Amplifiers: Gain, Bandwidth and Clipping
What Does an Amplifier Do?
An amplifier is a circuit that increases the power of a signal. Almost every electronic system contains one: a microphone produces a tiny voltage that must be boosted before it can drive a loudspeaker. In your exam you will meet two main types — voltage amplifier and power amplifier. Voltage amplifiers deal with small signals; power amplifiers deliver the current needed to drive an output device.
Voltage Gain
The key number for any amplifier is its voltage gain. It tells you how many times larger the output voltage is compared with the input voltage.
Voltage gain is defined as:
$$G = \frac{V_{OUT}}{V_{IN}}$$
Gain has no units — it is a pure ratio. An amplifier with \(G = 50\) produces an output 50 times larger than its input.
If an amplifier receives an input of 20 mV and produces an output of 1 V, its voltage gain is:
$$G = \frac{1\text{ V}}{0.02\text{ V}} = 50$$
You can rearrange the equation to find any missing quantity. To find the output voltage: \(V_{OUT} = G \times V_{IN}\). To find the input voltage: \(V_{IN} = \frac{V_{OUT}}{G}\).
Bandwidth and the Gain–Frequency Graph
Real amplifiers do not work equally well at all frequencies. At very low and very high frequencies, the gain falls. A gain–frequency graph (also called a frequency response graph) shows this. The horizontal axis is frequency (often on a logarithmic scale) and the vertical axis is gain.
The useful range of frequencies over which the amplifier works effectively is called the bandwidth. The bandwidth is defined between the two frequencies at which the gain drops to 70% of its maximum value. These points are sometimes called the “half-power points” or “−3 dB points.”
Bandwidth is the range of frequencies between the lower and upper frequencies at which gain falls to 70% of the maximum gain. It is measured in hertz (Hz) or kilohertz (kHz).
For example, if an amplifier has a maximum gain of 100 and the gain is at or above 70 between 200 Hz and 20 kHz, then the bandwidth is \(20\,000 - 200 = 19\,800\) Hz, or approximately 19.8 kHz. Audio amplifiers need a bandwidth covering at least 20 Hz to 20 kHz to reproduce the full range of human hearing faithfully.
Amplifiers based on operational amplifiers have a fixed gain–bandwidth product. This means that if you increase the gain, the bandwidth automatically narrows, and vice versa. This trade-off is an important design constraint.
For example, if the gain–bandwidth product of an op-amp is 1 MHz:
• At a gain of 10, the bandwidth is 100 kHz.
• At a gain of 100, the bandwidth falls to 10 kHz.
• At a gain of 1000, the bandwidth is only 1 kHz.
This is why high-gain amplifiers are only used in applications that need a narrow band of frequencies, such as a single radio station. A general-purpose audio amplifier uses a lower gain to keep a wide enough bandwidth for all audio frequencies.
Signal Waveforms on a Voltage–Time Graph
An amplifier should reproduce the shape of its input signal, just with a larger amplitude. The most common waveforms you will see on a voltage–time graph are:
- Sine wave — a smooth, continuously varying curve. Pure tones and AC mains are sine waves.
- Square wave — alternates sharply between two voltage levels. Used in digital clocking circuits.
- Triangular wave — rises and falls linearly between two levels. Used in some oscillator and waveform generator circuits.
Clipping Distortion
Every amplifier is powered by a supply voltage — typically \(+V_{CC}\) and \(-V_{CC}\) for a dual-supply op-amp. The output cannot exceed these rails. When the mathematically correct output would be larger than the supply voltage, the top (or bottom) of the waveform is cut flat. This is called clipping.
On a voltage–time graph, clipping is easy to spot: a sine wave that should have curved peaks instead has flat tops and/or flat bottoms at the supply rail voltage. For example, an amplifier running from ±10 V supplies will clip any output that tries to go above +10 V or below −10 V. A common exam error is failing to spot this and drawing the output as a perfectly shaped but oversize sine wave — always check whether the output amplitude is within the supply rails.
An inverting amplifier has a gain of −20 and is powered from ±10 V supplies. The input is a sine wave with a peak amplitude of 0.8 V.
Step 1 — Calculate the expected output peak: \(V_{OUT,peak} = |G| \times V_{IN,peak} = 20 \times 0.8 = 16\) V.
Step 2 — Compare with supply rails: the output would need ±16 V, but the supply is only ±10 V.
Step 3 — Conclusion: the output is clipped. On the voltage–time graph, the sine wave peaks are flattened at +10 V and −10 V. The waveform resembles a square wave at the top and bottom, with the sinusoidal shape visible only in the middle portion where the output is within ±10 V.
How to prevent clipping: reduce the input amplitude, reduce the gain, or increase the supply voltage.
Clipping introduces distortion. For audio, this produces a harsh, buzzing sound because the flat tops of the clipped wave contain many high-frequency harmonic components not present in the original sine wave. The next lesson explores how op-amp circuits control gain precisely through feedback resistors.