An RF chain is a cascade of electronic components and sub-units which may include
amplifiers
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost the v ...
,
filters
Filter, filtering or filters may refer to:
Science and technology
Computing
* Filter (higher-order function), in functional programming
* Filter (software), a computer program to process a data stream
* Filter (video), a software component tha ...
,
mixers,
attenuators and
detectors
A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon.
In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends ...
.
[Steer M., "Microwave and RF Design", Scitech Publ., Inc., N.C., 2010, also from Yes Dee Publ., India, 2016] It can take many forms, for example, as a wide-band receiver-detector for
electronic warfare
Electronic warfare (EW) is any action involving the use of the electromagnetic spectrum (EM spectrum) or directed energy to control the spectrum, attack an enemy, or impede enemy assaults. The purpose of electronic warfare is to deny the opponen ...
(EW) applications, as a tunable narrow-band receiver for communications purposes, as a
repeater
In telecommunications, a repeater is an electronic device that receives a signal and retransmits it. Repeaters are used to extend transmissions so that the signal can cover longer distances or be received on the other side of an obstruction. Some ...
in signal distribution systems, or as an amplifier and
up-converters for a transmitter-driver. In this article, the term RF (radio frequency) covers the frequency range "Medium Frequencies" up to "Microwave Frequencies", i.e. from 100 kHz to 20 GHz.
[Frenzel L.E.” Principles of Electronic Communication Systems”, 3rd Ed.,McGraw Hill, 2008]
The key electrical parameters for an RF chain are system gain,
noise figure Noise figure (NF) and noise factor (''F'') are figures of merit that indicate degradation of the signal-to-noise ratio (SNR) that is caused by components in a signal chain. These figures of merit are used to evaluate the performance of an amplifier ...
(or
noise factor Noise figure (NF) and noise factor (''F'') are figures of merit that indicate degradation of the signal-to-noise ratio (SNR) that is caused by components in a signal chain. These figures of merit are used to evaluate the performance of an amplifie ...
) and overload level.
[Egan W.F., "Practical RF System Design", Wiley, 2003] Other important parameters, related to these properties, are sensitivity (the minimum signal level which can be resolved at the output of the chain); dynamic range (the total range of signals that the chain can handle from a maximum level down to smallest level that can be reliably processed) and spurious signal levels (unwanted signals produced by devices such as mixers and non-linear amplifiers). In addition, there may be concerns regarding the immunity to incoming interference or, conversely, the amount of undesirable radiation emanating from the chain. The tolerance of a system to mechanical vibration may be important too. Furthermore, the physical properties of the chain, such as size, weight and power consumption may also be important considerations.
An addition to considering the performance of the RF chain, the signal and signal-to-noise requirements of the various signal processing components, which may follow it, are discussed because they often determine the target figures for a chain.
Parameter sets
Each two-port network in an RF chain can be described by a parameter set, which relates the voltages and currents appearing at the terminals of that network.
[Matthaei G., Young L., Jones E.M.T., “ Microwave Filters, Impedance-Matching Networks, and Coupling Structures”,McGraw Hill 1964, Artech House 1980] Examples are:
impedance parameters Impedance parameters or Z-parameters (the elements of an impedance matrix or Z-matrix) are properties used in electrical engineering, electronic engineering, and communication systems engineering to describe the electrical behavior of linear ele ...
, i.e.
z-parameters Impedance parameters or Z-parameters (the elements of an impedance matrix or Z-matrix) are properties used in electrical engineering, electronic engineering, and communication systems engineering to describe the electrical behavior of linear electr ...
;
admittance parameters
Admittance parameters or Y-parameters (the elements of an admittance matrix or Y-matrix) are properties used in many areas of electrical engineering, such as power, electronics, and telecommunications. These parameters are used to describe the ele ...
, i.e.
y-parameters
Admittance parameters or Y-parameters (the elements of an admittance matrix or Y-matrix) are properties used in many areas of electrical engineering, such as power, electronics, and telecommunications. These parameters are used to describe the el ...
or, for high frequency situations,
scattering parameters
Scattering parameters or S-parameters (the elements of a scattering matrix or S-matrix) describe the electrical behavior of linear electrical networks when undergoing various steady state stimuli by electrical signals.
