An RF chain is a cascade of electronic components and sub-units which may include amplifiers, filters, mixers, attenuators and detectors. It can take many forms, for example, as a wide-band receiver-detector for electronic warfare (EW) applications, as a tunable narrow-band receiver for communications purposes, as a repeater 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.
The key electrical parameters for an RF chain are system gain, noise figure (or noise factor) and overload level. 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. Examples are: impedance parameters, i.e. z-parameters; admittance parameters, i.e. y-parameters or, for high frequency situations, scattering parameters, i.e. S-parameters. 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, noise figure, 1 dB compression point and output thermal noise 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 nth 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
 formula_1
and Gcum"n"(dB) is given by
 formula_2
where Gcum"n"−1 [dB] is the total gain of the first "n" − 1 stages and "G""n" [dB] is the gain of the "n"th stage.
Conversion equations between logarithmic and linear terms are:
 formula_3
and
 formula_4
Cumulative noise factor (noise Figure).
The cumulative noise factor, after "n" stages of the overall cascade, Fcum"n" is given by
 formula_5
where Fcum"n"−1 is the noise factor of the first "n" − 1 stages, "F""n" is the noise factor of the "n"th stage, and Gcum"n" is the overall gain of "n" stages.
The cumulative noise figure is then
 formula_6
Cumulative 1 dB compression point.
For spreadsheet purposes, it is convenient to refer the 1 dB compression point to the input of the RF chain, i.e. P1cum"n"(input),
 formula_7
where P1cumn-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 "n"th stage, referred to its input and Gcum"n" is the overall gain including the "n"th stage. The unit is [mW] or [W].
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). In linear systems, this all results in AGC.
Cumulative noise power.
The thermal noise power present at the input of an RF chain, is a maximum in a resistively matched system, and is equal to "kTB", where "k" is the Boltzmann constant (= ‍), "T" is the absolute temperature, 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 
 formula_8
where "k" = the Boltzmann constant, "T" is the temperature in kelvins and "B" is the bandwidth in hertz, or
 formula_9
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 (ADC) must not be at too low a level, otherwise the noise (and any signals within it) is not properly characterized (see the section on ADCs, 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 (I2)" and the "third-order intercept point (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.
formula_10
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 "n"th stage, referred to its input and Gcum"n" is the overall gain including the nth stage.
Similarly,
 formula_11
where I3cumn-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 "n"th 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
 formula_12
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 ("P"sig) divided by the total noise power ("P"noise) from the "M" frequency bins, i.e.
 formula_13
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
 formula_14
where
[If 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 "P""N" = "kTB"R"F"′, a relationship between RF and video S:N ratios can be found.
 formula_15
(This result can be found elsewhere).
Inverting the relationship gives the RF signal-to-noise ratio required to achieve a given video S:N ratio:
 formula_16
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 and Skolnik).
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
 formula_17
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.
 formula_18
This equation shows that the S:N at RF is typically less than unity, in wideband systems, when the video output is at TSS. For example, if "B"R/"B"V = 500 then the equation gives (S:N)R = 0.17 (≈ −7.7 dB). (Note: a similar result is obtained by using the equation relating RF and video S:N ratios, given in the previous section).
The thumbnail shows the simulated video output (at TSS) corresponding to an RF pulse in wideband noise with S:N = 0.17 and a bandwidth ratio of 500.
A S:N guideline figure for pulse detection.
The sensitivity of a system may be taken as the "minimum detectable signal". This is that level of signal that exceeds a threshold value by a suitable margin (If the level is set too low, noise spikes will exceed it too frequently and if the signal+noise does not exceed it by a sufficient margin then it may fall below the threshold giving pulse termination prematurely. So, in determining the minimum detectable signal, it is necessary to choose the "false alarm rate" and