Modulation systems
Modulating means writing information onto a carrier by changing one of its three parameters: amplitude, frequency or phase. That choice determines the bandwidth occupied, the noise resistance and the complexity of the equipment.
01Three parameters, three families
A sinusoidal carrier is written v = A·sin(2πft + φ). There are exactly three things that can be modified in it, and every modulation that exists comes from them.
The carrier envelope follows the signal. Simple to generate and to detect; noise adds directly to the information.
The carrier is squeezed and stretched. The amplitude is constant, so amplitude noise can be clipped off: much better quality, at the cost of more bandwidth.
The carrier is advanced or delayed. It is a close relative of FM —one is the derivative of the other— and it is the basis of all modern digital modulations.
02Amplitude modulation
A 100 W carrier modulated at 80 % by a 5 kHz tone:
- Bandwidth: 2 × 5 kHz = 10 kHz, split into two sidebands around the carrier.
- Total power: P = Pc(1 + m²/2) = 100 × (1 + 0.32) = 132 W.
- Of those 132 W, the information travels only in the sidebands: 32 W. 76 % of the power is spent on the carrier, which carries no information.
- Even with m = 1, the maximum without distortion, the sidebands take barely 33 %.
That inefficiency is the big problem of AM, and what gave rise to its variants.
| Variant | What it transmits | BW | Where it is used |
|---|---|---|---|
| Full AM | Carrier + 2 sidebands | 2 fm | Broadcasting: a very cheap receiver, with a single detector diode. |
| DSB-SC | Only the 2 sidebands | 2 fm | Saves the carrier power, but requires coherent detection. This is what a product modulator does. |
| SSB | A single sideband | fm | Amateur radio, marine, HF aviation: half the bandwidth and all the power useful. |
| VSB | One sideband and a remnant of the other | Intermediate | Analog television: a compromise between saving bandwidth and receiver simplicity. |
With m > 1 the envelope tries to go negative and the carrier inverts: the envelope detector recovers a distorted signal, and the spectrum spreads far beyond the assigned channel, interfering with its neighbors. That is why every AM transmitter has a limiter that prevents going past m = 1, and why in practice the working point is around 0.8.
03Frequency modulation
Broadcast FM (wideband): deviation Δf = 75 kHz, audio up to fm = 15 kHz.
- β = 75/15 = 5.
- BW = 2 × (75 + 15) = 180 kHz. That is why FM channels are spaced 200 kHz apart.
Narrowband FM (handheld radios and utility services): Δf = 5 kHz, voice up to 3 kHz.
- β = 5/3 = 1.67.
- BW = 2 × (5 + 3) = 16 kHz: it fits in a 25 kHz channel with margin.
More deviation gives a better signal-to-noise ratio and poorer use of the spectrum. That is the central trade-off of FM.
- Atmospheric and industrial noise mostly affect the amplitude. Since in FM the amplitude carries no information, the receiver clips it with a limiter and the noise goes away.
- There is also the capture effect: given two signals on the same frequency, the receiver keeps the stronger one and the other disappears. In AM you would hear both superimposed.
- And pre-emphasis and de-emphasis are used: the highs are boosted when transmitting and attenuated when receiving, so the high-frequency noise drops even further.
04Comparison
| AM | FM | SSB | |
|---|---|---|---|
| Bandwidth | 2 fm | 2(Δf + fm) | fm |
| Power efficiency | Low (≤ 33 %) | High: constant amplitude | Highest |
| Noise immunity | Poor | Very good | Medium |
| Receiver complexity | Minimal | Medium | High: the carrier has to be reinserted |
| Range at low power | Medium | Medium | The best |
| Used in | AM broadcasting, aviation | FM broadcasting, handheld radios, TV audio | HF: amateur radio, marine |
Precisely because of what in broadcasting is a defect: in AM, if two aircraft transmit at the same time, the controller hears both signals superimposed and knows there was a collision of transmissions. With FM, the capture effect would make one disappear completely and nobody would notice. In aviation safety, that is decisive.
05Digital modulations at a glance
These are the same three families applied to a signal that takes only discrete values. They are covered in Year 7; here it is enough to recognize them.
| Acronym | What varies | Everyday example |
|---|---|---|
| ASK / OOK | Amplitude: the carrier is either present or not | Gate remote controls, 433 MHz sensors. The telegraph and Morse code are its direct ancestors. |
| FSK | Two frequencies, one per symbol | Old modems, radio beacons, LoRa (with a chirp variant) |
| PSK | The phase jumps between fixed values | Satellite communications, WiFi in its robust modes |
| QAM | Amplitude and phase at the same time | Digital TV, fast WiFi, cable modems: 64-QAM carries 6 bits per symbol |
06How demodulation works
- Envelope detector: a diode, a capacitor and a resistor. The R·C constant must be much greater than the carrier period and much smaller than that of the modulating signal.