The parameters are useful f ...
, i.e. S-parameters.
[Orfanidis S.J., “ Electromagnetic Waves and Antennas”, Rutgers University, 1999] Scattering parameters avoid the need for ports to be open or short-circuited, which are difficult requirements to achieve at microwave frequencies.
In theory, if the parameter set is known for each of the components in an RF chain, then the response of the chain can be calculated precisely, whatever the configuration. Unfortunately, acquiring the detailed information required to carry out this procedure is usually an onerous task, especially when more than two or three components are in cascade. A simpler approach is to assume the chain is a cascade of impedance matched components and then, subsequently, to apply a tolerance spread for mismatch effects (see later).
A system spreadsheet
A system spreadsheet has been a popular way of displaying the important parameters of a chain, in a stage-by-stage manner, for the frequency range of interest.
It has the advantage of highlighting key performance figures and also pin-pointing where possible problem areas may occur within the chain, which are not always apparent from a consideration of overall results. Such a chart can be compiled manually
or, more conveniently, by means of a computer program
In addition, 'tookits' are available which provide aids to the system designer.
Some routines, useful for spreadsheet development, are given next.
Key spreadsheet topics
For the parameters considered below, the chain is assumed to contain a cascade of devices, which are (nominally) impedance matched. The procedures given here allow all calculations to be displayed in the spreadsheet in sequence and no macros are used. Although this makes for a longer spreadsheet, no calculations are hidden from the user.
For convenience, the spread sheet columns, show the frequency in sub-bands, with bandwidths sufficiently narrow to ensure that any gain ripple is sufficiently characterized.
Consider the n
th stage in a chain of RF devices. The cumulative
gain
Gain or GAIN may refer to:
Science and technology
* Gain (electronics), an electronics and signal processing term
* Antenna gain
* Gain (laser), the amplification involved in laser emission
* Gain (projection screens)
* Information gain in de ...
,
noise figure Noise figure (NF) and noise factor (''F'') are figures of merit that indicate degradation of the signal-to-noise ratio (SNR) that is caused by components in a signal chain. These figures of merit are used to evaluate the performance of an amplifier ...
, 1 dB compression point
[Frenzel L., “ What's the difference between the third order intercept and the 1-dB compression points? ” Find at:
http://electronicdesign.com/what-s-difference-between-third-order-intercept-and-1-db-compression-point] and output
thermal noise
A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example ...
power for the preceding (n-1) devices are given by Gcum
n - 1, Fcum
n - 1, Pcum
n - 1 and Ncum
n - 1, respectively. We wish to determine the new cumulative figures, when the n
th stage is included, i.e. the values of Gcum
n, Fcum
n, Pcum
n and Ncum
n, given that the n
th stage has values of G
n, F
n, P1
n for its gain, noise figure and 1 dB compression point, respectively.
Cumulative gain
The cumulative gain, Gcum
n after n stages, is given by
:
and Gcum
n(dB) is given by
:
where Gcum
n-1(dB) is the total gain of the first (n-1) stages and G
n(dB) is the gain of the nth stage.
Conversion equations between dBs and linear terms are:
:
and
:
Cumulative noise factor (Noise Figure)
The cumulative
noise factor Noise figure (NF) and noise factor (''F'') are figures of merit that indicate degradation of the signal-to-noise ratio (SNR) that is caused by components in a signal chain. These figures of merit are used to evaluate the performance of an amplifie ...
, after n stages of the overall cascade, Fcum
n is given by
:
where Fcum
n-1 is the noise factor of the first (n-1) stages, F
n is the noise factor of the nth stage, and Gcum
n is the overall gain of n stages.
The cumulative
noise figure Noise figure (NF) and noise factor (''F'') are figures of merit that indicate degradation of the signal-to-noise ratio (SNR) that is caused by components in a signal chain. These figures of merit are used to evaluate the performance of an amplifier ...
is then
:
*Note 1: the use of an amplifier with high gain for the first stage will ensure that the noise figure degradations by later stages will be small or negligible. This will be best for system sensitivity, see later.
