Basic gain calculation: If a 2 mV input signal results in a 2 V output from an amplifier, what is the voltage gain A_v (ratio of output voltage to input voltage)?

Introduction:
Voltage gain is fundamental in amplifier analysis. It is defined as the ratio of output voltage to input voltage and is often expressed as a pure ratio or in decibels. Quick mental math on small signals and unit conversions is a practical skill when reviewing specifications or debugging circuits.

Given Data / Assumptions:

• V_in = 2 mV.
• V_out = 2 V.
• Linear operation (no clipping or compression).

Concept / Approach:
Compute A_v = V_out / V_in, taking care to convert millivolts to volts to avoid errors. Because 1 mV = 10^-3 V, 2 mV = 0.002 V. The ratio then becomes straightforward division.

Step-by-Step Solution:

Verification / Alternative check:
Cross-check by proportional reasoning: increasing input by a factor of 1000 (2 mV * 1000 = 2 V) matches the output, confirming the gain.

Why Other Options Are Wrong:

• 0.001 and 0.004: These invert the ratio or mix units incorrectly.
• 100: Underestimates the true ratio by a factor of 10.

Common Pitfalls:
Forgetting unit conversion (mV to V), or accidentally calculating V_in / V_out. Always normalize units first to avoid magnitude errors.

Final Answer:
1000