Editor's Picks

Phase Noise and Additive Phase Noise Limit Radar and Communications System Performance

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Phase noise and its time-domain counterpart, jitter have been studied in radar and communications systems since the phenomenon was first observed. Though always a concern, recent advances in high-speed digital modulation schemes and advanced radar, which also used complex digital modulation techniques for pulse compression, have led to radar and communication systems being more susceptible to phase noise performance degradation.

High-speed Digital Modulation Methods are More Phase Noise Susceptible

In a standard constellation diagram, or constellation plot, phase noise can be observed as the rotational blurring of the symbol location, over repeated trials, around the ideal symbol location. In low symbol position count digital modulation methods, this isn’t of particular concern. However, in higher quadrature amplitude modulation (QAM) systems and other high symbol location count modulation methods, inter-symbol interference can increase dramatically due to phase noise. Depending upon the density of the symbols, a communication scheme may even be phase noise limited, as opposed to interference or noise limited. This is a growing concern while evaluating upcoming 5G waveform candidates.

Doppler Radar and Digital Pulse Compression Techniques Must Also Beware Phase Noise

With radar systems, phase noise can be equally disruptive, specifically with Doppler radar and with advanced pulse compression techniques that rely on digital modulation methods. Using Doppler radar as an example, the range and velocity calculations for these radar are derived directly from the conversion of the frequency offset and shift of the original transmitted signal and the return signal. Any variation in the frequency offset or shift will result in an error to the frequency-to-time conversion of the Doppler radar, inducing range and velocity inaccuracy. Over long ranges, or while monitoring fast moving targets, phase noise variations in frequency accuracy could cause unacceptable radar performance degradation.

Additive Phase Noise Can’t Be Ignored

Though phase noise is typically relegated to an oscillator selection concern, the additive phase noise from amplifiers, mixers, and other active and passive signal chain components, can also become a limiting factor in the overall system phase noise performance. If the phase noise performance of the oscillator, used as a local oscillator (LO) for upconversion or downconversion, is adequate, but the additive phase noise of the low-noise amplifier (LNA) from the LO driving the mixer–and the mixer’s phase noise performance–is poor, then the overall phase noise in the signal may be below the expected range. As LNAs, power amplifiers (PAs), and mixers are used in many radar and communications architectures, extensively, the additive phase noise of these components must also be considered in phase noise limited designs.

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The Difference between MIL-STD, MIL-HDBK, MIL-DTL, MIL-PRF and MIL-SPEC

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The US defense standards, commonly referred to as MilSpec, are developed by the US DoD for the purpose of enhancing interoperability among critical defense systems. The goal of the standards is to provide precise descriptions on the procedures and practices for the design, manufacturing, and deployment of military devices and equipment. Ultimately, the standards aim to increase the maintenance, repair, and operations (MRO) capability across the US military organizations.

The military standards are presented in several forms, defense handbooks, standards, performance specifications, detailed specifications, and specifications. The DoD has a standard for the development of standards, Defense Standards Program policies and procedures (DoD 4120.24-M), MIL-STD-962, MIL-STD-967, and MIL-STD-961. An updated registry of the standards can be found here.

Though these standards provide an array of material on achieving military grade components and devices, there are many more factors to contend with when providing military grade components and equipment for deployment or distribution. These include ensuring that parts and materials are provided from approved vendors, known as the Qualified Manufacturers List (QML) and the Qualified Parts List (QPL), provided by the Defense Logistic Agency (DLA) Land and Maritime.

Also, import and export of military grade components and systems is also heavily regulated by organizations, such as International Traffic in Arms Regulations (ITAR) and the Export Administration Regulations (ERA). For these reasons, sourcing and supplying military grade components and devices is often a complex process that comes with long lead times and cumbersome paperwork. However, there are some suppliers that provide some in stock components that could meet military standards, but don’t include the military designations that restrict their immediate sale with same day shipping.

 

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Waveguides Inside Out

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Following from the name, a waveguide is a hollow conductive structure that guides an EM wave along a path. The conductive inner walls of the waveguide bounce EM energy along the path with low-loss and close to light speed.

Waveguides are commonly cylindrical, elliptical, or rectangular. In a rectangular waveguide, transverse electric (TE), or H-wave, can be formed when the magnetic field is in the direction of propagation. If the electric field is in the direction of propagation, it is known as transverse magnetic (TM), or E-wave.

