Pulse-Shaping Basics

Pulse shaping (i.e., base-band filtering) can vastly improve the behavior of wired or wireless communication links in an electrical system. With that in mind, Circuit Cellar columnist Robert Lacoste explains the advantages of filtering and examines Fourier transforms; random non-return-to-zero NRZ signaling; and low-pass, Gaussian, Nyquist, and raised-cosine filters.

Lacoste’s article, which appears in Circuit Cellar’s April 2014 issue, includes an abundance of graphic simulations created with Scilab Enterprises’s open-source software. The simulations will help readers grasp the details of pulse shaping, even if they aren’t math experts. (Note: You can download the Scilab source files Lacoste developed for his article from Circuit Cellar’s FTP site.)

Excerpts from Lacoste’s article below explain the importance of filtering and provide a closer look at low-pass filters:

WHY FILTERING?
I’ll begin with an example. Imagine you have a 1-Mbps continuous digital signal you need to transmit between two points. You don’t want to specifically encode these bits; you just want to transfer them one by one as they are.

Before transmission, you will need to transform the 1 and 0s into an actual analog signal any way you like. You can use a straightforward method. Simply define a pair of voltages (e.g., 0 and 5 V) and put 0 V on the line for a 0-level bit and put 5 V on the line for a 1-level bit.


This method is pedantically called non-return-to-zero (NRZ). This is exactly what a TTL UART is doing; there is nothing new here. This analog signal (i.e., the base-band signal) can then be sent through the transmission channel and received at the other end (see top image in Figure 1).


Note: In this article I am not considering any specific transmission channel. It could range from a simple pair of copper wires to elaborate wireless links using amplitude, frequency and/or phase modulation, power line modems, or even optical links. Everything I will discuss will basically be applicable to any kind of transmission as it is linked to the base-band signal encoding prior to any modulation.

Directly transmitting a raw digital signal, such as this 1-Mbps non-return-to-zero (NRZ) stream (at top), is a waste of bandwidth. b—Using a pulse-shaping filter (bottom) reduces the required bandwidth for the same bit rate, but with a risk of increased transmission errors.

Figure 1: Directly transmitting a raw digital signal, such as this 1-Mbps non-return-to-zero (NRZ) stream (top), is a waste of bandwidth. Using a pulse-shaping filter (bottom) reduces the required bandwidth for the same bit rate, but with a risk of increased transmission errors.


Now, what is the issue when using simple 0/5-V NRZ encoding? Bandwidth efficiency. You will use more megahertz than needed for your 1-Mbps signal transmission. This may not be an issue if the channel has plenty of extra capacity (e.g., if you are using a Category 6 1-Gbps-compliant shielded twisted pair cable to transmit these 1 Mbps over a couple of meters).


Unfortunately, in real life you will often need to optimize the bandwidth. This could be for cost reasons, for environmental concerns (e.g., EMC perturbations), for regulatory issues (e.g., RF channelization), or simply to increase the effective bit rate as much as possible for a given channel.


Therefore, a good engineering practice is to use just the required bandwidth through a pulse-shaping filter. This filter is fitted between your data source and the transmitter (see bottom of Figure 1).


The filter’s goal is to reduce as much as possible the occupied bandwidth of your base-band signal without affecting the system performance in terms of bit error rate. These may seem like contradictory requirements. How can you design such a filter? That’s what I will try to explain in this article….


LOW-PASS FILTERS

A base-band filter is needed between the binary signal source and the transmission media or modulator. But what characteristics should this filter include? It must attenuate as quickly as possible the unnecessary high frequencies. But it must also enable the receiver to decode the signal without errors, or more exactly without more errors than specified. You will need a low-pass filter to limit the high frequencies. As a first example, I used a classic Butterworth second-order filter with varying cut-off frequencies to make the simulation. Figure 2 shows the results. Let me explain the graphs.

Figure 2: This random non-return-to-zero (NRZ) signal (top row) was passed through a second-order Butterworth low-pass filter. When the cut-off frequency is low (310 kHz), the filtered signal (middle row) is distorted and the eye diagram is closed. With a higher cutoff (410 kHz, bottom row), the intersymbol interference (ISI) is lower but the frequency content is visible up to 2 MHz.

Figure 2: This random non-return-to-zero (NRZ) signal (top row) was passed through a second-order Butterworth low-pass filter. When the cut-off frequency is low (310 kHz), the filtered signal (middle row) is distorted and the eye diagram is closed. With a higher cutoff (410 kHz, bottom row), the intersymbol interference (ISI) is lower but the frequency content is visible up to 2 MHz.

