Design Pwm Ppm Pam and Pulse Code Modulation Using Ics

Pulse Amplitude Modulation

Sampling Theory

Luis F. Chaparro , Aydin Akan , in Signals and Systems Using MATLAB (Third Edition), 2019

8.2.1 Pulse Amplitude Modulation

A PAM system can be visualized as a switch that closes every $T_s$ seconds for Δ seconds, and remains open otherwise. The PAM signal is thus the multiplication of the continuous-time signal $x(t)$ by a periodic signal $p(t)$ consisting of pulses of width Δ, amplitude $1/\mathrm{\Delta }$ and period $T_s$ . Thus, $x_{PAM}(t)$ consists of narrow pulses with the amplitudes of the signal within the pulse width (for narrow pulses, the pulse amplitude can be approximated by the signal amplitude at the sampling time—this is called flat-top PAM). For a small pulse width Δ, the PAM signal is

(8.2) $x_{PAM}(t)=x(t)p(t)=\frac{1}{\mathrm{\Delta }}\sum _{m}x(m{T}_s)[u(t-m{T}_s)-u(t-m{T}_s-\mathrm{\Delta })].$

Now, as a periodic signal $p(t)$ is represented by its Fourier series

$p(t)=\sum _{k=-\infty }^{\infty }{P}_k{e}^{jk{\mathrm{\Omega }}_{0}t}{\mathrm{\Omega }}_0=\frac{2\pi }{T_s}$

where $P_k$ are the Fourier series coefficients. Thus the PAM signal can be expressed as

$x_{PAM}(t)=\sum _{k=-\infty }^{\infty }{P}_{k}x(t)e^{jk{\mathrm{\Omega }}_{0}t}$

and its Fourier transform is according to the frequency-shifting property

$X_{PAM}(\mathrm{\Omega })=\sum _{k=-\infty }^{\infty }{P}_{k}X(\mathrm{\Omega }-k{\mathrm{\Omega }}_0).$

Thus, the above is a modulation of the train of pulses $p(t)$ by the signal $x(t)$ . The spectrum of $x_{PAM}(t)$ is the spectrum of $x(t)$ shifted in frequency by $\{k{\mathrm{\Omega }}_0\}$ , weighted by $P_k$ and added.

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Communication Systems, Civilian

Simon Haykin , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

III.B Pulse-Analog Modulation

In pulse-amplitude modulation (PAM), the amplitudes of regularly spaced rectangular pulses vary with the instantaneous sample values of a continuous message signal in a one-to-one fashion. This method of modulation is illustrated in Figs. 6a, b, and c, which represent a message signal, the pulse carrier, and the corresponding PAM wave, respectively.

FIGURE 6. Different forms of pulse-analog modulation for the case of a sinusoidal modulating wave. (a) Modulating wave. (b) Pulse carrier. (c) PAM wave. (d) PDM wave. (e) PPM wave. [From Haykin, S. (1983). "Communication Systems," 2nd ed. Wiley, New York. © John Wiley & Sons, Inc.]

The PAM wave s(t) is easily demodulated by a low-pass filter with a cutoff frequency just large enough to accommodate the highest frequency component of the message signal m(t). However, the reconstructed signal exhibits a slight amplitude distortion caused by the aperture effect due to lengthening of the samples.

In pulse-duration modulation (PDM), the samples of the message signal are used to vary the duration of the individual pulses. This form of modulation is also referred to as pulse-width modulation or pulse-length modulation. The modulating wave may vary with the time of occurrence of the leading edge, the trailing edge, or both edges of the pulse. In Fig. 6d the trailing edge of each pulse is varied in accordance with the message signal.

In PDM, long pulses expend considerable power during the pulse while bearing no additional information. If this unused power is subtracted from PDM, so that only time transitions are preserved, we obtain a more efficient type of pulse modulation known as pulse-position modulation (PPM). In PPM the position of a pulse relative to its unmodulated time of occurrence is varied in accordance with the message signal (Fig. 6e).