The speed of the wavefront and the frequencies a waveguide can support depend upon the physical dimensions of the waveguide. Different frequencies will form various modes within a waveguide. The dominant mode of a waveguide is the one where EM energy is guided most efficiently. In rectangular waveguides, the TE10 mode is the most efficient, and in a cylindrical waveguide the TE11 mode is the dominant mode. These modes have lower-cutoff frequency and upper frequency boundaries where frequencies beyond this range operate in other modes. Multiple modes operating on the same waveguide can create unwanted interference to the dominant mode. Though, there are some applications which benefit from leveraging multiple modes within a waveguide.

For performance interconnect applications most waveguides are carefully designed to support only the dominant mode. These factors lead to a waveguides dimensions being directly tied to the lower frequency of the mode. This limits waveguide sizes to what dimensions can be supported by an application. For example, a 1MHz waveguide would be roughly 500 ft in the largest dimension. Though at microwave and millimeter wave frequencies, waveguides reduce dramatically in dimension and weight. Regardless, as the exact dimensions of a waveguide must be maintained throughout the structure, care must be taken during any bending or routing operation. Waveguides have limited flexibility as a function of the need for high mechanical precision.

The large conductive surface area of a waveguide leads to very little energy lost while channeling the EM energy. Plating the inside of a waveguide with a thin layer of greater conductivity material can also increase the efficiency of energy transfer and the power handling capability of a waveguide. Also, the dielectric within a waveguide is generally air, which has very low dispersion and loss compared to dielectric materials used in coaxial cables.

As all of the EM energy is contained within the waveguide, radiation losses are extremely low within a waveguide. Not surprisingly, the high level of isolation within a waveguide also prevents unwanted signal interference from external sources. On the other hand, the high performance of waveguide interconnects also comes at a high price. The precision machining, custom manufacture, and flange couplings at the joints tend to lead to an expensive final product.

To overcome these challenges, there are manufacturers that produce flexible waveguides that can be pre-molded or flexed multiple times. Additionally, creating high performance active devices and passive devices are relatively simple to manufacture mechanically. These devices also minimally impact the integrity of the signal path, enabling high performance interconnect and passives with waveguide technology.

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When and Where You Need RF Limiters and Detectors

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RF limiters and detectors are used widely throughout the RF and microwave industry in a wealth of circuit applications. For example, radar transceivers, telecommunication radios, test and measurement equipment, and other circuits rely on RF limiters for receiver protection, as well as the protection of critical circuit components that may experience high-peak voltage and current transients internal to a circuit. RF detectors are used to convert specific RF signal features to analog signals, which can then be used to trigger circuit functions or adjust internal gain control circuitry to the appropriate values. Both RF limiters and detectors can be found in transmitter and receiver circuits, and as these components are often integrated directly into the signal chain, their impact on circuit function bears consideration.

RF Limiters

RF limiters are commonly located from the antenna toward the amplifier and signal conditioning circuitry in a receiver, or anywhere in a signal chain that may experience high transient voltages/current and a sensitive component may need to be protected. The placement of an RF limiter could be right before a low-noise amplifier in a receiver, or inline throughout a circuit. Additionally, RF limiters are often placed in front of switch assemblies, power dividers/combiners, detectors, and mixers. As RF limiters can be packaged in surface mount, die, stripline, coaxial, or waveguide-based packages, RF Limiters can be placed throughout a circuit. Moreover, limiters are also commonly integrated into other circuit assemblies, such as detectors, amplifiers, and mixers.

A common implementation of an RF limiter is to use material features that enable incident-power-controlled, variable resistance. Typically, this involves the use of PIN diodes, and sometimes larger limiter assemblies with multiple diodes and other circuitry is used. The max/peak input power, insertion loss, threshold level, and series resistance/capacitance are the major parameters when considering a RF limiter. Certain applications may require specific combinations of parameters that cannot be met with a single diode, and the circuit complexity is increased. However, the higher threshold level and power handling leads to a tradeoff by increasing insertion loss and series resistance/capacitance.

RF Detectors

 RF detectors can be used in a wide range of signal detection applications, including peak detection, average detection, and video detection. An example application is to use a RF detector to gauge the received signal strength in a radio receiver, and adjust the gain control circuitry to properly maintain an optimized signal strength. Many telecommunications and spectrum regulations require precise levels of output power, and a RF detector could also be used in the output path of a transmitter to ensure that the output does not exceed the regulatory limits.

