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• Op-Amp: Consider using a dual op-amp package, like the LM358, since we'll need two op-amps.
• Resistors: To set the reference voltages for the high and low thresholds.
• Voltage Source: To provide the input voltage to be compared.
• Potentiometers: (optional) to adjust the reference voltage thresholds.

1. Op-Amp A (Low Threshold Comparator):
   • Connect the non-inverting input $+\text{Input1}$ of the first op-amp to the reference voltage for the low threshold.
   • Connect the inverting input $-\text{Input1}$ of the first op-amp to the input voltage.
   • The output will be high when the input voltage is below the low threshold.
2. Op-Amp B (High Threshold Comparator):
   • Connect the inverting input $-\text{Input2}$ of the second op-amp to the reference voltage for the high threshold.
   • Connect the non-inverting input $+\text{Input2}$ of the second op-amp to the same input voltage as above.
   • The output will be high when the input voltage is above the high threshold.
3. Combine Outputs:
   • Connect the outputs of the two op-amps to create a logic "window."
   • The window is "open" (i.e., both outputs are low) when the input voltage is between the thresholds; otherwise, it is "closed" (at least one output is high).

Plaintext
                 +V
                  |
                  |
      +-----------+-----------+
      |           |           |
+-----+-----+     |     +-----+-----+
| Op-Amp A  |     |     | Op-Amp B  |
| (-) (+)   |     |     | (+) (-)   |
|     \     |     |     |     \     |
|     /     |     |     |     /     |
|     |     +-----+-----+     |     |
+-----+-----------------------+-----+
      |                       |
      |                       |
      +-----------+-----------+
                  |
                  V

• Use a voltage divider to set the low and high thresholds with precision.
• If no reference voltages are specified, choose typical values like $1/3 , V_{cc}$ for low and $2/3 , V_{cc}$ for high, assuming a single supply op-amp.
• Ensure your op-amp is powered appropriately and is compatible with the voltage levels you are using.

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• Voltage Comparator IC: Like the LM393 or LM311.
• Voltage Reference: Zener diode for a fixed 12V reference, or a voltage divider for a custom reference.
• Relay or MOSFET: To switch between battery power and DC power.
• Resistors: For voltage divider and pull-down/up as needed.
• Battery: Already part of your design as BATT1.
• DC Power Input: Assuming an external DC adapter or input.

1. Voltage Comparator Configuration:
   • Connect the reference voltage (12V) to the inverting input of the comparator.
   • Use a voltage divider to scale down the DC power input voltage, then connect it to the non-inverting input.
2. Output Control:
   • The comparator output will drive a relay or a MOSFET.
   • When the input voltage is below 12V, the comparator output is low, energizing the relay to connect the battery to the circuit.
   • When the input voltage is above 12V, the comparator output is high, de-energizing the relay, thus disconnecting the battery and connecting the DC power.

• Power Supply Voltage Divider:
  • Connect one end of the divider to the DC input, the midpoint to the non-inverting input of the comparator, and the other end to GND.
• Comparator Output:
  • Connect this to the base or gate of the relay control transistor or MOSFET gate.
• Relay Connections:
  • Connect the common terminal to the circuit input.
  • Connect the normally closed (NC) terminal to the battery positive.
  • Connect the normally open (NO) terminal to the DC input.

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• Continuous Drain Current ($I_D$): The rating should be comfortably above 3A.
• Drain-Source Voltage ($V_{DS}$): Ensure this is higher than the maximum voltage the MOSFET will encounter in your circuit.
• On-Resistance ($R_{DS(on)}$): Lower values imply less power loss and heating.
• Gate-Source Threshold Voltage ($V_{GS(th)}$): Ensure compatibility with your control voltage levels.
• Package Type: Depending on whether you'll use it in a breadboard or PCB.

• $I_D$ = 47A (plenty of headroom)
• $V_{DS}$ = 55V
• $R_{DS(on)}$ ≈ 25mΩ
• Suitable for logic level gate drive

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1. Tie together: Connect the inverting input (-) to the output. This will form a unity-gain buffer.
2. Non-inverting input: Connect the non-inverting input (+) to a reference voltage, usually the ground (0V).

• Connect OpAmp:InvertingInput to OpAmp:Output.
• Connect OpAmp:NonInvertingInput to GND.