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Lab Project Examples

Nasser Kehtarnavaz , in Real-Time Digital Signal Processing, 2005

Lab 12 PAM Implementation

The pulse amplitude modulation is achieved by a PN sequence followed by the raised cosine filter for pulse shaping. The PN sequence is implemented by the linear feedback shift registers, and the raised cosine filter is implemented by using appropriate coefficients. For demonstration purposes, a 5 stage shift register structure generating random sequences with period 31 (= 2 ⁵ – 1) is chosen. The array g [ ] contains the coefficients of the raised cosine filter designed by using MATLAB. All the polyphase filters take the same PN sample as their input, and then calculate dot-products based on their own coefficients. In the code, the switch-case statement is used for the polyphase implementation. The code is shown below:

The effect of roll-off factor, which determines the bandwidth of the pulse shape, can be verified by deploying different coefficient sets corresponding to various roll-off factors between 0 and 1. The DSK output can be connected to an oscilloscope to see the eye diagram on the oscilloscope.

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The Analog-Digital Interface

James D. Broesch , in Digital Signal Processing, 2009

Encoding and Modulation

Assuming we have converted our analog signals to numbers in the digital world, there are many ways to encode the digital information into the shape of electrical signals. This process is called modulation. The most common method is probably pulse code modulation (PCM). There are two common ways of transmitting PCM, and they are parallel and serial mode. In an example of the parallel case, the information is encoded as voltage levels on a number of wires, called a parallel bus. We are using binary signals, which means that only two voltage levels are used, +5   V corresponding to a binary "1" (or "true"), and 0   V meaning a binary "0" (or "false"). Hence, every wire carrying 0 or +5   V contributes a binary digit ("bit"). A parallel bus consisting of eight wires will therefore carry 8 bits, a byte consisting of bits D0, D1–D7 (Figure 2.2).

Figure 2.2. Example, a byte (96H) encoded (weights in parenthesis) using PCM in parallel mode (parallel bus, 8 bits, eight wires) and in serial mode as an 8-bit pulse train (over one wire)

Technology Trade-offs

Parallel buses are able to transfer high information data rates, since an entire data word (a sampled value) is being transferred at a time. This transmission can take place between, for instance, an analog-to-digital converter (ADC) and a digital signal processor (DSP). One drawback with parallel buses is that they require a number of wires, taking up more board space on a printed circuit board. Another problem is that we may experience skew problems, i.e. different time delays on different wires, meaning that all bits will not arrive at the same time in the receiver end of the bus, and data words will be messed up. Since this is especially true for long, high-speed parallel buses, this kind of bus is only suited for comparatively short transmission distances. Protecting long parallel buses from picking up wireless interference or radiating interference may also be a formidable problem. The alternative way of dealing with PCM signals is to use the serial transfer mode where the bits are transferred in sequence on a single wire (see Figure 2.2). Transmission times are longer, but only one wire is needed. Board space and skew problems will be eliminated and the interference problem can be easier to solve.

There are many possible modulation schemes, such as pulse amplitude modulation (PAM), pulse position modulation (PPM), pulse number modulation (PNM), pulse width modulation (PWM) and pulse density modulation (PDM). All these modulation types are used in serial transfer mode (see Figure 2.3).

Figure 2.3. Different modulation schemes for serial mode data communication, PAM, PPM, PNM, PWM and PDM

•

Pulse amplitude modulation (PAM) The actual amplitude of the pulse represents the number being transmitted. Hence, PAM is continuous in amplitude but discrete in time. The output of a sampling circuit with a zero-order hold (ZOH) is one example of a PAM signal.

•

Pulse position modulation (PPM) A pulse of fixed width and amplitude is used to transmit the information. The actual number is represented by the position in time where the pulse appears in a given time slot.

•

Pulse number modulation (PNM) Related to PPM in the sense that we are using pulses with fixed amplitude and width. In this modulation scheme, however, many pulses are transmitted in every time slot, and the number of pulses present in the slot represents the number being transmitted.

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Pulse width modulation (PWM) Quite common modulation scheme, especially in power control and power amplifier contexts. In this case, the width (duration) T ₁ of a pulse in a given time slot T represents the number being transmitted.

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Pulse density modulation (PDM) May be viewed as a type of degenerated PWM, in the sense that not only the width of the pulses changes, but also the periodicity (frequency). The number being transmitted is represented by the density or "average" of the pulses.

Insider Info

Some signal converting and processing chips and subsystems may use different modulation methods to communicate. This may be due to standardization or due to the way the actual circuit works. One example is the so-called CODEC (coder–decoder). This is a chip used in telephone systems, containing both an analog-to-digital converter (ADC) and a digital-to-analog converter (DAC) and other necessary functions to implement a full two-way analog-digital interface for voice signals. Many such chips use a serial PCM interface. Switching devices and digital signal processors commonly have built-in interfaces to handle these types of signals.