There are several types of RF detectors that are designed to meet specific circuit requirements. Many RF detectors are made from simple diodes, and others are made from more advanced diode construction techniques, such as Schottky diodes or tunnel diodes. More complex detector circuits using multiple diodes exist, and can be used for voltage multiplication and increasing the detectable output voltage range of a detector. There are various diode technologies to improve the minimum detectable signal, such as zero-bias diodes and low-barrier diodes. Moreover, in order to isolate the signals being detected, a detector circuit may be integrated with a directional coupler to capture either the forward or reverse signal strength.

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Passive Intermodulation (PIM) Explained

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PIM, or Passive Intermodulation, is a type of signal distortion that has become increasingly important to detect and mitigate since LTE networks are particularly sensitive to it.

PIM is created when there are two or more carrier frequencies exposed to non-linear mixing. The resulting signal will contain additional, unwanted frequencies or intermodulation products. As the “Passive” portion of the name implies, this non-linear mixing does not involve active devices and is frequently caused by the metallic materials and workmanship of the interconnects and other passive components in the system.

Examples of causes of non-linear mixing:

> Imperfect electrical connections: surfaces are never perfectly smooth so the areas of contact can have high current densities which can cause heating through a restricted conduction path causing a resistance change. For this reason connectors should always be tightened to the correct torque.

>Most metal surfaces have at least a thin layer of oxide which can cause tunneling, or simply cause a reduced area of conduction. Some believe that this produces the Shottky effect. This is why a rusty bolt or metal roof near a cell tower can produce a strong PIM distortion signal.

>Ferromagnetic material: materials such as iron can generate large PIM distortion and should not be used in cellular systems.

As wireless networks become more complex with multiple technologies and system generations in use at a single site, the signals combine to generate this undesired distortion, which interferes with the LTE signals. Antennas, diplexers, cables, and dirty or loose connectors can be sources of PIM, as well as damaged RF equipment or metal objects near or at a distance from the cell site.

PIM interference can have substantial impacts on the performance of LTE networks, which is why it is so important to wireless operators and their contractors to be able to test for, locate and mitigate PIM.  Acceptable PIM levels vary by system but as an example Test Company Anritsu said that drive tests have found an 18% drop in download speeds when PIM levels were increased from -125 dBm to -105 dBm, even though the latter number can be considered an acceptable PIM level.

Where is PIM tested?

Individual components are often tested for PIM both in the design and production processes in order to ensure that they are not significant PIM sources once they are installed – however, installation is still a critical piece of PIM mitigation because proper connections are critical. In the case of distributed antenna systems, in some instances the system is tested for PIM as well as individual components. PIM-certified equipment is becoming more common. Antennas, for example, may be PIM-certified to a level of -150 dBc and those requirements are increasingly strict.

PIM is also assessed during the siting process for cellular sites, ideally before the cell site and antennas are placed as well as during the installation process.

Pasternack provides Low PIM cable assemblies, connectors, adapters, antennas and tappers designed to address applications where PIM can be an issue.

To see all of our Low PIM products click here and view the left Nav option menu.

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What you need to know about Reverse Polarized Connectors

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A reverse polarized coax connector is a variation of a standard polarity connector in which the gender of the interface has been reversed. The term “reverse polarity” refers not to the signal polarity of the connector itself but to the gender of the center contact pin.

A reverse polarized connector will have the same external housing (body) as a standard connector (jack or plug threading) but the center pin is altered to be reversed.

Thus, a reverse polarized jack has a male pin in place of the standard female type pin/receptacle and a reverse polarized plug will have a center receptacle (female) instead of a male pin.

The chart below outlines reverse polarized connecter body and pin options:

Reverse polarized coax connectors were developed to separate professional grade and commercially available components and equipment to comply with FCC regulations. The idea was that reverse polarized connectors would not be readily available or accessible to the general consumer audience so they would not try to or be able to connect certain gain components or equipment. This meant it would be very hard for consumers to say change to a higher gain antenna on a radio. Since then the rules have changed and today several variations of reverse polarized connectors are readily available allowing more design options to more people.

The most common reverse polarized connector types are RP-SMA and RP-TNC. They are typically used for Wi-Fi, Cellular, RF and GPS antenna and equipment applications.

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Sinusoidal Frequency Estimation Based on Time-Domain Samples

Rick Lyon's Blog on DSPRelated -

The topic of estimating a noise-free real or complex sinusoid's frequency, based on fast Fourier transform (FFT) samples, has been presented in recent blogs here on dsprelated.com. For completeness, it's worth knowing that simple frequency estimation algorithms exist that do not require FFTs to be performed . Below I present three frequency estimation algorithms that use...