The leftmost column shows the signal frequency spectrum after filtering with the filter frequency response in red as a reference. The middle column shows a couple of bits of the filtered signal (i.e., in the time domain), as if you were using an oscilloscope. Last, the rightmost column shows the received signal’s so-called “eye pattern.” This may seem impressive, but the concept is very simple.

Imagine you have an oscilloscope. Trigger it on any rising or falling front of the signal, scale the display to show one bit time in the middle of the screen, and accumulate plenty of random bits on the screen. You’ve got the eye diagram. It provides a visual representation of the difficulty the receiver will have to recover the bits. The more “open” the eye, the easier it is. Moreover, if the successive bits’ trajectories don’t superpose to each other, there is a kind of memory effect. The voltage for a given bit varies depending on the previously transmitted bits. This phenomenon is called intersymbol interference (ISI) and it makes life significantly more difficult for decoding.


Take another look at the Butterworth filter simulations. The first line is the unfiltered signal as a reference (see Figure 2, top row). The second line with a 3-dB, 310-kHz cut-off frequency shows a frequency spectrum significantly reduced after 1 MHz but with a high level of ISI. The eye diagram is nearly closed (see Figure 2, middle row). The third line shows the result with a 410-kHz Butterworth low-pass filter (see Figure 2, bottom row). Its ISI is significantly lower, even if it is still visible. (The successive spot trajectories don’t pass through the same single point.) Anyway, the frequency spectrum is far cleaner than the raw signal, at least from 2 MHz.

Lacoste’s article serves as solid introduction to the broad subject of pulse-shaping. And it concludes by re-emphasizing a few important points and additional resources for readers:

Transmitting a raw digital signal on any medium is a waste of bandwidth. A filter can drastically improve the performance. However, this filter must be well designed to minimize intersymbol interference.

The ideal solution, namely the Nyquist filter, enables you to restrict the used spectrum to half the transmitted bit rate. However, this filter is just a mathematician’s dream. Raised cosine filters and Gaussian filters are two classes of real-life filters that can provide an adequate complexity vs performance ratio.

At least you will no longer be surprised if you see references to such filters in electronic parts’ datasheets. As an example, see Figure 3, which is a block diagram of Analog Devices’s ADF7021 high-performance RF transceiver.

This is a block diagram of Analog Devices’s ADF7021 high-performance transceiver. On the bottom right there is a “Gaussian/raised cosine filter” block, which is a key factor in efficient RF bandwidth usage.

Figure 3: This is a block diagram of Analog Devices’s ADF7021 high-performance transceiver. On the bottom right there is a “Gaussian/raised cosine filter” block, which is a key factor in efficient RF bandwidth usage.

The subject is not easy and can be easily misunderstood. I hope this article will encourage you to learn more about the subject. Bernard Sklar’s book Digital Communications: Fundamentals and Applications is a good reference. Playing with simulations is also a good way to understand, so don’t hesitate to read and modify the Scilab examples I provided for you on Circuit Cellar’s FTP site.  

Lacoste’s full article is in the April issue, now available for membership download or single issue purchase. And for more information about improving the efficiency of wireless communication links, check out Lacoste’s 2011 article “Line-Coding Techniques,” Circuit Cellar 255, which tells you how you can encode your bits before transmission.

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Wireless Data Links (Part 2): Transmitters and Antennas

If you built your own ham radio “back in the day,” you’ll recall the frustration of putting it together with components that were basic at best.

But as columnist George Novacek points out in the second installment of his series examining wireless data links: “Today you can purchase excellent, reasonably priced low-power gear for data communications off the shelf.”

Transmitter and receiver

Photo 1: SparkFun Electronics’s WRL-10524 transmitter and WRL-10532 receiver are low cost, basic, and work well.

Part 2 of Novacek’s series, appearing in the March issue, looks at transmitters and antennas.

In one section, Novacek expands upon the five basic data-transmitter modules—a data encoder, a modulator, a carrier frequency generator, an RF output amplifier, and an antenna:

Low-power data transmitters often integrate the modulator, the carrier frequency generator, and the amplifier into one circuit. A single transistor can do the job. I’ll discuss antennas later. When a transmitter and a receiver are combined into one unit, it’s called a transceiver.

Modulation may not be needed in some simple applications where the mere presence of a carrier is detected to initiate an action. A simple push button will suffice, but this is rarely used as it is subject to false triggering by other transmitters working in the area in the same frequency band.

Digital encoder and decoder ICs are available for simple devices (e.g., garage door openers) or keyless entry where just an on or off output is required from the receiver. These ICs generate a data packet for transmission. If the received packet matches the data stored in the decoder, an action is initiated. Typical examples include Holtek Semiconductor HT12E encoders and HT12D decoders and Freescale Semiconductor MC145026, MC145027, and MC145028 encoder and decoder pairs. For data communications a similar but more advanced scheme is used. I’ll address this when I discuss receivers (coming up in Part 3 of this series).