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Digital Communication System Concepts

Vijay K. Garg , Yih-Chen Wang , in The Electrical Engineering Handbook, 2005

2.6 Pulse Amplitude Modulation

There are two operations involved in the generation of the pulse amplitude modulation (PAM) signal:

(1)

Instantaneous sampling of the message signal m(t) every T_s sec, where f_s = 1/T_s is selected according to the sampling theorem

(2)

Lengthening the duration of each sample obtained to some constant value T

These two operations are jointly referred to as sample and hold. One important reason for intentionally lengthening the duration of each sample is to avoid the use of an excessive channel bandwidth because bandwidth is inversely proportional to pulse duration.

The Fourier transform of the rectangular pulse h(t) is given as (see Figure 2.9):

FIGURE 2.9. Rectangular Pulse and Its Spectrum

(2.6) $H(f)=Tsin\text{c}(fT)e^{-j2\pi fT}.$

We observe that by using flattop samples to generate a PAM signal, we introduce amplitude distortion as well as a delay of T/2. This effect is similar to the variation in transmission frequency that is caused by the finite size of the scanning aperture in television. The distortion caused by the use of PAM to transmit an analog signal is called the aperture affect. This distortion may be corrected by using an equalizer (see Figure 2.10). The equalizer has the effect of decreasing the in-band loss of the filter as the frequency increases in such a manner to compensate for the aperture effect. For T/T_s ≤ 0.1, the amplitude distortion is less than 0.5%, in which case the need of equalization may be omitted altogether.

FIGURE 2.10. An Equalizer Application

Example 4

Sampled uniformly and then time-division multiplexed are 24 voice signals. The sampling operation involved flattop samples with 1 μs duration. The multiplexing operation includes provision for synchronization by adding an extra pulse of sufficient amplitude and also 1 μs duration. The highest frequency component of each voice signal is 3.4 kHz.

(1)

Assuming a sampling rate of 8 kHz, calculate the spacing between successive pulses of the multiplexed signal.

(2)

Repeat your calculations using Nyquist rate sampling.

$T_s=\frac{{10}^6}{8000}=125\mu \mathrm{s}\text{.}$

For 25 channels (24 voice channels +1 sync), time allocated for each channel is 125 25 = 5 μs. Since the pulse duration is 1 μs, the time between pulses is (5 − 1) = 4 μs.

The Nyquist rate is 7.48 Hz (2.2 × 3.4).

In addition:

$\begin{array}{c}{T}_s=\frac{{10}^6}{8000}=134\mu \mathrm{s}\text{.}\\ T_c=\frac{134}{25}=5.36\mu \mathrm{s}\text{.}\end{array}$

The time between pulses is 4.36 μs.

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Modulation

Rodger Ziemer , in Encyclopedia of Physical Science and Technology (Third Edition), 2002

II.C Analog Pulse Modulation

Recall that the three types of pulse-train carrier modulation, with carrier of the form (8), are PAM, PWM, and PPM. In PAM, the amplitude of the pulse carrier is modulated by the samples of the message signal taken at T _s-second intervals at a rate f _s  =   1/T _s  ≥   2W samples/second according to Nyquist's sampling theorem, where W is the bandwidth of the m(t). The PAM-modulated waveform is

(24) ${\text{x}}_{\text{c},\text{PAM}}\left(\text{t}\right)={\text{A}}_{\text{c}}\stackrel{\mathrm{\infty }}{\sum _{\text{n}=-\mathrm{\infty }}}\text{m}\left(\text{n}{\text{T}}_{\text{s}}\right)\Pi \left[\left(\text{t}-\text{n}{\text{T}}_{\text{s}}\right)/\tau \right]$

where the pulse width τ is held constant. The PAM signal (24) is called flat-top sampling, and the message can be recovered by a low-pass filter of bandwidth greater than W but less than f _s  − W. Ideally, the low-pass filter should be followed by an equalizer, which removes the distortion introduced by the flat-top pulse samples. In this idealized case, the equalizer has a frequency response that is the inverse of the spectrum of the rectangular pulse, or the inverse of

$\tau \text{sinc}(\text{f}\tau )\equiv \tau \frac{sin(\pi \text{f}\tau )}{\pi \text{f}\tau }.$

Equalization is unnecessary if τ   ≪ T _s .

