Amplitude Modulation Concepts PDF

IT2311 Amplitude Modulation Amplitude Modulation Concepts (TechnologyUK, 2023) Modulation is the process of converting raw message data into digital signals or waves over a modulator to optimize transmission. This process increases the strength of the sig...

IT2311 Amplitude Modulation Amplitude Modulation Concepts (TechnologyUK, 2023) Modulation is the process of converting raw message data into digital signals or waves over a modulator to optimize transmission. This process increases the strength of the signal to have maximum reach. In Figure 1, the carrier signal is the steady waveform in terms of amplitude (height) and frequency, the modulating signal is the message that must be transmitted, and the modulated signal is the output signal after the process. Figure 1. Modulation. Retrieved from https://www.technologyuk.net/ Modulation is done to improve signals often unsuitable for the transmission device. Just like a broadcast radio that plays news, music, and weather forecasts, the frequency people hear is in the audio spectrum only ranging from 20 𝐻𝑧– 20𝑘 𝐻𝑧. This makes sending audio signals wirelessly using radio frequency harder. One way to get a high-frequency signal to carry a low-frequency signal is by amplitude modulation. The instantaneous amplitude of a radio frequency carrier wave is varied in direct proportion to that of the modulating signal to obtain an amplitude-modulated signal. Figure 2. Amplitude modulation. Retrieved from https://www.technologyuk.net/ 03 Handout 1 *Property of STI  [email protected] Page 1 of 6  IT2311 In Figure 2, a microphone acts as a transducer that receives the input signal in the form of audio frequency. This input signal will serve as the carrier. It is only modulated by adding the input signal in a mixer, turning it into a radio frequency acceptable for the transmission device. Amplitude Modulation (AM) It is a modulation process focused on modulating or changing the signal's amplitude. A device or a circuit can convert data into an electrical signal in an AM communications system. This signal, either the message or modulating signal, is then used to modify the amplitude of another signal. Figure 3. Amplitude modulation theory. Retrieved from https://digilent.com/reference/test-and- measurement/guides/complementary-labs/lab5/start Figure 3 shows how the message modulates the carrier signal to produce the AM signal. Observe as the AM’s signal increases or decreases based on the waveform of the message signal. In detail, see Figure 4. Figure 4. Retrieved from Frenzel, L. (2022). Principles of electronic communication systems: Fifth edition. McGraw Hill. In Figure 4, (a) is the modulating signal, and (b) is the modulated carrier. Here are the characteristics observed in applying amplitude modulation (b): The carrier frequency stays constant during the modulation process, but its amplitude (height) changes based on the modulating signal. An increase in the amplitude of the modulating signal increases the amplitude of the carrier. 03 Handout 1 *Property of STI  [email protected] Page 2 of 6  IT2311 Changes in the positive and negative peaks of the carrier wave depend on the modulating signal. An imaginary line connects the positive and negative peaks of the carrier waveform. This imaginary line is called an “envelope,” which is the dashed line on (b). An increase/decrease in the amplitude of the modulating signal causes an increase/decrease in the positive and negative peaks of the carrier amplitude. Figure 5 is the simplified waveform that uses equally spaced vertical lines to represent high-frequency carrier waves. The amplitude of these vertical lines also varies based on the modulating signal. These illustrations show the variation of carrier amplitude concerning time and are to be in the time domain. Time domain signals are voltage or current variations that occur over time and are displayed on an oscilloscope screen. Figure 5. Retrieved from Frenzel, L. (2022). Principles of electronic communication systems: Fifth edition. McGraw