Widlar current source

[8] The variable IB2 is the base current of the output transistor, VBE refers to base-emitter voltage.

To design the mirror, the output current must be related to the two resistor values R1 and R2.

A basic observation is that the output transistor is in active mode only so long as its collector-base voltage is non-zero.

This minimum useful value of VA is called the compliance voltage of the current source.

Assume the current source is biased so the collector-base voltage of the output transistor Q2 is zero.

3 Eq.1 provides: These three relations are a nonlinear, implicit determination for the currents that can be solved by iteration.

An important property of a current source is its small signal incremental output impedance, which should ideally be infinite.

The Widlar circuit introduces local current feedback for transistor

Output resistance is found using a small-signal model for the circuit, shown in Figure 2.

The current dependence of the resistances rπ and rO is discussed in the article hybrid-pi model.

From earlier in this article (setting the scale currents equal for convenience): Eq.

Figure 3 shows that the circuit output resistance RO is not determined so much by feedback as by the current dependence of the resistance rO of the output transistor (the output resistance in Figure 3 varies four orders of magnitude, while the feedback factor varies only by one order of magnitude).

The center panel in Figure 3 shows the design trade-off between emitter leg resistance and the output current: a lower output current requires a larger leg resistor, and hence a larger area for the design.

Diagram from Widlar's original patent
Figure 1: A version of the Widlar current source using bipolar transistors.
Figure 2: Small-signal circuit for finding output resistance of the Widlar source shown in Figure 1. A test current I x is applied at the output, and the output resistance is then R O = V x / I x .
Figure 3: Design trade-off between output resistance and output current.
Top panel: Circuit output resistance R O vs. DC output current I C2 using the design formula of Eq. 5 for R 2 ;
Center panel: Resistance R O2 in output transistor emitter leg;
Bottom panel: Feedback factor contributing to output resistance. Current in the reference transistor Q 1 is held constant, thereby fixing the compliance voltage. Plots assume I C1 = 10 mA, V A = 50 V, V CC = 5 V, I S = 10 fA, β 1, = 100 independently of current.