What do RoHS, REACH, and WEEE Mean for RF/Microwave Components, Manufacturers and Assemblers?

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RoHS, also known as Lead-Free, stands for Restriction of Hazardous Substances. RoHS originated in the European Union and restricts the use of six hazardous materials found in electrical and electronic products. All applicable products in the EU market after July 1, 2006 must pass RoHS compliance. The substances banned under RoHS are lead (Pb), mercury (Hg), cadmium (Cd), hexavalent chromium (CrVI), polybrominated biphenyls (PBB), polybrominated diphenyl ethers (PBDE), and four different phthalates (DEHP, BBP, BBP, DIBP). The restricted materials are hazardous to the environment and pollute landfills, and are dangerous in terms of occupational exposure during manufacturing and recycling. Portable RoHS analyzers, also known as X-ray fluorescence or XRF metal analyzers, are used for screening and verification of RoHS compliance. Any business that sells applicable electronic products, sub-assemblies or components directly to EU countries, or sells to resellers, distributors or integrators that in turn sell products to EU countries, is impacted if they utilize any of the restricted materials.

REACH is a general regulation and stands for Registration, Evaluation, Authorization, Restriction of Chemicals, and addresses the production and use of chemical substances and their potential impact on human health and the environment. REACH is monitored by the ECHA and deals with 38 chemicals currently. It is the strictest law to date regulating chemical substances and will affect industries throughout the world. REACH entered into force on 1 June 2007, with a phased implementation over the next decade. The regulation also established the European Chemicals Agency, which manages the technical, scientific and administrative aspects of REACH. REACH also addresses the continued use of chemical substances of very high concern (SVHC) because of their potential negative impacts on human health or the environment. From 1 June 2011, the European Chemicals Agency must be notified of the presence of SVHCs in articles if the total quantity used is more than one tonne per year and the SVHC is present at more than 0.1% of the mass of the object. The European Commission supports businesses affected by REACH by handing out – free of charge – a software application (IUCLID) that simplifies capturing, managing, and submitting data on chemical properties and effects. Such submission is a mandatory part of the registration process. Under certain circumstances the performance of a chemical safety assessment (CSA) is mandatory and a chemical safety report (CSR) assuring the safe use of the substance has to be submitted with the dossier. Dossier submission is done using the web-based software REACH-IT.

WEEE is the acronym for Waste from Electrical and Electronic Equipment. WEEE, also known as Directive 2002/96/EC, mandates the treatment, recovery and recycling of electric and electronic equipment. All applicable products in the EU market after August 13, 2006 must pass WEEE compliance and carry the “Wheelie Bin” sticker. WEEE compliance aims to encourage the design of electronic products with environmentally-safe recycling and recovery in mind. RoHS compliance dovetails into WEEE by reducing the amount of hazardous chemicals used in electronics manufacture.

Put another way, RoHS regulates the hazardous substances used in electrical and electronic equipment, while WEEE regulates the disposal of this same equipment.

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RF Amplifier Packaging and Thermal Dynamics

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Packaging dimensions, weight, pinouts and material construction are critical features of any RF amplifier. These factors heavily weigh into the cost and feasibility of using a particular amplifier in a given design. Regardless of electrical and RF performance, if an amplifier can’t fit into the required footprint, the device won’t be serviceable for that application. It is also important to note that some RF amplifiers will require external components for optimal performance; these parts are often well defined in a specification sheet. But, these additional external components will increase cost and RF amplifier footprint. There are also many vibration, shock, dust, and ruggedness parameters that may be necessary to consider for applications requiring higher reliability devices.

Thermal dynamics are another element that must be considered when specifying an RF amplifier. The environmental factors and system factors can lead to very wide temperature ranges, as well as high peak temperatures. The maximum and recommended junction temperature of the transistors within an RF amplifier will be specified in a data sheet as a range of temperatures where the device can operate, or be stored without significant performance degradation.

Many of the performance characteristics will also be given over temperature, which must be maintained for desired performance. To ensure this, many specification sheets will also contain information on the proper landing pad design and methods to ensure proper thermal sinking.

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Cheap Waveguides can Ruin your Day

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Though there are many reputable and high quality waveguide vendors, some vendors, specifically offshore vendors, may use machining techniques that reduce time and cost of manufacture. These short-cuts could have dramatic impact on a waveguide component and system performance. Any misalignments or machined geometries beyond specified levels can reduce the VSWR performance of a waveguide, cause RF leakage between the flanges, and increase maintenance/service costs.