Hill. Sidebands During the modulation of a carrier wave by a modulating signal, new signals are generated at different frequencies as part of the process. These frequencies are called sidebands, or side frequencies found in the frequency spectrum above and below the carrier frequency. It is preferred to show the AM signal in the frequency domain rather than in the time domain if signals of more than one (1) frequency create a waveform. Sidebands are the sum and difference of the carrier and modulating frequencies, such as: 𝑓𝑈𝑆𝐵 = 𝑓𝑐 + 𝑓𝑚 𝑓𝐿𝑆𝐵 = 𝑓𝑐 − 𝑓𝑚 Wherein: 𝑓𝑈𝑆𝐵 = Upper sideband 𝑓𝑐 = Carrier Frequency 𝑓𝐿𝑆𝐵 = Lower sideband 𝑓𝑚 = Modulating Frequency Total bandwidth: 𝐵𝑊 = 𝑓𝑈𝑆𝐵 − 𝑓𝐿𝑆𝐵 or 𝐵𝑊 = 2𝑓𝑚 03 Handout 1 *Property of STI  [email protected] Page 3 of 6  IT2311 Sideband signals are illustrated in a frequency domain where the horizontal axis represents frequency, and the vertical axis represents the signal’s magnitude, whether in voltage, current, or power amplitude. See Figure 6. Figure 6. Retrieved from Frenzel, L. (2022). Principles of electronic communication systems: Fifth edition. McGraw Hill. Modulation Index and Percentage Modulation (Frenzel, 2022) The amplitude of the modulating signal must always be less than the amplitude of the carrier or 𝑉𝑚 < 𝑉𝑐. Otherwise, distortion will occur and will transmit incorrect information, thus making the relationship between the amplitudes of the modulating signal and the carrier signal important. This is known as the modulation index (𝑚), also referred to as the degree of modulation or modulating factor/coefficient. 𝑉𝑚 𝑚= 𝑉𝑐 As stated, 𝑉𝑚 and 𝑉𝑐 are the peak values of the signals, and the carrier voltage is the unmodulated value. 65 To get the percentage of modulation, multiply the modulation index by 100. An example if the carrier voltage is 8 𝑉 and the modulating signal is 6.5 𝑉: 𝑉𝑚 𝑚= 𝑉𝑐 6.5 𝑉 𝑚= 8𝑉 𝑚 = 0.8125, to get the percentage of modulation: 𝒎 = 0.8125 𝑥 100 = 𝟖𝟏. 𝟑% 03 Handout 1 *Property of STI  [email protected] Page 4 of 6  IT2311 Modulation Index Using Oscilloscope An oscilloscope can be used to derive the modulation index (𝑚) by measuring the values of the modulation and carrier voltages and then calculating the ratio. When the AM signal is seen on an oscilloscope, the modulation index is computed from 𝑉𝑚𝑎𝑥 and 𝑉𝑚𝑖𝑛. The peak value of the modulating signal (𝑉𝑚 ) is half the difference between the peak (𝑉𝑚𝑎𝑥 ) and trough (𝑉𝑚𝑖𝑛 ) values such as: 𝑉𝑚𝑎𝑥 − 𝑉𝑚𝑖𝑛 𝑉𝑚 = 2 Figure 7. Retrieved from Frenzel, L. (2022). Principles of electronic communication systems: Fifth edition. McGraw Hill. In Figure 7, 𝑽𝒎𝒂𝒙 is the peak value of the signal during modulation, while 𝑽𝒎𝒊𝒏 is the lowest, or the trough of the modulated wave. 𝑉𝑚𝑎𝑥 is also one-half of the peak value of the AM signal, such as: 𝑉max(𝑝−𝑝) 2 The values for 𝑉max(𝑝−𝑝) and 𝑉min(𝑝−𝑝) can be obtained from an oscilloscope screen and be used to compute the modulation index. Additionally, the depth of AM is more expressed as the percentage of modulation than as a fractional value. Subtracting 𝑉𝑚𝑖𝑛 from 𝑉𝑚𝑎𝑥 gives the peak-to-peak value of the modulating signal, wherein one-half is the peak value. On the other hand, the peak value of the carrier signal 𝑉𝑐 is the average of the 𝑉𝑚𝑎𝑥 and 𝑉𝑚𝑖𝑛 values. 𝑉𝑚𝑎𝑥 − 𝑉𝑚𝑖𝑛 𝑉𝑐 = 2 The modulation index is: 𝑉𝑚𝑎𝑥 − 𝑉𝑚𝑖𝑛 𝑚= 𝑉𝑚𝑎𝑥 + 𝑉𝑚𝑖𝑛 03 Handout 1 *Property of STI  [email protected] Page 5 of 6  IT2311 Example: An AM signal is read with 4.9 𝑉 divisions for 𝑉𝑚𝑎𝑥 and 1.4 𝑉 divisions for it’s 𝑉𝑚𝑖𝑛 from the graticule on the oscilloscope. What is the percentage of modulation? 𝑉𝑚𝑎𝑥 − 𝑉𝑚𝑖𝑛 𝑚= 𝑉𝑚𝑎𝑥 + 𝑉𝑚𝑖𝑛 4.9 𝑉 − 1.4 𝑉 𝑚= 4.9 𝑉 + 1.4 𝑉 3.5 𝑉 𝑚= 6.3 𝑉 𝑚 = 0.5555555 𝒎 = 0.5555555 𝑥 100 = 𝟓𝟓. 𝟔% References: Frenzel, L. (2022). Principles of electronic communication systems: Fifth edition. McGraw Hill. TechnologyUK (2023). Amplitude modulation (AM). [Web Article]. Retrieved on July 25, 2023, from https://www.technologyuk.net/telecommunications/telecom-principles/amplitude-modulation.shtml 03 Handout 1 *Property of STI  [email protected] Page 6 of 6  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