Question 10.4: Objective: Design a Widlar current source to achieve specifi...
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, V^{−} = −5 V. Assume V_{B E1} = 0.7 V. Design the circuit such that I_{REF} = 1 mA and I_{O} = 12 µA.
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.
Resistance R_{1} is
R_{1} = \frac{V^{+} − V_{B E1} − V^{−}}{I_{REF}} = \frac{5 − 0.7 − (−5)}{1} = 9.3 k \Omega
Resistance R_{E} is, from Equation (10.30),
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
From Equation (10.29), we can determine the difference between the two B–E voltages, as follows:
V_{B E1} − V_{B E2} = I_{O} R_{E} = (12 × 10^{−6})(9.58 × 10^{3}) = 0.115 V
Trade-offs: A slight variation in V_{B E1} 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 Q_{1} and Q_{2} 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 R_{E} gives the designer additional versatility in adjusting the load to reference current ratio.