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, I_C1 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 I_C1 and I_C2.
• We find a value for V_BE1:

• We find a new value for I_C1:

• We find a new value for I_C2:

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 V_CC changes, the output current will change. Hence, to keep the output current constant despite fluctuations in V_CC, the circuit should be driven by a constant current source rather than using the resistor R₁.