RF chain


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 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 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 and overload level. Other important parameters, related to these properties, are sensitivity ; dynamic range and spurious signal levels. 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.

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 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 nth stage in a chain of RF devices. The cumulative gain, noise figure, 1 dB compression point and output thermal noise power for the preceding devices are given by Gcumn−1, Fcumn−1, Pcumn−1 and Ncumn−1, respectively. We wish to determine the new cumulative figures, when the nth stage is included, i.e. the values of Gcumn, Fcumn, Pcumn and Ncumn, given that the nth stage has values of Gn, Fn, P1n for its gain, noise figure and 1 dB compression point, respectively.

Cumulative gain

The cumulative gain, Gcumn after n stages, is given by
and Gcumn is given by
where Gcumn−1 is the total gain of the first stages and Gn is the gain of the nth stage.
Conversion equations between logarithmic and linear terms are:
and

Cumulative noise factor (noise Figure)

The cumulative noise factor, after n stages of the overall cascade, Fcumn is given by
where Fcumn−1 is the noise factor of the first stages, Fn is the noise factor of the nth stage, and Gcumn is the overall gain of n stages.
The cumulative noise figure 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 section of the chain, the noise figure of the section equals the loss of that section. So, for example, a 3 dB attenuator has a noise figure of 3 dB.

    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. P1cumn,
where P1cumn-1 is the 1 dB compression point at the input of the first stages, P1n is the 1 dB compression point for the nth stage, referred to its input and Gcumn is the overall gain including the nth stage. The unit is or .
  • 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 . 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. 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, 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 GT and noise figure FT is given by
where k = the Boltzmann constant, T is the temperature in kelvins and B is the bandwidth in hertz, or
where Ncumn 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 must not be at too low a level, otherwise the noise is not properly characterized. 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 " and the "third-order intercept point ", 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 and three times the rate 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 I2cumn−1 is the second order intercept point at the input of the first stages, I2n is the third order intercept point for the nth stage, referred to its input and Gcumn is the overall gain including the nth stage.
Similarly,
where I3cumn-1 is the third order intercept point at the input of the first stages, I3n 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
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 is divided into M sub-bands of B/''M each, and for each sub-band 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 is the peak signal power of the pulse divided by the total noise power 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.