Triangulation, Trilateration, or Multilateration? (EE Tip #125)

Local Positioning System (LPS) and GPS (not just the US system) both use several transmitters to enable a receiver to calculate its geographical position. Several techniques are possible, each with its advantages and drawbacks. The important thing in all these techniques is the notion of a direct path (line of sight, or LoS). In effect, if the transmitter signal has not taken the shortest path to the receiver, the distance between them calculated by the receiver will be incorrect, since the receiver does not know the route taken by the radio signal.

Three mathematical techniques are usually used for calculating the position of a receiver from signals received from several transmitters: triangulation, trilateration, and multilateration. The last two are very similar, but should not be confused.

Triangulation

Triangulation (Figure 1) is a very ancient technique, said to date from over 2,500 years ago, when it was used by the Greek philosopher and astronomer Thales of Miletus to measure (with surprising accuracy) the radius of the Earth’s orbit around the Sun.

Triangulation

Figure 1—Triangulation: you are at A, from where you can see B and C. If you know their geographical positions, you can find your own position with the help of a compass.

It allows an observer to calculate their position by measuring two directions towards two reference points. Since the positions of the reference points are known, it is hence possible to construct a triangle where one of the sides and two of the angles are known, with the observer at the third point. This information is enough to defi ne the triangle completely and hence deduce the position of the observer.

Using triangulation with transmitters requires the angle of incidence (angle of arrival, or AoA) of a radio signal to be measured. This can be done using several antennas placed side by side (an array of antennas, for example, Figure 2) and to measure the phase difference between the signals received by the antennas.

Antenna array

Figure 2—An antenna array makes it possible to measure the angle of incidence of a radio signal, and hence its direction.

If the distance between the antennas is small, the incident front of the signal may be considered as straight, and the calculation of the angle will be fairly accurate. It’s also possible to use a directional antenna to determine the position of a transmitter. The antenna orientation producing the strongest signal indicates the direction of the transmitter. All you then have to do is take two measurements from known transmitters in order to be able to apply triangulation.

Trilateration

This technique requires the distance between the receiver and transmitter to be measured. This can be done using a Received Signal Strength Indicator (RSSI), or else from the time of arrival (ToA)—or time of flight (ToF) Figure 3—of the signal, provided that the receiver and transmitter are synchronized — for example, by means of a common timebase, as in GPS.

Arrival time

Figure 3—The length of the arrows corresponds to the arrival time at receiver P of the signals broadcast by three transmitters A, B, and C. It forms a measurement of the distances between the transmitters and the receiver.

Thus, when receiving a signal from a single transmitter, we can situate ourselves on a circle (for simplicity, let’s confi ne ourselves to two dimensions and ideal transmission conditions) with the transmitter at the center. Not very accurate. It gets better with two transmitters — now there are only two positions possible: the two points where the circles around the two transmitters intersect. Adding a third transmitter enables us to eliminate one of these two possibilities (Figure 4).

Trilateration

Figure 4—2-D trilateration. In 3-D, another transmitter has to be added in order to determine a position unambiguously.

When we extend trilateration to three dimensions, the circles become spheres. Now we need to add one more transmitter in order to fi nd the position of the receiver, as the intersection of two spheres is no longer at two points, but is a circle (assuming we ignore the trivial point when they touch). This explains why a GPS needs to “see” at least four satellites to work.

Multilateration

Using a single receiver listening to the signals (pulses, for example) from two synchronized transmitters, it is possible to measure the difference between the arrival times (time difference of arrival, or TDoA) of the two signals at the receiver. Then the principle is similar to trilateration, except that we no longer fi nd ourselves on a circle or a sphere, but on a hyperbola (2D) or a hyperboloid (3D). Here too, we need four transmitters to enable the receiver to calculate its position accurately.

The advantage of multilateration is that the receiver doesn’t need to know at what instant the signals were transmitted—hence the receiver doesn’t need to be synchronized with the transmitters. The signals, and hence the electronics, can be kept simple. The LORAN and DECCA systems, for example, work like this.—Clemens Valens, “Geolocalization without GPS,” Elektor, February 2011.

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.

Build an Inexpensive Wireless Water Alarm

The best DIY electrical engineering projects are effective, simple, and inexpensive. Devlin Gualtieri’s design of a wireless water alarm, which he describes in Circuit Cellar’s February issue, meets all those requirements.

Like most homeowners, Gualtieri has discovered water leaks in his northern New Jersey home after the damage has already started.

“In all cases, an early warning about water on the floor would have prevented a lot of the resulting damage,” he says.

You can certainly buy water alarm systems that will alert you to everything from a leak in a well-water storage tank to moisture from a cracked boiler. But they typically work with proprietary and expensive home-alarm systems that also charge a monthly “monitoring” fee.

“As an advocate of free and open-source software, it’s not surprising that I object to such schemes,” Gualtieri says.

In February’s Circuit Cellar magazine, now available for membership download or single-issue purchase, Gualtieri describes his battery-operated water alarm. The system, which includes a number of wireless units that signal a single receiver, includes a wireless receiver, audible alarm, and battery monitor to indicate low power.

Photo 1: An interdigital water detection sensor is shown. Alternate rows are lengths of AWG 22 copper wire, which is either bare or has its insulation removed. The sensor is shown mounted to the bottom of the box containing the water alarm circuitry. I attached it with double-stick foam tape, but silicone adhesive should also work.

