14-02-2013, 09:41 AM
Kautz–Volterra modelling of analogue-to-digital converters
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ABSTRACT
In many test and measurement applications, the analogue-to-digital converter (ADC) is the limiting
component. Using post-correction methods can improve the performance of the component as well as the
overall measurement system. In this paper an ADC is characterised by a Kautz–Volterra (KV) model, which
utilises a model-based post-correction of the ADC with general properties and a reasonable number of
parameters. It is also shown that the inverse model has the same dynamic properties as the direct KV model.
Results that are based on measurements on a high-speed 12-bit ADC show good results for a third-order
model.
Introduction
The ADC is a key component in many applications, e.g. radio base
stations and test&measurement instruments. In state-of-the-art designed
vector signal analyzers (VSAs) the ADC is the bottle neck and
an improvement in ADC performance directly improves the VSA
performance. The trend within in test&measurement of combining
RF and digital signal processing has been prevalent for some time, it
gives unique possibilities to create novel measurement technologies
to reduce test costs and give important feedback to design, i.e. key
issues for the users. These possibilities are directly dependent on the
VSA performance, i.e. the ADC performance. As a consequence of
this the requirements on the ADC are increasing. Post-processing of
measured data is commonly used for signal conditioning as well as to
facilitate new and flexible measurement methods. An ADC suffers from
a (weak) nonlinear and dynamic behaviour but these imperfections
can be adjusted for afterwards by using some kind of post-correction
method [1]. The use of model-based post-correction requires accurate
models of the ADC.
Theory
Model description
It has been shown in [13] that the input–output relation of any timeinvariant
nonlinear system with fading memory can be well approximated
by a finite Volterra series representation to any precision.
Volterra filters are simple to use and have nice properties. For example,
they are linear in the parameters and hence standard and well-behaved
parameter estimation techniques can be applied. However, the need of
intensive computational schemes somehow limited their practical use.
This ismainly due to the slowconvergence huge number of coefficients
that must be estimated in order to calculate the kernels.
Experiments
The test set-up (which is in detail described in [16]) used a state-ofthe-
art signal generator together with specially designed signal
conditioners ensured that the test signals are generated and distributed
to theADC input. For a three-tone scan test scenario, bandpass filters are
used to suppress spurs and noise from the test signal. However, the
filters attenuate the signals; therefore it was amplified (with an ultra
low distortion amplifier) to obtain sufficient drive level (−0.5 dBFS).
Inside the filter bandwidth the noise floor is far above the level of
distortion products from the ADC due to the intermodulation products
caused in the output stage of the arbitrary signal generator and the other
components in the signal chain.
To overcome this limitation on measurement the 3rd order IM
products pre-distortion was used to obtain spectrally pure three-tone
signals for the measurement. Generally, output signal from the generator
contains unwanted components (harmonics, IM products and
spurs). The idea behind pre-distortion is to add signals to the wanted
signals so that the output from the generator will be distortion-free.
The implemented method is further described in [17] and is based on
iterative algorithms and spectrum analyzer measurements.
Conclusions
Post-processing of measured data is commonly used for signal
conditioning which also facilitates that imperfections in the ADC can
be adjusted, by using model-based post-correction methods. In this
paper a Kautz–Volterra model of order three is used to characterize an
ADC. The properties of a KV model facilitate the use of an inverse
model with a reasonable number of parameters.
The KV model is obtained from 20 three-tone measurements in a
frequency range of 63.6–74.7 MHz. The dynamic behaviour is mainly
due to the third-order nonlinearity, while the linear and second order
nonlinearity dynamic effects were negligible.