Frequency and Phase Modulation PDF

IT2311 Frequency and Phase Modulation Principles of Frequency and Phase Modulation (Frenzel, 2022) Frequency Modulation (FM) A modulation process that puts the message in a carrier wave by changing the instantaneous frequency of the wave. Figure 1. Retri...

IT2311 Frequency and Phase Modulation Principles of Frequency and Phase Modulation (Frenzel, 2022) Frequency Modulation (FM) A modulation process that puts the message in a carrier wave by changing the instantaneous frequency of the wave. Figure 1. Retrieved from Frenzel, L. (2022). Principles of electronic communication systems: Fifth edition. McGraw Hill In Figure 1, a) is the carrier signal, b) is the modulating signal, and c) is the FM signal. There is an observable difference between Amplitude Modulation and Frequency Modulation wherein the carrier amplitude remains constant, and the carrier frequency is changed by the modulating signal based on its troughs. Here are other characteristics observed when FM is used: The carrier frequency shifts proportionately as the modulating signal’s amplitude varies. The carrier frequency increases as the modulating signal amplitude increases. If a reverse relationship is implemented, a decreasing modulating signal will increase the carrier frequency above its center value, while an increasing modulating signal will decrease the carrier frequency below the center value. 04 Handout 1 *Property of STI  [email protected] Page 1 of 7  IT2311 For clearer visualization, see Figure 2, which shows the modulating signal and the FM signal together. Figure 2. Frequency modulation. Retrieved from https://www.allaboutcircuits.com Frequency Deviation (𝒇𝒅 ) It is the amount of change in the carrier frequency caused by the modulating signal. The maximum frequency deviation happens at the maximum amplitude of the modulating signal. 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 + 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑀𝑖𝑛𝑖𝑚𝑢𝑛 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 − 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑓𝑑 = 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 − 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 For example, c) signal has a 150 𝑀𝐻𝑧 carrier frequency. If the peak amplitude of the modulating signal (b) causes a maximum frequency shift of 40 𝑘𝐻𝑧. What are the frequency deviations? For maximum and minimum deviation: 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 + 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 150 𝑀𝐻𝑧 + 40 𝑘𝐻𝑧 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 𝟏𝟓𝟎. 𝟎𝟒 𝑴𝑯𝒛 𝑀𝑖𝑛𝑖𝑚𝑢𝑛 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 − 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 150 𝑀𝐻𝑧 − 30 𝑘𝐻𝑧 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 𝟏𝟒𝟗. 𝟗𝟔 𝑴𝑯𝒛 For total frequency deviation: 𝑓𝑑 = 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 − 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑓𝑑 = 150.04 𝑀𝐻𝑧 − 149.96 𝑀𝐻𝑧 𝒇𝒅 = 𝟎. 