Question

How do you analyze a simple inverting op-amp amplifier circuit?

Answer 1

Analyzing a simple inverting op-amp amplifier circuit involves understanding its basic principles and using the operational amplifier's ideal characteristics. An inverting op-amp amplifier amplifies an input voltage while inverting its polarity. Let's go through the steps to analyze such a circuit:

Circuit Diagram:

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           +Vin
            |
            R1
            |
     +------+------+
     |             |
     |             R2
     |             |
  +--|---o   o---|--+
  |  |   |   |   |  |
  |  +---|---|---+  |
  |      |   |      |
  |      +---+      |
  |                 |
  |      Op-Amp     |
  |                 |
  |                 |
  +-------o---------+
           |
          -Vout


Step 1: Identify the Components:

Op-Amp: The operational amplifier (Op-Amp) is the heart of the circuit. It is an active device with high gain and used for amplification.
R1: The input resistor connected to the non-inverting terminal (+Vin) of the op-amp.
R2: The feedback resistor connected from the output (-Vout) to the inverting terminal of the op-amp.

Step 2: Understand the Op-Amp Assumptions:
For the analysis, we assume that the op-amp operates in the ideal mode. The ideal op-amp has the following characteristics:

Infinite open-loop gain (A).
Infinite input impedance (Zin) at both terminals.
Zero output impedance (Zout).
No input offset voltage.
Infinite bandwidth.

Step 3: Analyze the Circuit:
To analyze the inverting op-amp amplifier circuit, you can follow these steps:

Apply the concept of the virtual ground: Due to the infinite open-loop gain of the op-amp, the voltage at the inverting terminal (-Vout) is virtually equal to the voltage at the non-inverting terminal (+Vin). Hence, we can assume the inverting terminal is at virtual ground (i.e., V(-) = 0 V).

Apply the voltage divider rule: The voltage at the inverting terminal is also the voltage across resistor R1. Hence, we can write:
V(+Vin) = V(R1) = Vin

Apply Ohm's law for the feedback loop: The current flowing through the feedback resistor (R2) is the same as the current flowing through the input resistor (R1) due to the virtual ground assumption. The voltage across R2 is V(-Vout). Hence, we can write:
V(-Vout) = -Vout = I(R2) * R2

Apply the inverting amplifier gain equation: The relationship between the input and output voltages for an inverting op-amp amplifier is given by:
Vout = - (R2 / R1) * Vin

Step 4: Calculate the Gain:
The voltage gain of the inverting amplifier is given by the ratio of feedback resistor (R2) to the input resistor (R1), with a negative sign, as the output is inverted.

Step 5: Example Calculation:
Let's say R1 = 10 kΩ and R2 = 20 kΩ. The gain of the amplifier would be:
Gain (Av) = - (R2 / R1) = - (20 kΩ / 10 kΩ) = -2

So, in this example, the gain of the inverting op-amp amplifier is -2, meaning the output voltage will be twice the magnitude of the input voltage, but with inverted polarity.