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Consider the circuit with an ideal OPAMP shown in the figure ...


Ideal OPAMP Problem Solution

Consider the circuit with an ideal OPAMP shown in the figure.

Assuming |VIN| << |VCC| and |VREF| << |VCC|, determine the condition at which VOUT = 0.

Options:

  1. VIN = VREF
  2. VIN = 0.5 VREF
  3. VIN = 2 VREF
  4. VIN = 2 + VREF

Solution

Step 1: Identify the Op-Amp Configuration

The non-inverting terminal (+) is connected to ground. Therefore,

V+ = 0 V

Since the op-amp is ideal and operates with negative feedback, the inverting terminal is also at virtual ground.

V- = V+ = 0 V

Step 2: Apply KCL at the Inverting Node

Three currents meet at the inverting input:

  • Current from VIN
  • Current from VREF
  • Feedback current through RF

Current due to VIN

I1 = (VIN - 0)/R = VIN/R

Current due to VREF

Observe the polarity of the VREF source. Its positive terminal is connected to ground. Hence the resistor is connected to a voltage of -VREF.

I2 = (-VREF - 0)/R = - VREF/R

Feedback current

IF = (0 - VOUT)/RF = - VOUT/RF

Step 3: Apply Kirchhoff's Current Law

I1 + I2 + IF = 0
Substituting the current expressions,
VIN/R − VREF/R − VOUT/RF = 0
Rearranging,
VOUT = − (RF/R) (VIN − VREF)

Step 4: Condition for Zero Output

For
VOUT = 0
we obtain
VIN − VREF = 0
Therefore,
VIN = VREF
Correct Option: (A) VIN = VREF
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