One such example is the drilling of fastening holes in a waveguide flange. In order to achieve high precision alignment, the waveguide flange needs to be attached to the waveguide prior to drilling. However, some machining houses will drill the waveguide flanges prior to attachment. This could lead to x,y, and rotational displacement between the waveguide flange holes and the specified hole locations for the waveguide size and flange type. The errors may be so slight that there aren’t visually discernible or measurable with a pair of calipers. There are x,y, coordinate machines used to measure hole dimensions that are highly precise, and can be used to evaluate incoming parts.

Some high microwave and millimeter-wave waveguides also use guide pins with detailed specifications provided in MIL-DTL-3922. At higher frequencies these pins are specified at 0615, where some companies will use 0612 pins, as they are a standard stock pin. The pin sizes are not visually discernible and can also lead to misalignments.

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Practical Mixers 101

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Introduction to Mixers

A microwave frequency mixer is a 3-port electronic circuit that combines two or more signals into one or two composite output signals, and are categorized as switching mixers or nonlinear mixers– although many mixers are configured with both. Using diodes, the mixer is passive and has a conversion loss. Using active devices, such as transistors, a conversion gain is possible. A variety of circuit topologies exist for mixers and can be as simple as one that uses a single diode or more complex for enhanced performance.

Switching mixers include single-balanced and double-balanced mixers, widely used and known for reliability, while nonlinear mixers offer the ability for higher frequencies output. A single-ended mixer is usually based on a single Schottky diode or transistor. A balanced mixer typically incorporates two or more Schottky diodes or a Schottky quad. A balanced mixer offers advantages in third-order intermodulation distortion performance compared to a single-ended mixer, because of the balanced configuration. The popular modern mixer designs are Schottky diodes, GaAs FETs, and CMOS transistors depending upon the application. FET and CMOS mixers are often used in higher volume applications.

Basic Mixer Operation

Conceptually, the three ports on a mixer are the radio frequency (RF) port, the local oscillator port (LO), and the intermediate frequency port (IF). The RF port is where the high frequency signal is applied to down-convert it or where the high-frequency signal is output in an upconverter. The local oscillator (LO) port is where the power is applied. The LO signal is the strongest signal and turns the diodes on and off in a switching mixer which then reverses the path of the RF to the IF. In other words, the IF port is where the modified RF signal is filtered to become the IF signal.

While the mixer operates within its linear range, increases in IF output power corresponds to increases in RF input power. Conversion compression occurs outside the linear range. The 1-dB compression point is where the conversion-gain is 1dB lower than the conversion gain in the linear region of the mixer. The LO power coupled into the mixer controls performance. Inadequate LO power for a given mixer degrades conversion-gain and noise figure and, therefore, system sensitivity. Conversion gain factor is specified at a particular LO drive level and is defined as the ratio of the numeric single-sideband (SSB) IF output-power to the numeric RF input-power such that a positive value for an IF output-power greater than the RF input-power indicates conversion gain. Conversely, a negative result occurs for conversion loss.

Understand the System Requirements and Link Budget

When considering which mixers to use in a given system, the RF/Microwave signal-processing components performance data and specification will dictate the link budget limitations for gain, noise, frequency, and linearity parameters that can be applied to a mixer. Many system level design software, and well-designed system-level spreadsheet analysis, will include Link budgets and worst case performance requirements for each critical performance parameter of a system. Link budget calculations are an essential step in the design of any RF system. The link budget calculation allow the losses and gains to be planned, so that changes can be made to the system to meet its operational requirements or optimal performance. A simple link budget equation for Received Power can resemble: Received Power (dB) = Transmitted Power (dB) + Gains (dB) − Losses (dB), where the Gains and Losses are the component contributions of all components in the signal chain.

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RF and Microwave Attenuator Fundamentals

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Attenuators are fundamental components of RF and Microwave circuits and systems. Often found in virtually every RF application, attenuators play a vital role in receivers, transmitters, and test and measurement systems. The main purpose of attenuators is to reduce the signal strength before a sensitive circuit element. Attenuators can be fabricated using various technologies and knowledge of the available options can help an engineer choose the best attenuator for their application.

What Are Attenuators?

