Phase modulation as a method of data transmission

2024 Author: Trinity Chesterton | [email protected]. Last modified: 2024-01-02 00:28

As you know, a radio frequency signal consists of a carrier, which is based on radio emission in the form of a simple harmonic oscillation u (t)=U cos (ωt + φ). It follows from this that there are three independent parameters in the carrier frequency signal, by acting on which it is possible to capture changes in the control signal.

This implies the possibility of three types: amplitude (AM), frequency (FM) and phase modulation (PM).

Phase modulation is a method of transmitting analog or digital information by changing the initial angle (phase) φ_{0 of the carrier frequency of the transmitted signal.}

With it, the phase φ(t) depends on the amplitude of the control (modulating) signal, i.e. φ(t)=ω_0t + _Δφ∙sinΩt + φ₀==φ_{0 + ke (t), where k is the proportionality factor.}

A phase-modulated signal is generally described by the expression u (t)=U_{n sin [ωt + φ (t)].}

When modulating with one tone [e (t)=E sin Ωt] we have: φ(t)=φ₀ + kE sin Ωt=φ₀ +Δφ_{maxsin Ωt.}

After substituting the value of φ(t) into the equation of the phase-modulated signal, we get u (t)=U_n sin (ω_n t + φ₀ + Δφ_max sin Ωt), where Δφ_max is the maximum phase change proportional to amplitude of the control voltage. Δφ_{maxis otherwise called the angular modulation index and denoted by m.}

As you can see, at FM m=Δφ_max =kE. The instantaneous value of the time-varying phase angle Θ (t) is Θ (t)=ω_n t + φ₀ + msin Ωt, so ω=d Θ (t)/dt=ω_n + mΩ cosΩt, where mΩ=Δφ_maxΩ=Δ ω_n =kEΩ - maximum frequency deviation from ω_{nat PM, directly proportional to the amplitude and frequency of the modulating oscillation.}

Thus, with PM, the modulation index, which characterizes the maximum phase change, is proportional to the amplitude of the control signal and does not depend on the modulation frequency. The change in frequency relative to the average value (deviation) changes in direct proportion to the amplitude and frequency of the modulating voltage.

Depending on the conditions of use, phase modulation has several varieties. One of them, in particular, is relative phase shift keying.

In this form, depending on the modulating signal, only the phase of the signal changes, and the frequency andamplitude remain unchanged. With OFM, the information value is not the absolute change in the phase, but its change relative to the previous value.

The electronic circuit that causes the phase angle of the modulated waveform (relative to the unmodulated carrier) to change in accordance with the modulating signal is called a phase modulator.

Many types of such images have been developed. A simple modulator circuit contains a varicap - a diode capable of changing the junction capacitance under the action of a control voltage. In this circuit, the modulating voltage changes the capacitance of the varicap. The phase shift depends on the relative value of the capacitance of this diode and the load resistance R.

Thus, this shift depends on the modulating voltage. This is what causes the phase modulation of the radio signal. However, such a shift is non-linearly related to the modulating voltage, the capacitance of the varicap is non-linearly related to the modulating voltage, which creates additional problems in the design of phase modulators.

In its pure form, phase modulation has not been widely used due to its inherent serious drawback - low noise immunity.