*Note 2: for a passive (lossy) section of the chain, the noise figure of the section equals the loss of that section.
[Brooker G., “Sensors for Ranging and Imaging”, Chapter 9, Sci Tech Publ. 2009, YesDee Publ. 2012][ Pozar D.M., “Microwave Engineering”, Wiley, 4th Ed., 2012.] So, for example, a 3 dB attenuator has a noise figure of 3 dB.
Cumulative 1dB compression point
For spreadsheet purposes, it is convenient to refer the 1 dB compression point
[RF Cafe, “ Cascaded 1 dB Compression Point (P1dB)”. Find at: www.rfcafe.com/references/electrical/p1db.htm] to the input of the RF chain, i.e. P1cum
n(input),
:
where P1cum
n-1 is the 1 dB compression point at the input of the first (n-1) stages, P1
n is the 1 dB compression point for the nth stage, referred to its input and Gcum
n is the overall gain including the nth stage. The units are
Wor
att
*Note: for the best result, i.e. a system tolerant to high level signals, is achieved with a low front end gain. This is in conflict with the need for a low overall noise factor, which requires a high first-stage gain.
*Note 2: The 1 dB compression point is abbreviated as P1dB, iP1dB, or oP1dB. It is referenced to input or output power level measured in
Bm Overall system performance can be practically evaluated by the 1 dB compression method.
Related parameters, such as IP3 or IM3 are helpful fictive numbers used to evaluate the system. The device would burn, applying IP3 input level. Accuracy of the measurement with spectrum analyzer is (HP/Agilent specs: +-1.0 dB, and +-0.5 dB custom device). Don't chase fractions of dB. In linear systems, this all results in AGC.
Cumulative noise power
The
thermal noise
A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example ...
power present at the input of an RF chain,
[Connor F.R., “ Noise”, Edward Arnold, 2nd Ed. 1982][Terman F.E.,“ Electronic and Radio Engineering”, 4th. Ed., 1955][Vizmuller P., “ RF Design Guide”, Artech House, 1955] is a maximum in a resistively matched system, and is equal to kTB, where k is Boltzmann's constant (= 1.38044 × 10
−23 J/K), T is the absolute temperature, in
kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phys ...
s and B is the bandwidth in Hz.
At a temperature of 17 °C (≡ 290 K), kTB = 4.003 × 10
−15 W/MHz ≡ -114 dBm for 1 MHz bandwidth.
The thermal noise after n stages of an RF chain, with total gain G
T and noise figure F
T is given by
:
where k = Boltzmann's constant, T is the temperature in kelvins and B is the bandwidth in hertz, or
:
where Ncum
n(dBm) is the total noise power in dBm per 1 MHz of bandwidth,
In receivers, the cumulative gain is set to ensure that the output noise power of the chain at an appropriate level for the signal processing stages that follow. For example, the noise level at the input to an
analog-to-digital converter
In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide ...
(A/D) must not be at too low a level, otherwise the noise (and any signals within it) is not properly characterized (see the section on A/Ds, later). On the other hand, too high a level results in the loss of dynamic range.
Other related system properties
With the basic parameters of the chain determined, other related properties can be derived.
Second and third order intercept points
Sometimes performance at high signal levels is defined by means of the “
second-order intercept point
The Second-order intercept point, also known as the SOI, IP2, or IIP2 (Input intercept point), is a measure of linearity that quantifies the second-order distortion generated by nonlinear systems and devices. Examples of frequently used devices t ...
(I2)” and the “
third-order intercept point
In telecommunications, a third-order intercept point (IP3 or TOI) is a specific figure of merit associated with the more general third-order intermodulation distortion (IMD3), which is a measure for weakly nonlinear systems and devices, for exampl ...
(I3)”, rather than by the 1 dB compression point.
These are notional signal levels which occur in two-signal testing and correspond to the theoretical points where second and third order inter-modulation products achieve the same power level as the output signal.
The figure illustrates the situation.
