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The resistor goes in between the output and the adjustment pin (the ground pin on fixed regulators). This resistor's value sets the current flow, as the regulator's internal circuitry will strive to maintain a constant voltage across it, which will in turn define a constant current flow through the resistor and the regulator. If we limit the scope of the three-pin regulator as a current source to setting up the cathode bias voltage for an output tube, then the lightweight voltage limits for these devices should not pose too large a problem. For example, the EL84 needs about a -15 volt bias in most amplifier circuits. An adjustable three-pin regulator such as the LM317 or a fixed regulator such as the LM7805 will work comfortably with this voltage limit. The LM317 is the better choice as it requires much less current through its adjustment pin than any fixed three-pin regulator requires for its ground pin, 50 ľA vs. 5 mA. (Avoid fixed low-dropout voltage regulators. These regulators can draw a huge amount of current through their ground pin as they near their dropout voltage, which would undermine their use as current sources, as the that extra current would flow through their output as well.)
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The LM317 strives to maintain a 1.25 volt difference between its output and its adjustment pin. This voltage and the value of resistor R are used to set the desired current flow through the current source. I = 1.25 / R + Iadj. R = 1.25 / (I - Iadj.) As the current through the adjustment pin is only 50 ľA, the formula can be simplified to I = 1.25 / R, R = 1.25 / I If a bias voltage more along the lines of 80 volts is needed, then the better choice is the TI783C. This three-pin regulator boasts a 125 voltage limit and 700 mA current limit. The formulas are slightly different from those of the LM317: I = 1.27 / R + Iadj. R = 1.27 / (I - Iadj.) As the current through this regulator's adjustment pin is still only 80 ľA, the formula can be also simplified to I = 1.27 / R, R = 1.27 / I The minimum current requirement is greater for this device than the LM317 (15 mA vs. 5 mA), which will probably limit its use to biasing power tubes. Still, the TI783C regulator qua (as) current source is perfect for setting up an auto-bias 300B amplifier.
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