The other two types of analog pulse modulation, PWM and PPM, are nonlinear modulation techniques as contrasted to PAM, which is linear. As such, their baseband spectra are significantly wider than that of m(t). This disadvantage is counterbalanced by the advantage that they are more immune to the detrimental effects of noise than PAM. PWM can be demodulated by low-pass filtering, just as for PAM. PPM can also be demodulated by low-pass filtering after converting it to PWM with the aid of a reference clock signal.

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Multiplexing

Rodger Ziemer , in Encyclopedia of Physical Science and Technology (Third Edition), 2002

I.B Time-Division Multiplexing

Time-division multiplexing can be applied in instances where the messages are represented in pulse modulation format. Figure 2 illustrates such a scheme, where pulse amplitude modulation is used to represent the messages m ₁(t), m ₂(t),…, m _n (t), which are now assumed to all be of bandwidth W Hz. A commutator samples each message in turn, which according the to sampling theorem must be at a minimum rate of 2 W samples per second per message. At the receiving end, a second commutator, which is synchronized with the one at the transmitting end, deinterleaves the samples corresponding to the respective messages. A low-pass filter then allows the recovery of each message from its sample values. Using the sampling theorem in reverse, it can be shown that the theoretical minimum transmission bandwidth requirement for TDM is exactly the same as that for FDM.

FIGURE 2. A time-division multiplexed system.

Any analog pulse modulation format can be used in TDM, and in fact, there is no restriction to the pulses representing analog messages. However, additional considerations, such as framing, are necessary when the messages are digital (to be discussed later). Time-division multiplexing avoids the crosstalk problems of FDM. However, it is necessary to maintain synchronization of all message samples and to synchronize the decommutation at the receiving end with the commutation at the transmitting end. Time-division multiplexing can also accommodate messages of unequal bandwidths through the use of creative sampling. For example, for three messages m ₁, m ₂, and m ₃ of bandwidths W, W, and 2W, the commutator would consist of one contact for m ₁, one for m ₂, and two for m ₃ in the sequence m ₁ m ₃ m ₂ m ₃ m ₁ m ₃ m ₂ m ₃….

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Power Spectral Density

Scott L. Miller , Donald Childers , in Probability and Random Processes, 2004

10.6 Engineering Application: PSDs of Digital Modulation Formats

In this section, we evaluate the PSD of a class of signals that might be used in a digital communications system. Suppose we have a sequence of data symbols {Bk} that we wish to convey across some communication medium. We can use the data symbols to determine the amplitude of a sequence of pulses that we would then transmit across the medium (e.g., a twisted copper pair, or an optical fiber). This is known as pulse amplitude modulation (PAM). If the pulse amplitudes are represented by the sequence of random variables { …, A _–2, A_{– 1}, A ₀, A₁, A₂, …} and the basic pulse shape is given by the waveform p(t), then the transmitted signal might be of the form

(10.61) $S(t)=\sum _{k=-\infty }^{\infty }{A}_{k}p(t-k{t}_S-\Theta ),$

where ts is the symbol interval (that is, one pulse is launched every ts seconds) and Θ is a random delay, which we take to be uniformly distributed over [0, t_s ) and independent of the pulse amplitudes. The addition of the random delay in the model makes the process S(0 WSS. This is not necessary and the result we will obtain would not change if we did not add this delay, but it does slightly simplify the derivation.

If the data symbols are drawn from an alphabet of size 2ⁿ symbols, then each symbol can be represented by an n-bit word, and hence the data rate of the digital communication system is r = n/t_s bits/second. The random process S(0 used to represent this data has a certain spectral content, and thus requires a communications channel with a bandwidth adequate to carry that spectral content. It would be interesting to see how the required bandwidth relates to the data rate. Toward that end, we seek to determine the PSD of the PAM signal S(0. We will find the PSD by first computing the autocorrelation function of S(0 and then converting this to PSD via the Wiener-Khintchine-Einstein theorem.