𝟎𝟖 𝑴𝑯𝒛 𝒐𝒓 𝟖𝟎 𝒌𝑯𝒛 The total frequency deviation of this problem could also be expressed as ±40 𝑘𝐻𝑧 as frequency deviation is expressed as the amount of frequency shift of the carrier above and below the center frequency. The ± sign in ±40 𝑘𝐻𝑧 indicates that the modulating signal varies the carrier above and below its center frequency by 40 𝑘𝐻𝑧. Frequency-shift Keying (FSK) In FM, a series of rectangular waves, such as serial binary data, can represent the modulating signal. This kind of modulating signal will only have two amplitudes and will also make the carrier frequency have two values (1 and 0), such as this modulating signal: 04 Handout 1 *Property of STI  [email protected] Page 2 of 7  IT2311 Figure 3. Retrieved from Frenzel, L. (2022). Principles of electronic communication systems: Fifth edition. McGraw Hill. In Figure 3, the modulating signal starts at binary 0, making the carrier frequency the center frequency value. When the modulating signal is at binary 1, the carrier frequency rises to a higher frequency level. The amount of shift depends on the amplitude of the binary signal. This modulation is called frequency-shift keying. Figure 4. Retrieved from Frenzel, L. (2022). Principles of electronic communication systems: Fifth edition. McGraw Hill. In Figure 4, by translating the binary code signal into an FSK signal, it can be observed that the carrier frequency stretches if it is at binary 0 and it compresses when it is at a higher frequency or binary 1. Phase Modulation (PM) A modulation process wherein the phase of the carrier signal varies based on the amplitude variation of the message signal or modulating signal. Figure 5. Retrieved from Frenzel, L. (2022). Principles of electronic communication systems: Fifth edition. McGraw Hill. 04 Handout 1 *Property of STI  [email protected] Page 3 of 7  IT2311 In Figure 5, the sine wave is the modulating signal, the orange triangular wave is the PM, and the blue triangular signal is the FM. There is a noticeable lagging and leading between FM and PM. In the FM signal, the frequency compresses in accordance with the positive modulating signal while it stretches when at zero deviation. But for the PM signal, it starts to lag or stretch at the positive peak of the modulating signal until the second zero deviation. It starts to lead or compress at the second zero deviation until the next positive peak of the modulating signal. These are called lagging phase shifts and leading phase shifts. To further visualize, Figure 6 shows the modulating signal and the phase modulation signal together. Figure 6. Phase modulation. Retrieved from https://www.allaboutcircuits.com Phase-shift Keying (PSK) In PM, the modulating signal can also be used with the binary signal. When the binary 0 is 0 𝑉, the PM signal is simply the carrier frequency, and when a binary 1 voltage level occurs (3 𝑉), the modulator, or phase shifter, changes the phase of the carrier, and not its frequency. Figure 7. Retrieved from Frenzel, L. (2022). Principles of electronic communication systems: Fifth edition. McGraw Hill. In Figure 7, the phase shift is 180°. Each time the signal changes from 0 to 1 or 1 to 0, a 180°phase shift happens. Notice how the PSK signal does a 180°phase shift when it hits binary 1 or 0. The shift happens whether the signal is positive or negative. This process is called phase-shift keying or binary phase-shift keying. Sidebands and Modulation Index (Frenzel, 2022) When a constant-frequency sine wave modulates a carrier, two side frequencies or sidebands are produced. In FM and PM, just like with Amplitude Modulation (AM), it is the sum and difference of the carrier and the modulating frequency. The spectrum of an FM and a PM signal is wider than AM because of sideband pairs. 