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.

A Look at Low-Noise Amplifiers

Maurizio Di Paolo Emilio, who has a PhD in Physics, is an Italian telecommunications engineer who works mainly as a software developer with a focus on data acquisition systems. Emilio has authored articles about electronic designs, data acquisition systems, power supplies, and photovoltaic systems. In this article, he provides an overview of what is generally available in low-noise amplifiers (LNAs) and some of the applications.

By Maurizio Di Paolo Emilio
An LNA, or preamplifier, is an electronic amplifier used to amplify sometimes very weak signals. To minimize signal power loss, it is usually located close to the signal source (antenna or sensor). An LNA is ideal for many applications including low-temperature measurements, optical detection, and audio engineering. This article presents LNA systems and ICs.

Signal amplifiers are electronic devices that can amplify a relatively small signal from a sensor (e.g., temperature sensors and magnetic-field sensors). The parameters that describe an amplifier’s quality are:

  • Gain: The ratio between output and input power or amplitude, usually measured in decibels
  • Bandwidth: The range of frequencies in which the amplifier works correctly
  • Noise: The noise level introduced in the amplification process
  • Slew rate: The maximum rate of voltage change per unit of time
  • Overshoot: The tendency of the output to swing beyond its final value before settling down

Feedback amplifiers combine the output and input so a negative feedback opposes the original signal (see Figure 1). Feedback in amplifiers provides better performance. In particular, it increases amplification stability, reduces distortion, and increases the amplifier’s bandwidth.

 Figure 1: A feedback amplifier model is shown here.


Figure 1: A feedback amplifier model is shown.

A preamplifier amplifies an analog signal, generally in the stage that precedes a higher-power amplifier.

IC LOW-NOISE PREAMPLIFIERS
Op-amps are widely used as AC amplifiers. Linear Technology’s LT1028 or LT1128 and Analog Devices’s ADA4898 or AD8597 are especially suitable ultra-low-noise amplifiers. The LT1128 is an ultra-low-noise, high-speed op-amp. Its main characteristics are:

  • Noise voltage: 0.85 nV/√Hz at 1 kHz
  • Bandwidth: 13 MHz
  • Slew rate: 5 V/µs
  • Offset voltage: 40 µV

Both the Linear Technology and Analog Devices amplifiers have voltage noise density at 1 kHz at around 1 nV/√Hz  and also offer excellent DC precision. Texas Instruments (TI)  offers some very low-noise amplifiers. They include the OPA211, which has 1.1 nV/√Hz  noise density at a  3.6 mA from 5 V supply current and the LME49990, which has very low distortion. Maxim Integrated offers the MAX9632 with noise below 1nV/√Hz.

The op-amp can be realized with a bipolar junction transistor (BJT), as in the case of the LT1128, or a MOSFET, which works at higher frequencies and with a higher input impedance and a lower energy consumption. The differential structure is used in applications where it is necessary to eliminate the undesired common components to the two inputs. Because of this, low-frequency and DC common-mode signals (e.g., thermal drift) are eliminated at the output. A differential gain can be defined as (Ad = A2 – A1) and a common-mode gain can be defined as (Ac = A1 + A2 = 2).

An important parameter is the common-mode rejection ratio (CMRR), which is the ratio of common-mode gain to the differential-mode gain. This parameter is used to measure the  differential amplifier’s performance.

Figure 2: The design of a simple preamplifier is shown. Its main components are the Linear Technology LT112 and the Interfet IF3602 junction field-effect transistor (JFET).

Figure 2: The design of a simple preamplifier is shown. Its main components are the Linear Technology LT1128 and the Interfet IF3602 junction field-effect transistor (JFET).

Figure 2 shows a simple preamplifier’s design with 0.8 nV/√Hz at 1 kHz background noise. Its main components are the LT1128 and the Interfet IF3602 junction field-effect transistor (JFET).  The IF3602 is a dual N-channel JFET used as stage for the op-amp’s input. Figure 3 shows the gain and Figure 4 shows the noise response.

Figure 3: The gain of a low-noise preamplifier.

