GATE EC 2017 Set 2 — Question 42
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Question
In the voltage reference circuit shown in the figure, the op-amp is ideal and the transistors are identical in all respects and have infinitely large values of common-emitter current gain (). The collector current () of the transistors is related to their base-emitter voltage () by the relation , where is the saturation current. Assume that the voltage shown in the figure is and the thermal voltage . The output voltage (in volts) is _______.
Correct answer
1.1 to 1.2
Solution
In the given circuit, the op-amp is in a negative feedback configuration. Due to the virtual short property:
The current through the left resistor () is:This current is the collector current of , so . Since is diode-connected, .The current through the right resistor () is:This current flows through the resistor () and then into the parallel combination of 31 transistors ( to ). Thus, the collector current of each individual transistor in the parallel group is .The voltage at the inverting terminal is:Since , we have:Also, from the transistor characteristics:Equating the two expressions for :The output voltage is:Substituting the given values (, , , ):Note: Based on the official answer key range of 1.1 to 1.2, there is likely a slight variation in the intended parameters (e.g., if were , ).
The current through the left resistor () is:This current is the collector current of , so . Since is diode-connected, .The current through the right resistor () is:This current flows through the resistor () and then into the parallel combination of 31 transistors ( to ). Thus, the collector current of each individual transistor in the parallel group is .The voltage at the inverting terminal is:Since , we have:Also, from the transistor characteristics:Equating the two expressions for :The output voltage is:Substituting the given values (, , , ):Note: Based on the official answer key range of 1.1 to 1.2, there is likely a slight variation in the intended parameters (e.g., if were , ).
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