Objective: Design a Widlar current source to achieve specified reference and load currents. Specifications: The circuitto be designed hasthe configuration shown inFigure 10.9. Assume bias voltages of V^+ = +5 V and V^− = −5 V. Assume VB E1 = 0.7 V. Design the circuit such that IREF = 1 mA and IO =

Question

Objective: Design a Widlar current source to achieve specified reference and load currents.

Specifications: The circuitto be designed hasthe configuration shown inFigure 10.9. Assume bias voltages of [latex]V^{+} = +5 V, V^{−} = −5 V[/latex]. Assume [latex]V_{B E1} = 0.7 V[/latex]. Design the circuit such that [latex]I_{REF} = 1 mA[/latex] and [latex]I_{O} = 12 µA.[/latex]
Choices: Assume that matched transistors are available and that base currents can be neglected. Also assume that IC resistors of any value can be fabricated.

Accepted Answer

Resistance [latex]R_{1}[/latex] is
[latex]R_{1} = \frac{V^{+} − V_{B E1} − V^{−}}{I_{REF}} = \frac{5 − 0.7 − (−5)}{1} = 9.3 k \Omega[/latex]
Resistance [latex]R_{E}[/latex] is, from Equation (10.30),
[latex]R_{E} = \frac{V_{T}}{I_{O}} \ln \left( \frac{I_{REF}}{I_{O}} \right) = \frac{0.026}{0.012} \ln \left( \frac{1}{0.012} \right) = 9.58 k \Omega[/latex]
From Equation (10.29), we can determine the difference between the two B–E voltages, as follows:

[latex]V_{B E1} − V_{B E2} = I_{O} R_{E} = (12 × 10^{−6})(9.58 × 10^{3}) = 0.115 V[/latex]
Trade-offs: A slight variation in [latex]V_{B E1}[/latex] and slight tolerance variations in resistor values will change the current values slightly. These effects are evaluated in end-ofchapter problems.
Comment: A difference of 115 mV in the B–E voltages of [latex]Q_{1}[/latex] and [latex]Q_{2}[/latex] produces approximately two orders of magnitude difference between the reference and load currents. Therefore, we can produce a very low bias current using resistors in the low kilohm range. These resistors can easily be fabricated in an IC. Including the resistor [latex]R_{E}[/latex] gives the designer additional versatility in adjusting the load to reference current ratio.

Question 10.4: Objective: Design a Widlar current source to achieve specifi...

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