Figure 3: The is a low-noise preamplifier’s gain.

 

Figure 4: The noise response of a low-noise preamplifier

Figure 4: A low-noise preamplifier’s noise response is shown.

LOW NOISE PREAMPLIFIER SYSTEMS
The Stanford Research Systems SR560 low-noise voltage preamplifier has a differential front end with 4nV/√Hz input noise and a 100-MΩ input impedance (see Photo 1a). Input offset nulling is accomplished by a front-panel potentiometer, which is accessible with a small screwdriver. In addition to the signal inputs, a rear-panel TTL blanking input enables you to quickly turn the instrument’s gain on and off (see Photo 1b).

Photo 1a:The Stanford Research Systems SR560 low-noise voltage preamplifier

Photo 1a: The Stanford Research Systems SR560 low-noise voltage preamplifier. (Photo courtesy of Stanford Research Systems)

Photo 1 b: A rear-panel TTL blanking input enables you to quickly turn the Stanford Research Systems SR560 gain on and off.

Photo 1b: A rear-panel TTL blanking input enables you to quickly turn the Stanford Research Systems SR560 gain on and off. (Photo courtesy of Stanford Research Systems)

The Picotest J2180A low-noise preamplifier provides a fixed 20-dB gain while converting a 1-MΩ input impedance to a 50-Ω output impedance and 0.1-Hz to 100-MHz bandwidth (see Photo 2). The preamplifier is used to improve the sensitivity of oscilloscopes, network analyzers, and spectrum analyzers while reducing the effective noise floor and spurious response.

Photo 2: The Picotest J2180A low-noise preamplifier is shown.

Photo 2: The Picotest J2180A low-noise preamplifier is shown. (Photo courtesy of picotest.com)

Signal Recovery’s Model 5113 is among the best low-noise preamplifier systems. Its principal characteristics are:

  • Single-ended or differential input modes
  • DC to 1-MHz frequency response
  • Optional low-pass, band-pass, or high-pass signal channel filtering
  • Sleep mode to eliminate digital noise
  • Optically isolated RS-232 control interface
  • Battery or line power

The 5113 (see Photo 3 and Figure 5) is used in applications as diverse as radio astronomy, audiometry, test and measurement, process control, and general-purpose signal amplification. It’s also ideally suited to work with a range of lock-in amplifiers.

Photo 3: This is the Signal Recovery Model 5113 low-noise pre-amplifier.

Photo 3: This is the Signal Recovery Model 5113 low-noise preamplifier. (Photo courtesy of Signal Recovery)

Figure 5: Noise contour figures are shown for the Signal Recovery Model 5113.

Figure 5: Noise contour figures are shown for the Signal Recovery Model 5113.

WRAPPING UP
This article briefly introduced low-noise amplifiers, in particular IC system designs utilized in simple or more complex systems such as the Signal Recovery Model 5113, which is a classic amplifier able to obtain different frequency bands with relative gain. A similar device is the SR560, which is a high-performance, low-noise preamplifier that is ideal for a wide variety of applications including low-temperature measurements, optical detection, and audio engineering.

Moreover, the Krohn-Hite custom Models 7000 and 7008 low-noise differential preamplifiers provide a high gain amplification to 1 MHz with an AC output derived from a very-low-noise FET instrumentation amplifier.

One common LNA amplifier is a satellite communications system. The ground station receiving antenna will connect to an LNA, which is needed because the received signal is weak. The received signal is usually a little above background noise. Satellites have limited power, so they use low-power transmitters.

Telecommunications engineer Maurizio Di Paolo Emilio was born in Pescara, Italy. Working mainly as a software developer with a focus on data acquisition systems, he helped design the thermal compensation system (TCS) for the optical system used in the Virgo Experiment (an experiment for detecting gravitational waves). Maurizio currently collaborates with researchers at the University of L’Aquila on X-ray technology. He also develops data acquisition hardware and software for industrial applications and manages technical training courses. To learn more about Maurizio and his expertise, read his essay on “The Future of Data Acquisition Technology.”