In this lecture. System Model Power Penalty Analog transmission Digital transmission

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2 System Model Power Penalty Analog transmission Digital transmission In this lecture Analog Data Transmission vs. Digital Data Transmission Analog to Digital (A/D) Conversion Digital to Analog (D/A) Conversion Pulse code modulation (PCM)

3 SYSTEM MODEL The transmitter (includes modulation) consists of a set of DFB (distributed-feedback) lasers, one for each wavelength. The signals at the different wavelengths are combined into a single fiber by means of an optical multiplexer. An optical power amplifier may be used to increase the transmission power. what is the difference Between power amplifier and preamplifier?

4 After some distance along the fiber, the signal is amplified by an optical in-line amplifier. Depending on the distance, bit rate, and type of fiber used, the signal may also be passed through a dispersion-compensating module, usually at each amplifier stage. At the receiving end, the signal may be amplified by an optical preamplifier before it is passed through a demultiplexer. Each wavelength is then received by a separate photodetector (A photodetector is an optoelectronic device that absorbs optical signals and converts them into electrical signals)

5 POWER PENALTY The physical layer design must take into account the effect of a number of system impairments (for example the noise). Usually, each impairment results in a power penalty to the system. One way to define the power penalty is as the increase in signal power required (in db) to maintain the same bit error rate in the presence of impairments. The optical signal-to-noise ratio (OSNR) is another way to identify the quality of the signal OSNR is the ratio of the signal power to the noise. Attenuation can be compensated for by amplifying the optical signal. Optical amplifiers amplify the signal as well as the noise. Over time and distance, the receivers cannot distinguish the signal from the noise, and the signal is completely lost.

6 DECIBELS (DB) When the light travels from its source through a medium, it loses energy. The decibel was originally used to measure the strength of sounds as perceived by the human ear. To calculate the decibel value of a gain or loss in signal power, use the following equation: db = 10Log10(Pout Pin)

7 CONTINUE To calculate the gain or loss If the decible value is known: Calculate the power loss in decibels of a signal that starts at 3 milliwatts and arrives at 1.8 milliwatts. 1. Use the db equation db = 10Log 10 (P out P in ). 2. Plug in the Pin and Pout values: db = 10Log 10 ( ) = 10Log 10 (0.6) Log 10 (0.6) = 10 * = The power loss in db is

8 CONTINUE If you know the decibel value and want to calculate the gain or loss, you will have to rearrange the equation as shown here: (Pout Pin) = antilog(db 10) Calculate the remaining power after a 3.5 milliwatt signal is subjected to a loss of 0.9 decibels. 1. Use the db equation (Pout Pin) = antilog(db 10). 2. Plug in the Pin and db values: (Pout ) = antilog( ) = antilog 0.09 = Pout = = The remaining power is 2.8 milliwatts.

9 ANALOG TRANSMISSION Amplitude modulation is a form of analog transmission. Analog (or analogue) transmission is a transmission method of conveying voice, data, image, signal or video information using a continuous signal which varies in Amplitude, Phase, or Frequency. In telecommunications, modulation is the process of conveying a message signal, for example a digital bit stream or an analog audio signal, inside another signal that can be physically transmitted

10 DIGITAL TRANSMISSION If information is to be stored, carried, or manipulated by computers, however, it must be in a digital form that is, represented by a series of on-off or high-low voltage readings. Because only two states or digits are used, the numbering system is referred to as binary

11 Analog Data Transmission vs. Digital Data Transmission A digital signal is superior to an analog signal because it is more robust to noise and can easily be recovered, corrected and amplified. For this reason, the tendency today is to change an analog signal to digital data. 4.11

12 Analog to Digital (A/D) Conversion In A/D conversion, the smooth, continuously variable analog signal is translated into a digital signal that carries the same information. There are two factors that affect the quality of the digital sample: sample rate and quantizing error: o Sample Rate o Quantization Error

13 Analog to Digital (A/D) Conversion Sample Rate When an analog signal is Digitized, any information between the samples is lost so instead of a smooth transition over time, the digital information jumps from one voltage to the next in the signal. To smooth out the transitions and retain more of the information from the original analog signal, more samples Must be taken over time. The higher the sampling rate, the more accurately the original analog signal can be digitized. Sampling rate f s = 1/T where T is the time interval

14 Continue As with frequency measurements, the sample rate is measured in terms of cycles, or hertz. A rate of one sample per second would be designated 1 Hz. A rate of 1000 samples per second would be 1 kilohertz, or 1 khz. Typically, audio signals for CDs and other digital music are sampled at 44.1 khz or 48 khz.

