The circuit

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The peaking current source is shown in the schematic below:

Application

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The characteristics of this type of source is that even if ${\mathit{I}}_{\mathit{I}\mathit{N}}$ changes a lot ${\mathit{I}}_{\mathit{O}\mathit{U}\mathit{T}}$ changes very little. So it is useful to generate a constant current from a changing supply where ${\mathit{I}}_{\mathit{I}\mathit{N}}$ can be replaced by just a resistor.

Design

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If ${\mathit{I}}_{\mathit{I}\mathit{N}}$ changes then the change the change in the Vbe and the drop on the R should be equal and opposite. When that happens the current in the output transistor will remain constant since its Vbe won't change. If $\mathit{\Delta }{\mathit{I}}_{\mathit{I}\mathit{N}}\mathit{R}=\frac{\mathit{\Delta }{\mathit{I}}_{\mathit{I}\mathit{N}}}{{\mathit{g}}_{\mathit{m}}}$ then this condition will be fulfilled. Thus we have:

Since ${\mathit{I}}_{\mathit{I}\mathit{N}}$ changes there will be just 1 point in the whole ${\mathit{I}}_{\mathit{I}\mathit{N}}$ range where the above relation holds and that is the point where the ${\mathit{I}}_{\mathit{O}\mathit{U}\mathit{T}}$ curve is flat, it tapers lower on either sides.
A simulation with R=259 ohms causing the peak to be at 100uA is shown below:

Extensions

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The output transistor can be degenerated with a resistor like a Widlar Source to make the output current curve more flat as well.