In practice, the intercept levels are never achieved because an amplifier has gone into limiting before they are reached, but they are useful theoretical points from which to predict intercept levels at lower input powers. In dB terms, they decrease at twice the rate (IP2) and three times the rate (IP3) of the fundamental signals.
When products, stage to stage, add incoherently, the cumulative results for these products are derived by similar equations to that for the 1 dB compression point.
:
where I2cum
n-1 is the second order intercept point at the input of the first (n-1) stages, I2
n is the third order intercept point for the nth stage, referred to its input and Gcum
n is the overall gain including the nth stage.
Similarly,
:
where I3cum
n-1 is the third order intercept point at the input of the first (n-1) stages, I3
n is the third order intercept point for the nth stage, referred to its input.
The cumulative intercept points are useful when determining the “spurious free dynamic range”
of a system.
There is an approximate relationship between the third order intercept level and the 1 dB compression level which is
[East P.W., “ Microwave System Design Tools and EW Applications”, 2nd ed., Artech House 2008]
:
Although only an approximation, the relationship is found to apply to a large number of amplifiers.
Signal-to-noise ratio
In the spread sheet, the total frequency band of interest B(Hz) is divided into M sub-bands (spreadsheet columns) of B/M (Hz) each, and for each sub-band (m = 1 to M) the thermal noise power is derived, as described above. In practice, these results will differ slightly, from column to column, if the system has gain ripple.
The signal-to-noise ratio (S:N) is the peak signal power of the pulse (Psig) divided by the total noise power (Pnoise) from the M frequency bins, i.e.
:
This is the S:N ratio at RF frequencies. It can be related to the video S:N ratio as shown next.
Relating RF and video S:N ratios
For spreadsheet purposes it can useful to find the RF signal to noise ratio which corresponds to a desired video signal to noise figure after demodulation or detection. As an RF chain usually has sufficient gain for any noise contribution from the detector diode to be ignored, the video S:N can be shown to be
[
:
where
*PS =input RF signal power;
*8BV and BR are the video and RF bandwidths;
*F' = F -1/G where G is the chain gain and F the effective noise figure;
*k = Boltzmann's constant; and
*T = the ambient temperature
f there is significant gain variation across the band, then it can be divided into M sub-bands and results summed for these sub-bands, as described earlier.
From the above equation, as the noise power in the RF band is PN = kTBRF’, a relationship between RF and Video S:N ratios can be found.
:
(This result can be found elsewhere][Lipsky S.E., "Microwave Passive Direction Finding", Wiley, N.Y., 1987]).
Inverting the relationship gives the RF signal-to-noise ratio required to achieve a given video S:N ratio:
:
Signal sensitivity
Signal sensitivity is important for receiving systems and refers to the minimum signal level at the input that is necessary to give a signal that can be resolved reliably by the detection process at the end of the RF chain. This parameter is less important in the case of repeaters and transmitter drivers where signal levels tend to be higher and other concerns such as stage overload and spurious signal generation tend to be more relevant.
Determining a value for system sensitivity can be difficult and depends on many things, including the method of detection, the signal coding method, the bandwidth of the RF channel, and whether or not digital processing is involved. Two important parameters used in assessing sensitivity performance of a system are the "Probability of Detection" and the "False Alarm Rate".
Statistical methods are often used in the decision process (see Tsui[Tsui J.B., " Microwave Receivers with Electronic Warfare Applications", Kreiger Pub. Co., USA, 1992] and Skolnik[Skolnik M.I., "Introduction to Radar Systems", McGraw Hill Kogakusha, 2nd Ed. 1980, 1962]).
Tangential sensitivity
Tangential sensitivity, (TSS), defines that input power which results in a video signal to noise ratio of approximately 8 dB from the detector. The thumbnail shows an example of a typical detected pulse at the TSS limit, with the pulse + noise sitting at a level just clear of the noise floor. The TSS level is too low a value for reliable pulse detection in a practical scenario, but it can be determined with sufficient accuracy in bench tests on a receiver to give a quick guide figure for system performance.
In a wideband receiver, with a square-law detector, the TSS value at the chain input terminals is given by,
:
From this, the S:N of the RF signal, at the input to the detector can be obtained when the video output is at TSS.
: