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Desiging a battery charger

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.

Attachments

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4.00pm
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<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 ...

Solution Summary

Battery charge circuit is explained with necessary mathematical steps.

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