Using the definition of autocorrelation, the autocorrelation function of the PAM signal is given by

(10.62) $\begin{array}{l}{R}_{SS}(t,t+\tau )=E[s(t)S(t+\tau )]=E\left[\sum _{k=-\infty }^{\infty }\sum _{m=-\infty }^{\infty }{A}_k{A}_{m}p(t-k{t}_S-\Theta )(p(t+\tau -m{t}_S-\Theta ))\right]\\ =\sum _{K=-\infty }^{\infty }\sum _{M=-\infty }^{\infty }E[A_k{A}_m]E[p(t-k{t}_S-\Theta )p(t+\tau -m{t}_S-\Theta )]\\ =\frac{1}{t_S}\sum _{K=-\infty }^{\infty }\sum _{M=-\infty }^{\infty }E[A_k{A}_m]\underset{0}{\overset{t_S}{\int }}p(t-k{t}_S-\theta )p(t+\tau -m{t}_S-\theta )]d\theta .\end{array}$

To simplify notation, we define R_AA[N] to be the autocorrelation function of the sequence of pulse amplitudes. Note that we are assuming the sequence is stationary (at least in the wide sense). Going through a simple change of variables (v = t – kt_s – θ) then results in

(10.63) $R_{SS}(t,t+\tau )=\frac{1}{t_S}\sum _{k=-\infty }^{\infty }\sum _{m=-\infty }^{\infty }{R}_{AA}[m-k]{\int }_{t-(k+1)t_S}^{t-k_S}p(\upsilon )p(\upsilon +\tau -(m-k)t_S)d\upsilon .$

Finally, we go through one last change of variables (n = m – k) to produce

(10.64) $\begin{array}{l}{R}_{SS}(t,t+\tau )=\frac{1}{t_S}\sum _{k=-\infty }^{\infty }\sum _{n=-\infty }^{\infty }{R}_{AA}[n]{\int }_{t-(k+1)t_S}^{t-k_S}p(\upsilon )p(\upsilon +\tau -n{t}_S)d\upsilon \\ =\frac{1}{t_S}\sum _{n=-\infty }^{\infty }{R}_{AA}[n]\sum _{k=-\infty }^{\infty }{\int }_{t-(k+1)t_S}^{t-k{t}_s}p(\upsilon )p(\upsilon +\tau -n{t}_S)d\upsilon \\ =\frac{1}{t_S}\sum _{K=-\infty }^{\infty }{R}_{AA}[n]{\int }_{-\infty }^{\infty }p(\upsilon )p(\upsilon +\tau -n{t}_S)d\upsilon .\end{array}$

To aid in taking the Fourier transform of this expression, we note that the integral in this equation can be written as a convolution of p(t) with p(–t):

(10.65) ${\int }_{-\infty }^{\infty }p(\upsilon )p(\upsilon +\tau -n{t}_s)d\upsilon =p(-t){|}_{t=\tau -n{t}_S}.$

Using the fact that convolution in the time domain becomes multiplication in the frequency domain along with the time reversal and time shifting properties of Fourier transforms (see Appendix C, Review of Linear Time Invariant Systems), the transform of this convolution works out to be

(10.66) $F\left[{\int }_{-\infty }^{\infty }p(\upsilon )p(\upsilon +\tau -n{t}_S)d\upsilon \right]=|p(f){|}^2{e}^{-j2\pi fts},$

where P(f) = F[p(t)] is the Fourier transform of the pulse shape used. With this result, the PSD of the PAM signal is found by taking the transform of Equation 10.64, resulting in

(10.67) $S_{SS}(f)=\frac{|P(f){|}^2}{t_S}\sum _{n=-\infty }^{\infty }{R}_{AA}[n]e^{-j2\pi nf{t}_s}.$

It is seen from the previous equation that the PSD of a PAM signal is the product of two terms, the first of which is the magnitude squared of the pulse shapes spectrum, while the second term is essentially the PSD of the discrete sequence of amplitudes. As a result, we can control the spectral content of our PAM signal by carefully designing a pulse shape with a compact spectrum and also by introducing memory into the sequence of pulse amplitudes.

EXAMPLE 10.12: To start with, suppose the pulse amplitudes are an IID sequence of random variables that are equally likely to be +1 or –1. In that case, R_AA [n] = δ[n] and the PSD of the sequence of amplitudes is

$\sum _{n=-\infty }^{\infty }{R}_{AA}[n]e^{-j2\pi nf{t}_s}=1.$

In this case, S_SS (f) = |P(f)|²/t_s and the spectral shape of the PAM signal is completely determined by the spectral content of the pulse shape. Suppose we use as a pulse shape a square pulse of height a and width t_s,

$p(t)=arect(t/t_s)\leftrightarrow p(f)=a{t}_{s}sin\text{c(}f{t}_s\text{)}\text{.}$

