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**Principles of analogue modulation**

Lecture 3

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**Analogue Modulation Techniques**

Theory of amplitude modulation Representation of AM Power relations in the AM wave Single-sideband techniques

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Amplitude Modulation This is the simplest and oldest form of modulation. In this type, the information signal (intelligence) causes the amplitude of the carrier to vary in time, in proportion to the instantaneous magnitude of their sum

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Amplitude Modulation Apart from transforming the signal into a form suitable for transmission, modulation allows many signals originally at the same frequency to be transferred to other parts of the electromagnetic spectrum.

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**Mathematical description**

To describe amplitude modulation mathematically, consider the carrier wave given as a sinusoidal wave , with a frequency of and amplitude . This can be written as

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Amplitude Modulation Without modulation this sine wave will convey no information. Reason: We can calculate its value at anytime from previously known values. What modulation does is to modify the constant value with the signal, which carries the information. This results in the amplitude of the modulated carrier varying in proportion to the amplitude of the information signal.

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**Derivation of the AM equation**

Let the information signal be given by Let and then and

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**Derivation of the AM equation**

The amplitude of the resulting modulation is the sum of the amplitude of the carrier and the signal. Substituting for

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**where this is index of modulation**

The resulting AM wave will thus be

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**Expanding the brackets**

but such that

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**If we rewrite this in terms of frequencies**

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Examples In an AM radio broadcast the tone has a frequency of 1000Hz and the carrier frequency is 1500kHz. What are the resulting sidebands. What will be the frequency of the sidebands if the carrier is at 1250kHz? If the tone has a spectrum of 300 to 3000Hz and the carrier is at 100kHz then one of the sidebands will range from to 103 and the other will be from 97 to 99.7kHz.

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**Modulating with different carriers**

Modulation can be used to translate signals originally at the same frequency to different parts of the frequency spectrum. Assume that AM radio stations have a voice and music spectrum from 0 to 5kHz. Assume that they are spaced 10kHz apart in the broadcast band. If the broadcast from each station is then modulated with a different carrier frequency, then the broadcast will not overlap. Reason: the signal is less than half the difference between adjacent carriers. Example: Stations broadcast at 1000, 1010 and 1020kHz. Draw the frequency spectrum of the stations if the signal bandwidth is 5kHz What happens if the modulating signal bandwidth is now 8kHz?

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**Modulation Index and Signal Power**

It is a measure of how fully the carrier has been modulated. Examples: The modulated peak value of a signal is 10 V and the unmodulated carrier is 8 V. Find the modulation index. A modulated signal seen on an oscilloscope has a maximum span of 5 V and a minimum of 1 V. What is the modulation index?

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**Signal Power The power in a system can be defined through voltage as**

and through current as Assume that R = 1 ohm The carrier power is then Power in each side band is the given as

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**The power in both side-bands**

The total transmitted power is since

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Comment The maximum power in the sidebands is 50% of the carrier power at m = 1. The carrier and one sideband may be suppressed without destroying the information Examples A carrier of 1000W is modulated with an index of 0.8. What is the total power? For a carrier of 250W and 90% modulation, what is the total power? What is the carrier power if the total power is 1000W and the modulation index is 0.95.

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**Single-sideband techniques**

Conventional AM systems have two main disadvantages: Two thirds or more of the total transmitted power is in the carrier The bandwidth required is twice that which will be needed in SSB Such systems are therefore both power and bandwidth inefficient. The mathematical foundation for single sideband systems was laid in 1914. There are many variations of the single sideband systems

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**AM SSB Full carrier (SSBFC)**

Carrier is transmitted at full power with only one of the sidebands. In this only half as much bandwidth will be required The power relations will be as follows: Power in carrier = Power in lower sideband = 0 Power in upper sideband = Total power What is the ratio of sideband power to carrier power at 100% modulation?

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**AM Single sideband suppressed carrier (SSBSC)**

In this the carrier is totally removed together with one of the sidebands. Only half the bandwith is required. Power Relations The sideband power will constitute 100% of the total transmitted power. Power in carrier, Power in lower sideband = 0 Power in upper sideband =

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**AM SSB Reduced carrier (SSBRC)**

In this one sideband is removed and the carrier reduced to about 10% of the unmodulated amplitude. The carrier will have to be reinserted at reduced amplitude for the purpose of demodulation Power relations Power in carrier, Power in lower sideband = 0 Power in upper sideband = Total power =

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**Comparison of SSB to Double sideband AM**

Advantages of SSB Bandwidth conservation: Only half the bandwidth is required Power conservation: Only one sideband with carrier removed or suppressed. Hence total transmitted power will be less. This allows smaller transmitters to be used. Selective fading: In double sideband, the two sidebands may experience different impairments as the propagate along different paths in the medium. This could result in carrier phase shift. This cannot happen if only one sideband is transmitted. Noise Reduction: Thermal noise is reduced to half, because the bandwidth is also half.

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Disadvantages Complex receivers Tuning Difficulties: More difficult to tune than conventional AM receivers. More expensive tuning circuits can be used. Examples: A double sideband AM radio transmitter gives a power output of 5 kW when the carrier is modulated to a depth of 95%. A speech signal is then used to modulate the carrier with a depth of 20% and the carrier and one sideband are suppressed. Find the output power in the other sideband.

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