Method and arrangement for reducing the linearity influences in high-frequency circuits, particularly in A/D converters

To reduce linearity error influences in a HF circuit, particularly in an A/D converter, an input signal of the circuit is multiplied by a first auxiliary signal, and an output signal of the circuit is multiplied by a second auxiliary signal, the first and second auxiliary signals being selected such that a harmonic spectrum of the circuit is broadened.

BACKGROUND OF THE INVENTION 
The invention relates to a method and an arrangement for reducing the 
linearity error influences in HF circuits, particularly in A/D converters. 
Linearity errors of the transmitting function of electronic circuits, of 
the preselection of a receiver or of an A/D converter, for example, often 
sharply limit the possibilities to use such circuits for measuring 
purposes. The non-linearities of such circuits act mainly by means of 
harmonic waves. Spectrally seen secondary lines (what are known as 
spurious lines) arise. In an A/D converter, such spurious lines lead to a 
falsification of the signal to be digitized. 
To reduce the linearity errors of A/D converters, what is known as 
dithering is taught (Large-Scale Dithered ADC, Hewlett Packard Journal, 
December 1993). An artificially generated auxiliary signal is therein 
added to the useful signal at the input of the A/D converter, said signal 
being separated from the useful signal again at the output. In this known 
method, whose effectiveness depends on the conditions of use and is 
difficult to assess, particularly for integral non-linearities, the 
effective control range of the A/D converter is reduced and the useful 
bandwidth is restricted. 
SUMMARY OF THE INVENTION 
It is thus an object of the invention to demonstrate a method which avoids 
these disadvantages and which enables a better suppression of the effects 
of linearity errors of such electronic circuits as A/D converters. A 
simple arrangement for carrying out the method is also provided. 
According to the method of the invention for reducing linearity air 
influences in an HF circuit, an input signal of the circuit is multiplied 
by a first auxiliary signal, and an output signal of the circuit is 
multiplied by a second auxiliary signal, the first and second auxiliary 
signals being selected such that a harmonic wave spectrum of the circuit 
is broadened. 
The method of the invention permits a very effective and strong suppression 
of the harmonic waves generated by such non-linearities of electronic 
circuits. It is suitable for arbitrary electronic circuits wherein 
corresponding harmonic waves arise due to the non-linearities of the 
transfer function of the circuit. The method of the invention is 
particularly suitable for an A/D converter, however. Contrary to the known 
addition according to the dithering method, the multiplication by two 
auxiliary signals at the input and output does not restrict the useful 
bandwidth or the effective control range of an AND converter. 
The invention is detailed below in exemplifying embodiments, in the example 
of an A/D converter, specifically, with the aid of schematic drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1 depicts the general construction for carrying out the method. The 
analog input signal g(t) is fed to a multiplier 1, which, by multiplying 
by an auxiliary signal h.sub.1 (t), generates a signal s(t) with the 
following form: 
EQU s(t)=g(t).multidot.h.sub.1 (t). 
This signal is fed to the real A/D converter 2, which, according to the 
model, is composed of an arbitrary non-linearity 2a and an ideal A/D 
converter 2b. The non-linearity can be represented by a polynomial of nth 
order with the coefficients k.sub.n. At the output of the AD converter 2, 
i.e. after passage through the non-linearity 2a and of the ideal A/D 
converter 2b, the scanned signal a(t) is present in the form 
##EQU1## 
"A{ }" references the general scanning process of the ideal A/D converter. 
##EQU2## 
with t.sub.0 =1 /f.sub.a fa--scanning frequency of the A/D converter 
After the A/D converter 2, another multiplication by an auxiliary signal 
h.sub.2 (t) occurs by means of the multiplier 3. 
##EQU3## 
This other multiplication has the object of compensating the effects of the 
multiplication of the auxiliary signal h.sub.1 (t) carried out before the 
converter such that the now digitized useful signal A{g(t)} is 
extractable, and at the same time a spectral broadening of the harmonic 
waves takes place. 
The digitized useful signal is extractable specifically if the nature of 
the auxiliary signal is such that the term 
EQU A{k.sub.1 .multidot.g(t).multidot.h.sub.1 (t).multidot.h.sub.2 (t)} 
can be split into two linearly independent terms 
EQU A{k.sub.1 .multidot.g(t)} and A{x(t).multidot.g(t)}. 