The PSD of the resulting PAM signal is then S_SS (f) = a²t_ssinc²f(t_s ). Note that the factor a² t_s is the energy in each pulse sent, Ep. A sample realization of this PAM process along with a plot of the PSD is given in Figure 10.13. Most of the power in the process is contained in the main lobe, which has a bandwidth of 1/t_s (equal to the data rate), but there is also a nontrivial amount of power in the sidelobes, which die off very slowly. The high-frequency content can be attributed to the instantaneous jumps in the process. These frequency sidelobes can be suppressed by using a pulse with a smoother shape. Suppose, for example, we used a pulse that was a half cycle of a sinusoid of height a,

$\begin{array}{l}p(t)=acos\left(\frac{\pi t}{t_s}\right)\text{rect}\left(\frac{\text{t}}{{\text{t}}_{\text{s}}}\right)\leftrightarrow p(f)\\ =\frac{a{t}_s}{2}\left[sinc\left(f{t}_s-\frac{1}{2}\right)+sinc\left(f{t}_s+\frac{1}{2}\right)\right]=\frac{a{t}_s}{2\pi }\frac{cos\left(\pi f{t}_s\right)}{\frac{1}{4}-{(f{t}_s)}^2}.\end{array}$

Figure 10.13. A sample realization and the PSD of a PAM signal with square pulses.

The resulting PSD of the PAM signal with half-sinusoidal pulse shapes is then

$S_{ss}(f)=\frac{a^2{t}_s}{4{\pi }^2}\frac{{cos}^2(\pi f{t}_s)}{\left[\frac{1}{4}-{(f{t}_s)}^2\right]}.$

In this case, the energy in each pulse is Ep = a²t_s/2. As shown in Figure 10.14, the main lobe is now 50 percent wider than it was with square pulses, but the sidelobes decay much more rapidly.

Figure 10.14. A sample realization and the PSD of a PAM signal with half-sinusoidal pulses.

EXAMPLE 10.13: In this example, we show how the spectrum of the PAM signal can also be manipulated by adding memory to the sequence of pulse amplitudes. Suppose the data to be transmitted {…, B_{– 2} , B_– 1, B ₀ , B₁, B ₂ , …} is an IID sequence of Bernoulli random variables, Bk ∈ {+1, −1}. In the previous example, we formed the pulse amplitudes according to A_k = B_k. Suppose instead that we formed these amplitudes according to A_k = B_k + B_{k –1} . Now the pulse amplitudes can take on three values (even though each pulse still carries only 1 bit of information. This is known as duobinary precoding. The resulting autocorrelation function for the sequence of pulse amplitudes is

$R_{AA}[n]=E[A_k{A}_{k+n}]=E[(B_k+B_{k-1})(B_{k+n}+B_{k+n-1})]=\{\begin{array}{cc}2& n=0\\ 1& n=\pm 1\\ 0& \text{otherwise}\end{array}.$

The PSD of this sequence of pulse amplitudes is then

$\begin{array}{l}\sum _{n=-\infty }^{\infty }{R}_{AA}[n]e^{-j2\pi f{t}_s}=2+e^{j2\pi f{t}_s}+e^{-j2\pi nf{t}_s}\\ =2+2cos(2\pi f{t}_s)=4{cos}^2(\pi f{t}_s).\end{array}$

This expression then multiplies whatever spectral shape results from the pulse shape chosen. The PSD of duobinary PAM with square pulses is illustrated in Figure 10.15. In this case, the duobinary precoding has the benefit of suppressing the frequency sidelobes without broadening the main lobe.

Figure 10.15. A sample realization and the PSD of a PAM signal with duobinary precoding and square pulses.

EXAMPLE 10.14: The following MATLAB code creates a realization of a binary PAM signal where the pulse amplitudes are either +1 or −1. In this example, a half-sinusoidal pulse shape is used, but the code is written so that it is easy to change the pulse shape (just change the sixth line where the pulse shape is assigned to the variable p). After a realization of the PAM signal is created, the PSD of the resulting signal is estimated using the segmented periodogram technique given in Example 10.10. The resulting PSD estimate is shown in Figure 10.16. Note the agreement between the estimate and the actual PSD shown in Figure 10.14. The reader is encouraged to try running this program with different pulse shapes to see how the pulse shape changes the spectrum of the PAM signal.