Attenuators simply decrease the wanted or unwanted signal strength along a signal path. They can be used to decrease the output signal of a device-under-test before a sensitive test and measurement receiver, to ensure a more conformal impedance match, or to ensure precise control of the signal amplitude at the output of a transmitter. The attenuation level of a device—the amount of signal power/voltage lost through the device—is commonly measured in either decibels (dB) or as a voltage ratio.

The most common attenuators are broadband attenuators. But, some attenuator types and technologies may have frequency dependant performance and limitations. Though terminations also reduce the signal strength at the load of a system, attenuators differ from terminations as they are in-line to the signal path.

What Types and Technologies of Attenuators are Available?

Attenuators are based on passive resistors, absorptive material/techniques, PIN diodes, or field-effect transistor (FET) technologies. Additionally, attenuators can be developed from coaxial transmission line, stripline, surface mount, or even waveguide interconnect technologies. The performance and physical properties of these different technologies vary widely. The quality of construction and costs also contribute to the range in performance, thermal, and physical properties.

Attenuators also come as fixed attenuators or adjustable types. The adjustable types of attenuators can be switched attenuators with discrete levels of attenuation, or as continuously variable attenuators with analog adjustment. Both types can be designed with electrical or mechanical control. Some attenuators are programmatically controlled, through digital signals and even software.

Attenuators input and output impedance can vary depending on which application they are designed for. This could be a common 50Ω, 75Ω, or a custom impedance value. Also, some attenuator designs enable DC bias passing, and are known as DC bias passing attenuators.

Additionally, depending upon the attenuator technology, an attenuator may be reflective or non-reflective. A reflective attenuator reflects the attenuated signal energy, instead of absorbing it. The amount of signal energy reflected is a function of the attenuation level.

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RF Amplifier Power and Gain Considerations

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The input and output power characteristics of an RF amplifier are dominant characteristics, as increasing signal strength is the primary purpose of an amplifier. An RF amplifier will be specified with a maximum and nominal range for input and output power based on certain conditions. These specifications will further extend to a maximum and nominal range for input and output voltage and current. If the power, current, or voltage presented at the inputs or outputs exceeds the specification, undesirable operation and even device damage may occur.

An important note with amplifiers used in pulsed or other applications with signal modulation is that certain types of modulation may change the power, voltage, or current of the base continuous wave signal. This could potentially lead to exceeding certain recommended limits. For example, frequency or phase modulation doesn’t increase signal power, but amplitude modulation can increase signal power up to four times that of a continuous wave (CW) signal. Knowledge of the input and output power characteristics over frequency is necessary to ensure acceptable operation ranges at every frequency.

A common parameter given to represent the input and output power characteristics for any amplifier is gain, or the output signal power compared to the input signal power. For RF amplifiers, this parameter is given over a frequency range. As the RF amplifier gain will not be completely consistent over frequency, the gain flatness of the frequency response can be derived by measuring the peak to peak gain behavior. In some circumstances, a signal may be presented at the output port of an RF amplifier, either through reflection or other system dynamics. The output to input gain, or reverse gain, is used to gauge the effects of signals present on the output of the amplifier to the input of the amplifier and the upstream signal chain. Additionally, some energy will be lost within the RF amplifier device, which may need to be factored into system performance considerations.

No physical device will output all of the input supply power and input signal power. There are RF conversion losses, internal resistive losses, impedance mismatches, and coupling effects that pull power away from the output of the amplifier. A measure of the power input to the amplifier compared to the realized output power is known as efficiency. As this is a main consideration in many RF power amplifier (PA) applications, power-added efficiency (PAE) includes the RF input power into the calculation. There are several other methods of calculating efficiency, which should be investigated to determine if it is adequate for a particular application.

 

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Fundamentals of Vector Network Analysis Primer

Microwaves and RF Magazine -

Sponsored by Rohde & Schwarz Circuits that are analyzed using network analyzers range from simple devices such as filters and amplifiers to complex modules used in communications satellites. As a measurement instrument a network analyzer is a versatile, but also one of the most complex pieces of precision test equipment and therefore great care has to be taken in the measurement setup and calibration procedures. Download this primer to find out why a VNA is among the most essential tools for RF/microwave measurement.

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Frequency Translation by Way of Lowpass FIR Filtering

Rick Lyon's Blog on DSPRelated -

Some weeks ago a question appeared on the dsp.related Forum regarding the notion of translating a signal down in frequency and lowpass filtering in a single operation [1]. It is possible to implement such a process by embedding a discrete cosine sequence's values within the coefficients of a traditional lowpass FIR filter. I first learned about this process from Reference [2]. Here's the...

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