15 NYQUIST THEROM In order for pulse code modulation to be effective, an analog signal must be sampled at a rate that is at least twice the highest expected frequency, this is called Nyquist Therom. For example, in a telephone conversation, the highest frequency encountered is about 4 khz. That means sampling must take place at the Nyquist Minimum of 8 khz to maintain a basic signal quality

16 Example Consider for example a signal composed of a single sinewave at a frequency of 1Hz: Sampling with frequency 2Hz we have:

17 Example It is easy to see that this sampling frequency (3 Hz) allows us to capture each peak and trough of the curve. A higher sampling ratio will give us more details about the curve :

18 Example Sampling at a lower frequency (1.5 Hz) gives the following result: The person receiving these samples, without any previous knowledge of the original signal, may well be mislead in to thinking that the signal has quite a different form

19 Continue The discretization of Time is called sampling and the discretization of Amplitude is called quantization Quantization Quantization is the conversion of a sampled signal, which is discrete in time but continuous in value, into a signal which is discrete in value. Quantization makes a sampled signal truly digital and ready for processing by a computer.

20 CONTINUE The quantizer can not search over an infinite number of possibilities and must restrict itself to a limited set of potential values. So essentially the analog-to-digital conversion is a combination of sampling and quantization The size of this set corresponds to the range of the quantizer and is always a power of 2 Since the value is necessarily contained in the complete set of 2 N potential values Only N bits are required to represent all the binary encoded numbers that can be generated by the quantizer.

21 CONTINUE ADCs are often referred to as N-bit ADCs, where N represents the number of bits used by the ADC to encode its digitized values. The quantization and encoding process cannot be infinitely accurate and can only provide an approximation of the real values present the ADC s analog input. The higher the resolution of the quantizer, the closer this approximation will be to the actual value of the signal

22 WHAT IS QUANTIZATION ERRORS? The conversion process will always introduce systematic quantization errors. for example, a 4-bit number can represent 16 voltage levels from 0 to 15. So, the maximum error =voltage range / the number of increments = 15/(2^4-1)=1 Increase the number of bits to eight, The maximum error will be= 15/(2^8-1)=0.05

23 DIGITAL TO ANALOG (D/A) CONVERSION When digital data is converted to analog, two processes take place Digital-to-Analog converter converts each sequential binary sample to a proportional voltage. The steps between each digital sample must be smoothed out to provide a transition from one voltage to another When reconstructing an encoded analog signal, the higher the sampling rate and the greater the number of bits in each sample, the more accurate the analog reconstruction can be.

24 PULSE CODE MODULATION (PCM). When an analog signal has been digitally encoded, transmitted, and reconstructed at the receiving end as an analog signal, a process known as pulse code modulation (PCM). Pulse code modulation is the most common method of digitizing data for transmission. Data transmission using PCM is serial, which means that the binary words are sent one after another in the order they were generated. The circuitry that converts the data also sends a timing, or clock, signal so the receiver can synchronize itself with the data that is being transmitted and reconstruct it accurately.

25 In order for pulse code modulation to be effective, an analog signal must be sampled at a rate that is at least twice the highest expected frequency. This number is referred to as the Nyquist Minimum. In practice, though, the sampling rate is usually closer to three times the highest expected frequency or more. This formula ensures that sampling will capture some portion of even the highest frequencies. For example, in a telephone conversation, the highest frequency encountered is about 4 khz. That means sampling must take place at the Nyquist Minimum of 8 khz to maintain a basic signal quality.

26 The Modulation see amplitude modulation See frequency modulation