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Desiging a battery charger

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The attached file shows the circuit in question along with information about the components (zener diode, op-amp, and BJT transistor).

Problem Statement:
The simple circuit shown below is a battery-charge circuit. It operates from a DC power supply having Vcc=22V. The fully charged NiCd battery pack exhibits Vb=12.08V. Operation starts when switch S1 is opened. After the battery is fully charged, switch S1 is closed. Define the appropriate values of R1, R2, and R3.

IMPORTANT NOTE: Disregard the verification process mentioned in the attachment (I can do this myself with PSPICE). I only need to be shown the method for achieving the resistor values.

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Solution Summary

Battery charge circuit is explained with necessary mathematical steps.

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4.00pm
<br>
<br>The output of the opamp comparator goes high when the voltage at + input is more than the voltage at the - input. We need a high output to switch on the npn transistor.
<br> Vin and the voltage across the zener diode serves as two voltage sources for comparison. If Vin is less than the voltage across zener, IC switches to a high output and as soon as the voltage across the battery reaches the value, 12.08V, the value of Vin goes above or equal to ...

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