Signal Modulation Simulator — AM / FM / PM

The core idea is a carrier wave, $c(t)$, which is a pure sinusoid. The message signal, $m(t)$, modifies a specific property of this carrier. The general form of the modulated signal, $s(t)$, depends on the type.

Here, $A_c$ is the carrier amplitude, $f_c$ is the carrier frequency (adjustable in the simulator), and $t$ is time. This is the wave you start with before any modulation is applied.

For Amplitude Modulation (AM), the message signal directly multiplies the carrier's amplitude. The equation for a standard AM (DSB-LC) wave is:

Here, $k_a$ is the amplitude sensitivity, and the term $k_a m(t)$ creates the amplitude variations you see. The "1 +" ensures the amplitude never goes negative, which simplifies receiver design. The modulation index $\mu = k_a \cdot \max|m(t)|$ controls the depth of these variations.

For Frequency Modulation (FM), the message signal changes the instantaneous frequency of the carrier. The equation is:

Here, $k_f$ is the frequency sensitivity. The integral means the message changes the phase of the carrier, and the derivative of phase is frequency. The modulation index in FM is $\beta = (k_f \cdot \max|m(t)|) / f_m$, where $f_m$ is the message frequency. It determines the bandwidth of the FM signal.

AM Radio Broadcasting (535–1705 kHz): This is the classic application of Amplitude Modulation. Its advantage is simple receiver circuitry, which is why it was the first commercially successful broadcast technology. However, it's susceptible to static from lightning and electrical interference, which also affect amplitude.

FM Radio Broadcasting (88–108 MHz): FM provides high-fidelity audio because noise typically affects a signal's amplitude, not its frequency. This superior noise immunity is why music stations use FM. The trade-off is a more complex receiver and a wider bandwidth requirement per station.

Aviation Voice Communication (VHF Band): Aircraft communicate with towers using AM, not FM. This might seem counterintuitive, but in crowded airspace, the weaker signal from a distant aircraft on the same frequency is still audible as background static in an AM system, alerting others to its presence. In FM, a weaker signal might be completely rejected by the receiver ("capture effect"), which is a safety hazard.

Phase Modulation in Digital Communications (Wi-Fi, Bluetooth): While our simulator shows analog PM, its digital cousin (Phase Shift Keying, PSK) is everywhere. By shifting the phase of the carrier to specific, discrete values, it can represent digital bits (0s and 1s). This is a fundamental technology in modern wireless data transmission due to its spectral efficiency and robustness.

First, there is a misconception that "a larger modulation index is always better." While increasing the "maximum frequency deviation" in FM improves sound quality, it also widens the occupied frequency bandwidth. For example, if the highest frequency of an audio signal is 5 kHz and the modulation index β is set to 5, Carson's rule gives a bandwidth of approximately 2*(25 kHz+5 kHz)=60 kHz. This is an extremely "generous" usage within limited radio resources and carries a high risk of interfering with other communications. In practice, the basic principle is to choose the minimum modulation index that meets the required quality.

Next, you need to be cautious about the behavior when using a square wave as the "message signal" in a simulator. Abrupt changes like those in a square wave theoretically contain infinite high-frequency components. Applying FM modulation to this state theoretically generates infinite sidebands, causing the bandwidth to diverge. While a simulator displays this within a finite bandwidth, in real circuits, such steep changes cause distortion and unwanted radiation. In practical systems, it is essential to process the message signal with a low-pass filter (pre-emphasis) to suppress high-frequency components.

Finally, there is the issue of incorrect "modulation depth" settings in AM. In an "overmodulation" state where the modulation depth m_a exceeds 1, the waveform's peaks and troughs are clipped, and unwanted components spread in the spectrum. Demodulating in this state not only causes severe distortion in the audio but also leads to interference (crosstalk) in adjacent frequency bands. Radio station operations strictly monitor this. If you set m_a to, say, 1.2 in a simulator and observe the changes in the waveform and spectrum, the impact becomes immediately clear.