NationMaster - Encyclopedia: Widlar current source

A Widlar current source is a current source attributed to the late Bob Widlar, in which an emitter degeneration resistor is only applied to Q₂ (designated as R2 in the schematic). This has the effect of turning off Q₂ relative to Q₁. The current source is commonly used to generate low currents. Analysis is as follows, Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... An ideal current source, I, driving a resistor, R, and creating a voltage V A current source is an electrical or electronic device that delivers or absorbs electric current. ... Robert J. Widlar (November, 1937-February 27, 1991) was a brilliant electronics pioneer who made his fame with Fairchild Semiconductor in the 1960s. ... Resistor symbols (non-European) Resistor symbols (Europe, IEC) Axial-lead resistors on tape. ...

Neglecting the base current of Q2, the output current $I C 2$ is also the current through R2. Hence,

$V B E 1 = V B E 2 + I C 2 R 2$ ... (1)

Since in general the base-emitter voltage is given by,

$V_{BE} = V_T lnleft(frac{I_C}{I_S}right)$ ... (2)

Rearranging (1),

$I C 2 R 2 = V B E 1 - V B E 2$ ... (3)

Substituting for $V B E$ from (2) into (3) we get,

$I_{C2}R2 = V_T lnleft(frac{I_{C1}}{I_{S}}right) - V_T lnleft(frac{I_{C2}}{I_{S}}right)$ ... (4)

$= V_Tleft[lnleft(frac{I_{C1}}{I_S}right) - lnleft(frac{I_{C2}}{I_S}right)right]$ ... (5)

So,

$I_{C2} = frac{V_T}{R2}lnleft(frac{I_{C1}}{I_{C2}}right)$ ... (6)

The current through R1 is the input or reference current given as,

$I R 1 = I C 1 + I B 1 + I B 2$ ... (7)

$= I_{C1} + frac{I_{C1}}{beta} + frac{I_{C2}}{beta}$ ... (8)

If $β$ is large, the last two terms of the above equation can be neglected. Hence,

$I_{R1} approx I_{C1}$

Thus assuming the forward base-emitter voltage of Q1 to be 0.7 V,

$I_{C1} approx I_{R1} = frac{V_{CC} - 0.7}{R1}$ ... (9)

Substituting (9) in (6) we get,

$I_{C2} = frac{V_T}{R2}lnleft(frac{I_{R1}}{I_{C2}}right) = frac{V_T}{R2}lnleft(frac{V_{CC} - 0.7}{I_{C2}R1}right)$ ... (10)

The above equation is the approximate solution for the output current $I C 2$ and is non-linear. An iterative process has to be employed to arrive at a value for R1 which gives a value of $I C 2$ which is reasonably close to that desired.

Knowing the desired values of $I C 1$ and $I C 2$ , R2 can be easily calculated.

Note that with the circuit as shown, if V_CC changes, the output current will change. Hence the circuit must be driven by a constant current source instead of R1 to keep the output current constant. An ideal current source, I, driving a resistor, R, and creating a voltage V A current source is an electrical or electronic device that delivers or absorbs electric current. ...

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 around transistor $Q 2$ . The loop gain is $G = (1 + g m 2 R 2)$ where $g m 2$ is the transconductance of $Q 2$ . The feedback loop magnifies the nominal output resistance $r o$ of the transistor by the factor $(1 + G)$ . Hence the Widlar is a better current source than the traditional current mirror.

Also note that the Widlar topology is not restricted to bipolar transistors and applies to MOS transistors and even vacuum tubes.

References

Widlar current source (PDF)

Category: Analog circuits An ideal current source, I, driving a resistor, R, and creating a voltage V A current source is an electrical or electronic device that delivers or absorbs electric current. ... A current mirror is a circuit designed to copy a current flowing through one active device by controlling the current in another active device of a circuit, keeping the output current constant regardless of loading. ... A Wilson current source is a circuit configuration designed to provide a constant current source or sink. ...

Results from FactBites:

Widlar current source - Wikipedia, the free encyclopedia (218 words)
	A Widlar current source is a current source attributed to the late Bob Widlar, in which an emitter degeneration resistor is only applied to Q
	The current source is commonly used to generate low currents.
	Hence the circuit must be driven by a constant current source instead of R1 to keep the output current constant.

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