents oscillation. Often the feedback loop is perfectly stable even without R4, depending on device choices and bias levels. But designers include R4 anyway, as an inexpensive belt-and-suspenders safety measure.
 
Q1 and Q2 are connected in a negative feedback loop, which like all NFB loops, might possibly oscillate. Resistor R4 works with the collector-to-base capacitance of Q1 to provide dominant pole (Miller) compensation, which stabilizes the loop and prevents oscillation. Often the feedback loop is perfectly stable even without R4, depending on device choices and bias levels. But designers include R4 anyway, as an inexpensive belt-and-suspenders safety measure.
Very good explanation, thank you!
 
Follow-up question if the OP permits,
Does it also serve its purpose if it contributes to adjusting output dc offset?
At times when I couldn't make the dc offset set to an almost zero dc, I attached a small resistor at their bases.
 
Check out the pin compatible, vastly more stable, version made by Diodes Inc: the AS-431 . I used it in the Bon Homme Richard front end card for VFET/Theseus and had no problems at all. I like to believe the AS in the part number means Augmented Stability.

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