04 Handout 1 *Property of STI  [email protected] Page 4 of 7  IT2311 Figure 8. Retrieved from Frenzel, L. (2022). Principles of electronic communication systems: Fifth edition. McGraw Hill. Figure 8 shows a frequency spectrum of an FM signal with sample carrier and sideband amplitudes. Sidebands can be spaced in two ways; one is from the carrier (𝑓𝑐 ) and the second is from one another by a frequency equal to the modulating frequency (𝑓𝑚 ). The values of the lower (𝒇𝑳𝑺𝑩 ) and upper (𝒇𝑼𝑺𝑩 ) sidebands are computed as: 𝒇𝑳𝑺𝑩𝟏 = 𝑓𝑐 − 𝑓𝑚 for the first sideband from the carrier, 𝒇𝑳𝑺𝑩𝟐 = 𝑓𝑐 − 2𝑓𝑚 for the second, 𝒇𝑳𝑺𝑩𝟑 = 𝑓𝑐 − 3𝑓𝑚 for third, and so on. 𝒇𝑼𝑺𝑩𝟏 = 𝑓𝑐 + 𝑓𝑚 for the first sideband from the carrier,𝒇𝑼𝑺𝑩𝟐 = 𝑓𝑐 + 2𝑓𝑚 for the second, 𝒇𝑼𝑺𝑩𝟑 = 𝑓𝑐 + 3𝑓𝑚 for third, and so on. If Figure 8 has a modulating frequency of 1 𝑘𝐻𝑧 and a carrier by 1 𝑀𝐻𝑧, the first pair, upper and lower of sidebands is: 𝑓𝑈𝑆𝐵1 = 𝑓𝑐 + 𝑓𝑚 𝑓𝑈𝑆𝐵1 = 1,000,000 𝐻𝑧 + 1000 𝐻𝑧 𝒇𝑼𝑺𝑩𝟏 = 𝟏, 𝟎𝟎𝟏, 𝟎𝟎𝟎 𝑯𝒛 𝒐𝒓 𝟏. 𝟎𝟎𝟏 𝑴𝑯𝒛 𝑓𝐿𝑆𝐵 = 𝑓𝑐 − 𝑓𝑚 𝑓𝐿𝑆𝐵1 = 1,000,000 𝐻𝑧 − 1000 𝐻𝑧 𝒇𝑳𝑺𝑩𝟏 = 𝟗𝟗𝟗, 𝟎𝟎𝟎 𝑯𝒛 𝒐𝒓 𝟎. 𝟗𝟗𝟗 𝑴𝑯𝒛 For the second pair, upper and lower, of the sidebands is: 𝑓𝑈𝑆𝐵2 = 𝑓𝑐 + 2𝑓𝑚 𝑓𝑈𝑆𝐵2 = 1,000,000 𝐻𝑧 + (2)1000 𝐻𝑧 𝑓𝑈𝑆𝐵2 = 1,000,000 𝐻𝑧 + 2000 𝐻𝑧 𝒇𝑼𝑺𝑩𝟐 = 𝟏, 𝟎𝟎𝟐, 𝟎𝟎𝟎 𝑯𝒛 𝒐𝒓 𝟏. 𝟎𝟎𝟐 𝑴𝑯𝒛 𝑓𝐿𝑆𝐵2 = 𝑓𝑐 − 2𝑓𝑚 𝑓𝐿𝑆𝐵2 = 1,000,000 𝐻𝑧 − (2)1000 𝐻𝑧 𝑓𝐿𝑆𝐵2 = 1,000,000 𝐻𝑧 − 2000 𝐻𝑧 𝒇𝑳𝑺𝑩𝟐 = 𝟗𝟗𝟖, 𝟎𝟎𝟎 𝑯𝒛 𝒐𝒓 𝟎. 𝟗𝟗𝟖 𝑴𝑯𝒛 04 Handout 1 *Property of STI  [email protected] Page 5 of 7  IT2311 For the third pair, upper and lower, of the sidebands is: 𝑓𝑈𝑆𝐵3 = 𝑓𝑐 + 3𝑓𝑚 𝑓𝑈𝑆𝐵3 = 1,000,000 𝐻𝑧 + (3)1000 𝐻𝑧 𝑓𝑈𝑆𝐵3 = 1,000,000 𝐻𝑧 + 3000 𝐻𝑧 𝒇𝑼𝑺𝑩𝟑 = 𝟏, 𝟎𝟎𝟑, 𝟎𝟎𝟎 𝑯𝒛 𝒐𝒓 𝟏. 𝟎𝟎𝟑 𝑴𝑯𝒛 𝑓𝐿𝑆𝐵3 = 𝑓𝑐 − 3𝑓𝑚 𝑓𝐿𝑆𝐵3 = 1,000,000 𝐻𝑧 − (3)1000 𝐻𝑧 𝑓𝐿𝑆𝐵3 = 1,000,00 𝐻𝑧 − 3000 𝐻𝑧 𝒇𝑳𝑺𝑩𝟑 = 𝟗𝟗𝟕, 𝟎𝟎𝟎 𝑯𝒛 𝒐𝒓 𝟎. 𝟗𝟗𝟕 𝑴𝑯𝒛 The same process applies until the last available pair of sidebands. Modulation Index The amplitudes of the carrier and sidebands of the frequency spectrum of an FM signal still depend on the modulation index 𝑚𝑓 , still unitless, such as: 𝑓𝑑 𝑚𝑓 = 𝑓𝑚 Wherein: 𝑓𝑑 = frequency deviation 𝑓𝑚 = modulating frequency For example, if the maximum modulating frequency is 3.5 𝑘𝐻𝑧 and the maximum frequency deviation of the carrier is ±14 𝑘𝐻𝑧 and : 𝑓𝑑 𝑚𝑓 = 𝑓𝑚 14 𝑘𝐻𝑧 𝑚𝑓 = 3.5 𝑘𝐻𝑧 𝒎𝒇 = 𝟒 Bessel Functions The number and amplitudes of the sidebands are obtained by solving the FM signal equation: 𝑉𝐹𝑀 = 𝑉𝑐 sin[2𝜋 𝑓𝑐 𝑡 + 𝑚𝑓 sin (2𝜋𝑓𝑚 𝑡)] This equation is solved with a complex mathematical process, Bessel functions. For the amplitudes of the sidebands, Bessel functions have a widely available table for different carrier and sideband amplitudes for different modulation indexes of FM signals. 04 Handout 1 *Property of STI  [email protected] Page 6 of 7  IT2311 Table 1. Bessel functions. Retrieved from https://www.coursehero.com/ Table 1 has various modulation indices for relative amplitudes of the carrier and the sideband pairs. The carrier and sideband amplitudes with negative signs mean the signal represented by that amplitude is shifted in phase 180°. References: Frenzel, L. (2022). Principles of electronic communication systems: 5th ed. McGraw Hill. Shaik, A. (2023). Phase modulation. [Web Article]. Retrieved on August 3, 2023, from https://www.physics-and-radio- electronics.com/blog/phase-modulation/ 04 Handout 1 *Property of STI  [email protected] Page 7 of 7