Signal Processing Group Inc., technical memorandum. Generated by the technical staff of
Signal Processing Group Inc. Visit our website at http://www.signalpro.biz for more info.
Notes on cascade analysis of systems ( Copyrighted
material)
1.0
Introduction: A typical cascade is shown below. It consists of building block
components such as amplifiers, mixers, filters etc.
FIGURE 1 Example of a cascade
The idea is to analyze/synthesize a cascade to meet real world requirements. In order to
do that, first an approximate design must be done, and then optimization carried out in
many different steps ( with the help of CAD programs). This is the usual case.
To synthesize a cascade some important quantities must be understood and used. A
minimal set of these quantities are listed and described below.
2.0
Cascade design variables: The following variables must be used ( and
understood) as a minimal set for cascade synthesis and analysis.
2.1
2.2
2.3
2.4
Gain: Relatively well understood quantity.
1 dB compression point: The input power at which the small signal gain
departs from a linear curve and compresses by 1 dB. See the notes in the
website “Notes on 1 dB compression and intercept points” for more detail.
Inter-modulation and intercept points: Measures of linearity and
distortion. Both third order and second order should be understood. Again
see “Notes on 1 dB compression and intercept points”.
Noise figure: The noise figure for a single block and for cascaded systems
needs to be understood. See “Notes on noise and noise figure” in this
website.
Brief discussions of the relevance of these variables follows:
Gain: The gain of the device is needed ( preferably under matched conditions) in
estimating most of the other quantities. Here we are using the gain in dB with
inputs and outputs in dBm.
Signal Processing Group Inc., technical memorandum. Generated by the technical staff of
Signal Processing Group Inc. Visit our website at http://www.signalpro.biz for more info.
1 dB compression point: Inputs lower than the 1 dB compression point provide
linear output and therefore linear gain. At the 1dB compression point, ( an input
quantity) nonlinearities appear in the output. Higher order inter-modulation
products start appearing in the output. Therefore we must try to keep the input
well within the range of input for the device. From the noise floor lower limit, to
the 1 dB compression point upper limit.
Third and second order intercept points: There are two points associated with
each of these. An input intercept point ( IIP) and an output intercept point (OIP).
From the discussion in the file “Notes on 1 dB compression and intercept points”,
it can be seen that the second order inter-modulation products increase at a rate of
2X with respect to the fundamental signal while the third order products grow at a
3X rate.
Operating at an input equal to IP2 may cause the fundamental output signal to be
corrupted since at that point the second order nonlinearities are at the same level
as the main output signal. However, the more critical of these inter-modulation
products is the third order product which lies close to the fundamental signal
outputs and can severely affect the desired signal or completely wipe it out if the
input is at the (input) third order intercept point IIP3. The output OIP3 is then
found from the gain and the IIP3 knowing that the third order products grow at a
3X rate with respect to the main component of signal. In addition the cascaded
IP3 can be a challenge as the IP3 of a cascaded system, with gain in the
blocks, will be lowered significantly. This effect must be borne in mind.
Noise figure: Noise is always present in the blocks and the way to quantify the
effect of the noise is through the use of the noise figure, NF. As shown in “Notes
on noise and noise figure”, the noise figure of the first stage in the cascade is the
most important one, specially if the cascade has amplifying blocks throughout.
Therefore the cascade needs to be designed with respect to the noise figure of the
various stages to achieve the overall required NF.
CAD tools for cascade analysis: Many CAD tools are available for cascade
analysis. The analysis part has been made quite fast because of the availability of
these tools. However, the synthesis is still the domain of the creative design
engineer. In order to design robust cascades an understanding of all the above
effects must be intuitive so that multiple iterations can be avoided. Obviously
with experience one becomes better and better at synthesis. And the CAD tools
can be a huge help in this endeavor.