Photo 1: An interdigital water detection sensor is shown. Alternate rows are lengths of AWG 22 copper wire, which is either bare or has its insulation removed. The sensor is shown mounted to the bottom of the box containing the water alarm circuitry. I attached it with double-stick foam tape, but silicone adhesive should also work.

Because water conducts electricity, Gualtieri sensors are DIY interdigital electrodes that can lie flat on a surface to detect the first presence of water. And their design couldn’t be easier.

“You can simply wind two parallel coils of 22 AWG wire on a perforated board about 2″ by 4″, he says. (See Photo 1.)

He also shares a number of design “tricks,” including one he used to make his low-battery alert work:

“A battery monitor is an important feature of any battery-powered alarm circuit. The Microchip Technology PIC12F675 microcontroller I used in my alarm circuit has 10-bit ADCs that can be optionally assigned to the I/O pins. However, the problem is that the reference voltage for this conversion comes from the battery itself. As the battery drains from 100% downward, so does the voltage reference, so no voltage change would be registered.

Figure 1: This is the portion of the water alarm circuit used for the battery monitor. The series diodes offer a 1.33-V total  drop, which offers a reference voltage so the ADC can see changes in the battery voltage.

Figure 1: This is the portion of the water alarm circuit used for the battery monitor. The series diodes offer a 1.33-V total drop, which offers a reference voltage so the ADC can see changes in the battery voltage.

“I used a simple mathematical trick to enable battery monitoring. Figure 1 shows a portion of the schematic diagram. As you can see, the analog input pin connects to an output pin, which is at the battery voltage when it’s high through a series connection of four small signal diodes (1N4148). The 1-MΩ resistor in series with the diodes limits their current to a few microamps when the output pin is energized. At such low current, the voltage drop across each diode is about 0.35 V. An actual measurement showed the total voltage drop across the four diodes to be 1.33 V.

“This voltage actually presents a new reference value for my analog conversion. The analog conversion now provides the following digital values:

EQ1Table 1 shows the digital values as a function of battery voltage. The nominal voltage of three alkaline cells is 4.75 V. The nominal voltage of three lithium cells is 5.4 V. The PIC12F675 functions from approximately 2 to 6.5 V, but the wireless transmitter needs as much voltage as possible to generate a reliable signal. I arbitrarily coded the battery alarm at 685, or a little above 4 V. That way, there’s still enough power to energize the wireless transmitter at a useful power level.”

Table 1
Battery Voltage ADC Value
5 751
4.75 737
4.5 721
4.24 704
4 683
3.75 661

 

Gaultieri’s wireless transmitter, utilizing lower-frequency bands, is also straightforward.

Photo 2 shows one of the transmitter modules I used in my system,” he says. “The round device is a surface acoustic wave (SAW) resonator. It just takes a few components to transform this into a low-power transmitter operable over a wide supply voltage range, up to 12 V. The companion receiver module is also shown. My alarm has a 916.5-MHz operating frequency, but 433 MHz is a more popular alarm frequency with many similar modules.”

These transmitter and receiver modules are used in the water alarm. The modules operate at 916.5 MHz, but 433 MHz is a more common alarm frequency with similar modules. The scale is inches.

Photo 2: These transmitter and receiver modules are used in the water alarm. The modules operate at 916.5 MHz, but 433 MHz is a more common alarm frequency with similar modules. The scale is inches.

Gualtieri goes on to describe the alarm circuitry (see Photo 3) and receiver circuit (see Photo 4.)

For more details on this easy and affordable early-warning water alarm, check out the February issue.

Photo 3: This is the water alarm’s interior. The transmitter module with its antenna can be seen in the upper right. The battery holder was harvested from a $1 LED flashlight. The box is 2.25“ × 3.5“, excluding the tabs.

Photo 3: This is the water alarm’s interior. The transmitter module with its antenna can be seen in the upper right. The battery holder was harvested from a $1 LED flashlight. The box is 2.25“ × 3.5“, excluding the tabs.

Photo 4: Here is my receiver circuit. One connector was used to monitor the signal strength voltage during development. The other connector feeds an input on a home alarm system. The short antenna reveals its 916.5-MHz operating frequency. Modules with a 433-MHz frequency will have a longer antenna.

Photo 4: Here is my receiver circuit. One connector was used to monitor the signal strength voltage during development. The other connector feeds an input on a home alarm system. The short antenna reveals its 916.5-MHz operating frequency. Modules with a 433-MHz frequency will have a longer antenna.

 

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.”

Small Plug-In Embedded Cellular Modem

Skywire plug-in modem

Skywire plug-in modem

The Skywire is a small plug-in embedded cellular modem. It uses a standard XBee form factor and 1xRTT CDMA operating mode to help developers minimize hardware and network costs. Its U.FL port ensures antenna flexibility.

The Skywire modem features a Telit CE910-DUAL wireless module and is available with bundled CDMA 1xRTT data plans from leading carriers, enabling developers to add fully compliant cellular connectivity without applying for certification. Future versions of the Skywire will support GSM and LTE. Skywire is smaller than many other embedded solutions and simple to deploy due to its bundled carrier service plans.

Skywire is available with a complete development kit that includes the cellular modem, a baseboard, an antenna, a power supply, debug cables, and a cellular service plan. The Skywire baseboard is an Arduino shield, which enables direct connection to an Arduino microcontroller.

Skywire modems cost $129 individually and $99 for 1,000-unit quantities. A complete development kit including the modem costs $262.

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