Amplifier Voltage Gain: Calculation & Formula

Instructor: Gerald Lemay

Gerald has taught engineering, math and science and has a doctorate in electrical engineering.

In this lesson we describe a voltage amplifier and one of the common specifications for voltage amplifiers. In particular, examples will use a formula for calculating the voltage gain.

A Box

Let's say we have a box. But it's not an ordinary box. This box has two openings. One of the openings lets us input a signal, Vi. The other opening allows the signal to leave the box. This output signal is labeled Vo.

A box with two openings

Think of it this way:

  • a signal, Vi goes into the box
  • something happens to this signal while it is in the box
  • a signal, Vo, leaves the box

The box could be lots of different things. To name just a few of the possibilities, it could be a filter, a differentiator, a delay or an integrator. The box could also be an amplifier. In this lesson we explore the voltage amplifier and we discuss a way to relate the output signal to the input signal.

The Voltage Amplifier

The word ''amplify'' means to make bigger. An amplified sound is louder. You can think of a voltage amplifier as a box. You put a voltage, Vi, into the box. Out of the box comes a voltage, Vo. The voltage, Vo is bigger than Vi.

Let's say Vo is 3 times Vi. Then,


This ratio of output to input for an amplifier is called the gain. But what do we mean by '' Vo is 3 times Vi''? To answer this question we will use an example.


If we have a way to measure Vo and Vi, then we can say something quantitative about the amplifier. A voltmeter is an instrument for measuring voltage. We could connect a voltmeter across a battery. The display on the voltmeter tells us the number of volts for the battery. We can use the voltmeter to measure the voltage at the input and at the output of our amplifier.

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