Widlar Current Source - Finding The Current With Given Resistor Values

Finding The Current With Given Resistor Values

The inverse of the design problem is finding the current when the resistor values are known. An iterative method is described next. Assume the current source is biased so the collector-base voltage of the output transistor Q2 is zero. The current through R1 is the input or reference current given as,

Rearranging, IC1 is found as:

Eq. 2

The diode equation provides:

Eq. 3

Eq.1 provides:

These three relations are a nonlinear, implicit determination for the currents that can be solved by iteration.

  • We guess starting values for IC1 and IC2.
  • We find a value for VBE1:
  • We find a new value for IC1:
  • We find a new value for IC2:

This procedure is repeated to convergence, and is set up conveniently in a spreadsheet. One simply uses a macro to copy the new values into the spreadsheet cells holding the initial values to obtain the solution in short order.

Note that with the circuit as shown, if VCC changes, the output current will change. Hence, to keep the output current constant despite fluctuations in VCC, the circuit should be driven by a constant current source rather than using the resistor R1.

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