- Product detector: multiplies by a local carrier. It is mandatory for DSB and SSB, and it is what an MC1496 does.
- Discriminator or ratio detector: converts frequency variations into amplitude variations and then detects them.
- PLL: it locks onto the carrier and its correction voltage is the demodulated signal. It is the modern solution and the most stable.
- Before all that, always a limiter, which is where the noise immunity comes from.
No receiver demodulates directly at the received frequency. All of them translate the signal to a fixed intermediate frequency —455 kHz in AM, 10.7 MHz in FM— by mixing it with a local oscillator, and do the filtering and demodulation there. The advantage is enormous: the most selective filter is designed just once, for a fixed frequency, and tuning is simply a matter of shifting the local oscillator. It is the architecture of practically every radio for a century.
07In the lab
With a generator that has AM modulation, observe the envelope on the oscilloscope and measure Vmax and Vmin. Calculate m with the formula and compare it with the value set on the generator. Raise the modulation until it goes past 1 and observe the overmodulation: the envelope “crosses over.”
Build the detector with a 1N4148, 10 nF and 10 kΩ, and recover the modulating signal from an AM signal. Change the capacitor to 1 nF and to 100 nF and observe the two defects: with too little filtering there is carrier left superimposed; with too much, the detector does not follow the peaks of the modulating signal and distortion appears.
Modulate the same signal in AM and in FM and add noise to it with a generator. Listen to and look at the two demodulated outputs: AM degrades gradually, FM stays clean until it suddenly falls apart below the threshold. That behavior —the threshold effect— is also characteristic of FM.
With a spectrum analyzer or an SDR receiver, look at a single-tone AM signal: the carrier appears and two symmetric lines separated by the frequency of the modulating signal. Change the tone and see how they move apart. Measure the relative height of the sidebands and compare it with the modulation index.
08Common mistakes
| Symptom | Usual cause |
|---|---|
| The AM sounds distorted and bothers the neighboring channels | Overmodulation: m greater than 1. |
| The envelope detector distorts the peaks | R·C constant too large: it cannot follow the modulating signal. |
| The carrier is heard superimposed on the audio | R·C too small: not enough carrier filtering. |
| The FM takes up more channel than expected | Excessive deviation. The amplitude of the modulating signal has to be limited before the modulator. |
| The SSB sounds like Donald Duck | The carrier reinserted in the receiver is off: the BFO has to be adjusted to within tens of hertz. |
| With two transmitters on the same frequency only one is heard | FM capture effect. It is an advantage in broadcasting and a problem in safety services. |
| The receiver picks up a station at two points on the dial | Image frequency: not enough selectivity ahead of the superheterodyne mixer. |
09Self-assessment
Which three parameters of a carrier can be modulated?
Amplitude, frequency and phase. From them come AM, FM and PM, and their digital equivalents ASK, FSK and PSK.
In an AM signal, a maximum peak of 8 V and a minimum of 2 V are measured. What is the index?
m = (8 − 2)/(8 + 2) = 6/10 = 0.6, that is, 60 %.
A 200 W carrier modulated at 100 %: what are the total power and the useful power?
P = 200 × (1 + 1/2) = 300 W. The sidebands carry 100 W: 33 % of the total. The rest is spent on the carrier, which carries no information.
What concrete advantage does SSB have over AM?
It takes up half the bandwidth and all the power goes to information: with the same transmitter power, the useful range is much greater.
FM with Δf = 40 kHz and fm = 10 kHz: what are the index and the bandwidth?
β = 40/10 = 4. BW = 2 × (40 + 10) = 100 kHz according to Carson's rule.
Why is FM more immune to noise than AM?
Because the information is in the frequency and not in the amplitude: the receiver clips the amplitude with a limiter and removes with it almost all the noise, which is essentially amplitude noise.
What is the capture effect?
In FM, given two signals on the same frequency the receiver keeps the stronger one and the weaker one disappears. In AM you would hear both mixed.
Why does aviation use AM and not FM?
Because if two aircraft transmit simultaneously, in AM you hear both and the controller detects the overlap. With FM, the capture effect would hide one transmission completely.
What does a superheterodyne receiver do, and why?
It translates the received signal to a fixed intermediate frequency by mixing it with a local oscillator. That way the filtering and demodulation are always done at the same frequency, with an optimized filter, and tuning comes down to moving the local oscillator.
How is the R·C constant of an envelope detector chosen?
Much greater than the carrier period —to filter it out— and much smaller than that of the fastest modulating signal —so it can follow it—. If the second condition is not met, distortion appears on the peaks.