Novacek’s column goes on to explain modulation types, including OOK and ASK modulation:

OOK modulation is achieved by feeding the Data In line with a 0-to+V-level  datastream. ASK modulation can be achieved by the data varying the transistor biasing to swing the RF output between 100% and typically 30% to 50% amplitude. I prefer to add a separate modulator.

The advantage of ASK as opposed to OOK modulation is that the carrier is always present, thus the receiver is not required to repeatedly synchronize to it. Different manufacturers’ specifications claim substantially higher achievable data rates with ASK rather than OOK.

For instance, Photo 1 shows a SparkFun Electronics WRL-10534 transmitter and a WRL-10532 receiver set for 433.9 MHz (a 315-MHz set is also available), which costs less than $10. It is a bare-bones design, but it works well. When you build supporting circuits around it you can get excellent results. The set is a good starting point for experimentation.

The article also includes tips on a transceiver you can purchase to save time in developing ancillary circuits (XBee), while noting a variety of transceiver, receiver, and transmitter modules are available from manufacturers such as Maxim Integrated, Micrel, and RF Monolithics (RFM).  In addition, the article discusses design and optimization of the three forms of antennas: a straight conductor (monopole), a coil (helical), and a loop.

“These can be external, internal, or even etched onto the PCB (e.g., keyless entry fobs) to minimize the size,” Novacek says.

Do you need advice on what to consider when choosing an antenna for your design?  Find these tips and more in Novacek’s March issue article.

Wireless Product Regulations (EE Tip #123)

Are you working on a wireless design that you’d like to bring to market? If so, be sure to anticipate regulatory constraints right from the start. Planning upfront will save you a lot of time, money, and hassle.

Electrical engineer Robert Lacoste notes:

Unless you’re working on a prototype that won’t ever leave your lab, there is a high probability that you will need to comply with some regulations. FCC and CE are the most common, but you’ll also find local regulations as well as product-class requirements for a broad range of products, from toys to safety devices to motor-based machines. (Refer to my article “CE Marking in a Nutshell,” Circuit Cellar 257, for more information.CE Mark

Let’s say you design a wireless gizmo for the U.S. market and later find that your customers want to use it in Europe. This means you lose years of work, as well as profits, because you overlooked your customers’ needs and the regulations in place in different locales.

When designing a wireless gizmo that will be used outside the U.S., having adequate information from the start will help you make good decisions. An example would be selecting a worldwide-enabled band like the ubiquitous 2.4 GHz. Similarly, don’t forget that EMC/ESD regulations require that nearly all inputs and outputs should be protected against surge transients. If you forget this, your beautiful, expensive prototype may not survive its first day at the test lab.

Lacoste’s full article appeared in Circuit Cellar’s anniversary issue, CC25.

An Organized Space for Programming, Writing, and Soldering

AndersonPhoto1

Photo 1—This is Anderson’s desk when he is not working on any project. “I store all my ‘gear’ in a big plastic bin with several smaller bins inside, which keeps the mess down. I have a few other smaller storage bins as well hidden here and there,” Anderson explained.

AndersonPhoto2

Photo 2—Here is Anderson’s area set up for soldering and running his oscilloscope. “I use a soldering mat to protect my desk surface,” he says. “The biggest issue I have is the power cords from different things getting in my way.”

Al Anderson’s den is the location for a variety of ongoing projects—from programming to writing to soldering. He uses several plastic bins to keep his equipment neatly organized.

Anderson is the IT Director for Salish Kootenai College, a small tribal college based in Pablo, MT. He described some of his workspace features via e-mail:

I work on many different projects. Lately I have been doing more programming. I am getting ready to write a book on the Xojo development system.

Another project I have in the works is using a Raspberry Pi to control my hot tub. The hot tub is about 20 years old, and I want to have better control over what it is doing. Plus I want it to have several features. One feature is a wireless interface that would be accessible from inside the house. The other is a web control of the hot tub so I can turn it on when we are still driving back from skiing to soak my tired old bones.

I am also working on a home yard sprinkler system. I laid some of the pipe last fall and have been working on and off with the controller. This spring I will put in the sprinkler heads and rest of the pipe. I tend to like working with small controllers (e.g., the Raspberry Pi, BeagleBoard’s BeagleBone, and Arduino) and I have a lot of those boards in various states.

Anderson’s article about a Raspberry Pi-based monitoring device will appear in Circuit Cellar’s April issue. You can follow him on Twitter at @skcalanderson.