For h.sub.1 (t) and h.sub.2 (t), the relationship 
EQU A{k.sub.1 .multidot.g(t).multidot.h.sub.1 (t).multidot.h.sub.2 
(t)}=A{k.sub.1 .multidot.g(t)}+A{x(t).multidot.g(t)} 
ultimately results in the ratio, 
##EQU4## 
x(t) is an arbitrary term which fulfils the condition 
##EQU5## 
Given the appropriate selection of the auxiliary signals h.sub.1 (t) and 
h.sub.2 (t), the spectral broadening of the harmonic waves occurs by the 
factor of 
EQU h.sub.1 (t).sup.m .multidot.h.sub.2 (t), 
which arises in the harmonic wave term. 
This means that the energy of the harmonic waves is divided into a broad 
spectral range, particularly given narrow-band input signals g(t). As a 
result, the spectral maxima fall off corresponding to the spectral 
broadening and potentially become invisible in the noise floor. 
In comparison, without the method of the invention, i.e. given the input 
signal's passage through the real A/D converter 2, exclusively, an input 
signal d*(t) in the form of 
##EQU6## 
would arise, which, contrary to the method of the invention, does not 
contain an additional factor in the harmonic wave term. 
A theoretically possible, simple auxiliary signal constellation results 
from 
##EQU7## 
with 
EQU f(t)=f.sub.0 +c.sub.1 .multidot.t. 
These auxiliary signals represent a linear frequency sweep with the carrier 
frequency f.sub.0 and with a rise factor c.sub.f. 
This results in the following: 
##EQU8## 
For these auxiliary signals, the residual term r(t) even becomes identical 
to zero, so that a specific extraction is not necessary. 
For the function f(t) as defined above, the factor 
##EQU9## 
in the harmonic term represents a frequency sweep which depends on the 
order of the harmonic waves. This frequency sweep leads to a defined 
spectral broadening of the harmonic wave portions by 
##EQU10## 
Advantageous realization 
FIG. 2 depicts the block wiring diagram of an arrangement for advantageous, 
practical realization of the method for application in a spectrum 
analyzer, for example. The analog signal g(t) is fed to a multiplier 1, 
which, by multiplication by an auxiliary signal h.sub.1 (t), generates a 
signal s(t) with the form 
EQU s(t)=g(t).multidot.h.sub.1 (t). 
An analog mixer is utilized as multiplier 1. As auxiliary signal h.sub.1 
(t), the real signal with the form 
EQU h.sub.1 (t)=cos(2.multidot..pi..multidot..intg.(f.sub.0 +c.sub.f 
.multidot.t).multidot.dt) 
is used. h.sub.1 (t) is thus a signal which is linearly rising in frequency 
and which has the carrier frequency f.sub.0, as can be generated by a 
typical synthesizer present in spectrum analyzers. The rise of the 
frequency can be varied by means of the constant c.sub.f. 
The resultant signal s(t) is fed to the A/D converter 2, so that the signal 
a(t) with the form 
##EQU11## 
results. 
The now digitized signal is fed to a conventional digital I/Q mixer and 
mixed with the auxiliary signal h.sub.2 (t). Such l/Q mixers can be 
realized by means of software on a digital processor (e.g. on a digital 
signal processor), or by means of hardware in a specific circuit. They 
enable the multiplication by a complex signal via the relation 
EQU e.sup.-j.multidot.x =cos(x)-j.multidot.sin(x) 
The auxiliary signal h.sub.2 (t) is therein described by 
EQU h.sub.2 (t)=cos(2.multidot..pi..intg.(f.sub.0 +c.sub.f 
.multidot.t).multidot.dt) 
The signal b(t), which can be interpreted as a complex signal and which is 
composed of the real portion bi(t) and the imaginary portion b.sub.q (t), 
arises in this way. 
The following applies: 
##EQU12## 
In the subsequent filtering stage 4, the intensely energy-rich noise 
portion is separated out by the large factor k.sub.1. This can be done 
easily with conventional digital filters, given appropriate selection of 
the carrier frequency f.sub.0 of the two auxiliary signals h.sub.1 (t) and 
h.sub.2 (t). Besides the digitized useful signal, the resultant output 
signal d(t) consequently still contains the spectrally broadened harmonic 
waves. 
The method functions not only in A/D converters, but also in all non-linear 
components and functional blocks which are connected between the 
multiplier 1 and the multiplier 2 as demonstrated. 
Although various minor modifications might be suggested by those skilled in 
the art, it should be understood that my wish to embody within the scope 
of the patent warranted hereon all such modifications as reasonably and 
properly come with the scope of my contribution to the art.