Figure 10.16. An estimate of the PSD of a PAM signal with half-sinusoidal pulse shapes.

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Wavelength-Division-Multiplexed Passive Optical Networks (WDM PONs)

Y.C. Chung , Y. Takushima , in Optical Fiber Telecommunications (Sixth Edition), 2013

23.5.3 Utilization of advanced modulation formats

To overcome the limited modulation bandwidth of the inexpensive colorless light sources such as the RSOAs and utilize them in the high-speed WDM PON, the baud rate of the signal can be reduced by using the advanced modulation formats. Various modulation formats have already been examined for this purpose including the 4-ary pulse amplitude modulation (PAM) [90], direct duobinary [89], OFDM [198], and QPSK [141,197]. However, the use of these multi-level modulation formats can increase the complexity of the transmitter/receiver and degrades the receiver sensitivity [206]. Thus, it is critical to select the proper modulation format for the cost-effective implementation of the high-speed WDM PON. In this sense, it is desirable to avoid the modulation formats which require the use of expensive external modulators.

When the 4-ary PAM format is used, the baud rate of the driving signal is reduced to half. Thus, this format can alleviate the impacts of the limited modulation bandwidth of the RSOA as well as the sensitivity to the chromatic dispersion significantly. In addition, it is relatively simple to generate the 4-ary PAM signal (since it only requires modulating the RSOA with four-level electrical signal). It has been demonstrated that this format can be used to generate the 11-Gb/s signal (5.5-Gbaud) by using an RSOA having a bandwidth of merely 2.2   GHz [90]. This signal can be transmitted over >20   km with a relatively small penalty induced by the chromatic dispersion.

The duobinary signal has also been used to generate the 10-Gb/s signal from the bandwidth-limited RSOA [89]. For this purpose, the 10-Gb/s driving signal is filtered out by using a low-pass filter having a cutoff frequency of 2.5   GHz (i.e. 1/4 of the bit rate). As a result, the filtered signal has three levels (−1,   0,   +1). When this direct duobinary signal is applied to the RSOA under a certain bias condition, it is transmitted as a three-level PAM signal. At the receiver, the dc component in the three-level signal is eliminated, and then the binary signal (0,   1) is recovered by rectification. By using this format together with the pre-emphasis technique, the 10-Gb/s transmission has been demonstrated by using an RSOA having a bandwidth of only 1.5   GHz.

There have been some attempts to utilize the directly modulated OFDM format in the RSOA-based WDM PON [198]. In this demonstration, RSOA is directly modulated with an OFDM signal at the ONU. Thus, the intensity of the RSOA is modulated with the OFDM signal and there is no need to utilize the expensive external modulator. In this OFDM signal, its subcarriers are modulated in the quadrature amplitude modulation (QAM) format. As a result, the spectrum of the driving electrical signal becomes very compact. It has been demonstrated that, by using this direct OFDM signal, the 10-Gb/s transmission can be achieved by using an RSOA having a modulation bandwidth of only 1   GHz [198].

In the previous demonstrations described above, the RSOAs have been used to generate the intensity-modulated multi-level signals. However, when the RSOA is directly modulated, its refractive index is modulated as well as the gain due to the modulated carrier density. In fact, it is well known that the semiconductor optical amplifier usually has a large chirp (i.e. large linewidth enhancement factor) [204,212]. Thus, the RSOA can also be used to generate the multi-level phase-modulated signal such as the QPSK signal, as shown in Figure 23.21 [141,197]. This is attractive since the phase-modulated signals have much superior sensitivities to the intensity-modulated signals. For example, the receiver sensitivity of the QPSK signal is better than that of the 4-level PAM signal by >8   dB [213]. However, for its detection, it is necessary to utilize the coherent detection or the differential detection technique. It is also interesting to note that the receiver sensitivities of the QPSK and BPSK signals are the same (when the coherent receivers are used). Thus, by modulating the RSOA for the QPSK signal, it is possible to achieve the high-speed operation without sacrificing the receiver sensitivity. Recently, there have been many efforts to develop the coherent detection technique cost-effective enough for use in the WDM PON, as described in Section 23.4.3. By using such a coherent receiver and the QPSK signal generated by directly modulating an RSOA having a bandwidth of 2.2   GHz, it has been demonstrated that 80-km-reach, 10-Gb/s WDM PON can be realized without using any remote optical amplifiers [141].

