gen-define-the-operational-amplifier-and-give-one-short-worked-e-c024

Define the operational amplifier and give one short worked example.

# Operational Amplifier (Op-Amp) ## Definition An **operational amplifier** is a high-gain voltage amplifier with differential inputs and a single-ended output. It has: - Very high input impedance (ideally infinite) - Very low output impedance (ideally zero) - Very high open-loop gain (typically 10⁵ to 10⁶) - Two inputs: inverting (-) and non-inverting (+) In ideal analysis, we assume: 1. No current flows into the input terminals 2. The voltage difference between inputs is zero when negative feedback is applied --- ## Worked Example: Inverting Amplifier **Problem:** Design an inverting amplifier with a gain of -5 using a 10 kΩ input resistor. If the input voltage is 0.5 V, what is the output voltage? **Solution:** For an inverting amplifier: $$V_{out} = -\frac{R_f}{R_{in}} \times V_{in}$$ Where: - Gain = -5, so $\frac{R_f}{R_{in}} = 5$ - $R_{in} = 10 \text{ kΩ}$ - Therefore: $R_f = 5 \times 10 = 50 \text{ kΩ}$ **Output voltage:** $$V_{out} = -5 \times 0.5 = -2.5 \text{ V}$$ The output is **-2.5 V** (inverted and amplified 5 times).