What an amplifier does
A signal is a voltage that changes with time and carries information, like sound or a radio message. Many signals are very weak. An amplifier takes a weak signal and makes a stronger copy of it.
The extra power does not appear from nothing. The amplifier takes it from a power supply (a battery or adapter) and uses the input signal to control how much of it reaches the output.
The main part inside is usually a transistor (a small switch-like part that a tiny current can control) or a chip full of transistors.
Gain and decibels
Voltage gain tells us how many times bigger the output is: Av = Vout / Vin. It has no unit because it is a ratio.
Engineers often use decibels (dB): gain in dB = 20 × log10(Vout / Vin). A gain of 10 is 20 dB. A gain of 100 is 40 dB. A gain of 1000 is 60 dB. Every extra 20 dB is 10 times more gain.
When two amplifier stages are joined one after another, the gains multiply, but the decibel values simply add.
Power gain = Pout / Pin, and in dB it is 10 × log10(Pout / Pin).
Low-frequency (audio) amplifiers
Low-frequency amplifiers work on signals from a few hertz up to about 20 kHz, the range of human hearing. You find them in music players, radios, public address systems and the last stage of a TV.
- Biasing: a small steady voltage keeps the transistor ready (partly on) so it can follow the signal both up and down.
- Coupling capacitor: it lets the changing signal pass from one stage to the next but blocks the steady bias voltage. This is why gain drops at very low frequencies.
- Voltage stage then power stage: first stages make the voltage bigger; the last stage (the power amplifier) supplies enough current to move a speaker.
- Push-pull: two transistors share the job; one pushes the positive half of the wave and the other pulls the negative half. This wastes less heat than one transistor working all the time (class A).
Frequency response and bandwidth
An amplifier does not give the same gain at every frequency. A graph of gain against frequency is its frequency response. It rises in the middle and falls at both ends.
The two points where the gain has dropped to about 70% (0.707) of the middle value, which is 3 dB down, are the cut-off frequencies. The gap between them is the bandwidth: BW = fhigh − flow.
The low end falls because of coupling capacitors. The high end falls because of tiny stray capacitances inside the transistor and wiring, which leak the fast wiggles away.
High-frequency (radio) amplifiers
High-frequency amplifiers work on radio signals from hundreds of kilohertz to many gigahertz. They need parts that stay fast and wiring kept very short, because stray capacitance matters more at high speed.
- RF amplifier: sits right after the aerial and boosts a very weak station without adding much noise.
- IF amplifier: in a radio receiver, boosts the signal after it has been shifted to a fixed middle frequency.
- Tuned amplifier: uses a coil and capacitor (an LC circuit) so it only boosts a narrow band of frequencies around one station and ignores the rest.
- Power amplifier: in a transmitter, gives the big power needed for the aerial.
For a wide-band amplifier, the gain × bandwidth is roughly fixed: if you ask for more gain, you get less bandwidth.
Limits: clipping, noise and distortion
The output can never go above the supply voltage. If the input is too big or the gain too high, the tops of the wave are cut flat. This is clipping, a kind of distortion. It adds new, unwanted sounds.
Noise is a random hiss added by the parts. An amplifier boosts noise too, so the first stage must be low-noise.
Negative feedback (sending a little of the output back to reduce the input) lowers gain but makes it steadier and cleaner.
Try it
In the 3D scene, set gain to 12 and look at the output. Count how many volts it should be (0.5 V × 12 = 6 V). The supply limit is 3.5 V, so it clips. Now lower the gain until the clipping stops. At home, plug earphones into a phone and play music very loudly: the harsh buzz you may hear is clipping in the phone's amplifier.
Key formulas and definitions
- Voltage gain Av = Vout / Vin
- Gain in dB = 20 log10(Vout / Vin)
- Power gain in dB = 10 log10(Pout / Pin)
- Cascaded stages: Av = Av1 × Av2; dB = dB1 + dB2
- Bandwidth BW = f(high) − f(low)
- Largest output ≈ supply voltage (beyond it, clipping)
Worked examples
1. An amplifier turns a 20 mV input into a 1 V output. Find the voltage gain.
Convert 20 mV = 0.02 V. Av = 1 / 0.02 = 50.
2. Find the gain of 50 in decibels.
dB = 20 log10(50) = 20 × 1.699 ≈ 34 dB.
3. A microphone gives 5 mV. A two-stage amplifier has stage gains of 20 and 40. What is the output?
Total gain = 20 × 40 = 800. Output = 5 mV × 800 = 4000 mV = 4 V.
4. Stage 1 has 20 dB gain and stage 2 has 26 dB gain. What is the total gain in dB and as a ratio?
dB add: 20 + 26 = 46 dB. Ratio: 20 dB is 10 times and 26 dB is about 20 times, so total is about 200.
5. A tuned radio amplifier has cut-off frequencies of 455 kHz and 465 kHz. What is its bandwidth?
BW = 465 − 455 = 10 kHz.
6. An amplifier with gain 30 and a ±9 V supply gets a 0.5 V peak input. Sketch what happens to the output peaks.
Ideal output peak = 0.5 × 30 = 15 V. The supply limit is about 9 V, so the wave is clipped flat at 9 V (both tops and bottoms). It is distorted.
7. A speaker amplifier takes 0.2 W in and gives 20 W out. Find the power gain in dB.
Ratio = 20 / 0.2 = 100. dB = 10 log10(100) = 20 dB.
Common mistakes
- Thinking the amplifier makes energy. It only uses the supply's energy, shaped by the input.
- Adding gains when stages are joined. Ratios multiply; only decibels add.
- Using 10 log instead of 20 log for voltage gain. Use 20 log for voltage and 10 log for power.
- Forgetting units: 20 mV must be changed to 0.02 V before dividing.