Figure 23.21. (a) Generation of the QPSK signal by directly modulating an RSOA with 4-level PAM signal and (b) the measured constellation diagram of the generated QPSK signal [197]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this book.)

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The Likely Course of Silicon Photonics

Daryl Inniss , Roy Rubenstein , in Silicon Photonics, 2017

8.2.1 Near-Term Opportunities: 2016–21

Fig. 8.1 shows the likely timescales of emerging markets for silicon photonics as well as important developments. As shown, telecom and datacom are markets where silicon photonics is already playing a role, and this is the obvious main opportunity for the next 5 years.

Figure 8.1. Opportunities for silicon photonics and application timings.

These opportunities include 100-Gb transceivers from mid-reach links in the data center and 100-Gb and faster modules for coherent optical transport. Mid-reach optics spans 0.5–2   km and is served currently by such module designs as PSM4 and the CWDM4 and CLR4. There are also 100-, 200-, and 400-Gb coherent applications using the CFP and CFP2-ACO designs.

It is also likely that multiwavelength terabit-plus coherent photonic integrated circuits will appear, as indicated by the emerging CFP8-ACO pluggable module [6].

Also shown are Microsoft's Madison module requirements. Microsoft has data centers made up of several buildings distributed on a campus that are separated by distances of 2   km. It also has buildings making up a data center spread as far as 70   km apart. The Madison modules are the optical components industry's answer to Microsoft's demand for optics outside standard multisource agreement initiatives—an example of an Internet content provider driving new optical developments.

The first Madison QSFP28 module will support 100   Gb using just two wavelengths, each 25   Gb, coupled with four-level pulse-amplitude modulation (PAM4) signaling. Microsoft is working with semiconductor supplier Inphi to develop the module. Microsoft is also talking to interested optical module makers to develop a follow-on, known as Madison 1.5, to create a 100-Gb QSFP28 design using one wavelength only based on 50-GBd signaling and PAM4. The specification is to achieve a total bandwidth of between 6.4 and 7.2   Tb down a fiber.

Lastly, Microsoft is also interested in a tailored coherent optics solution that will allow up to 38   Tb transmission. Madison 2.0 is designated to be implemented using the Consortium of On-Board Optics (COBO) form factor (see Sections 5.5.1 and 7.5.4).

One multisource agreement, the OpenOptics wavelength division multiplexing design cofounded by Ranovus and Mellanox, is being aimed at higher-than-100-Gb links within the data center [7]. New higher-capacity pluggable form factors will also be launched during this period, such as the QSFP-DD, the µQSFP, and the QSFP56.

Data center networking will also drive new Ethernet speed standards such as 25-, 50-, 200-, and 400-Gb Ethernet. The simplest way to implement 50-Gb signaling will be to use two 25-Gb lanes but that will quickly be replaced with more elegant 50-Gb single lanes. A 50-Gb lane—25-GBd optics and PAM4 modulation—will enable these new-speed Ethernet configurations. And the combination of 50-GBd optics and PAM4 will enable 100-Gb single lanes. Mellanox is one company that will use 50-Gb nonreturn-to-zero signaling and is confident that the approach can be extended to 100-Gb using its silicon photonics technology. But at 100-Gb, copackaged optics will be needed.

Midboard optics designs using COBO are also to be expected, with first hardware supporting 400 and 800   Gb/s projected toward the end of 2017. Midboard optics will become a more pressing need as switch chip companies announce 6.4-, 12.8-, and 25.6-Tb switch silicon.

New system architectures using silicon photonics will also be deployed in the near term, such as Rockley's switch architecture for the data center, and chip-to-chip optical designs. Other innovations will be developed by start-ups that are still in stealth mode, and silicon photonics will also be adopted by systems vendors in their own equipment, developments that are not always announced.

In turn, it is possible that high-capacity sliceable transponders will emerge for long-distance optical transmission toward the end of the near term.

Thus the number and diversity of silicon photonics products will grow as we move into the 2020s.

While this book has focused on emerging silicon photonic opportunities for datacom and telecom, spectroscopic products will also benefit from photonic integration on a CMOS platform. The new Fourier transform infrared spectrometer being developed by Lumux Technology is one example [8].

The sensor is a potential high-volume, low-cost product for applications like environmental monitoring in the oil and gas industries. The company's goal is a consumer spectrometer that works with personal mobile devices.

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Design Pwm Ppm Pam and Pulse Code Modulation Using Ics

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