Note: Descriptions are shown in the official language in which they were submitted.
r~ / l I M
709
TITLC OF TIIE INVENTION
A DEVICE FOR LINEARIZING A l-IIGII FREQUENCY AMPLIFIER WITII
COMPLEX NON LINEARITY COEFFICIENTS
5 BACKGROlJND OF TIIE INVENTION
1. Field of the Invention
The present invention relates to a device for linear-
izirlgahigh frequerlcy amplifier with complex non linearity
coefficients and intended to amplify a multi tone signal.
The non linearity of an amplifier causes the
appearance of parasite signals called intermodulation
products, when it is energized simultaneously by several
signals whose frequencies are different. l.~hen the high
frequency signals to be amplified are close to each other,
15 for example in the case of modulated signals, the inter-
modulation phenomenon results then, outside the modulation
band, in a disturbance of the communications using
adjacent channels and, in the modulation band, in sound
distortion and especially in an increase of the error rate
20 in the case of multi carrier digital transmission.
2. ~escription of the Prior Art
To avoid such effects it is advisable to minimize the
consequences of the non linearity phenomena. ~ifferent
25 solutions have been proposed for that. They may be
classified in two categories: permanent slaving devices
and precorrector devices.
These two methods consist in applying to the input
of the high frequency amplifier not directly the signal
30 e(t) to be amplified but a signal h(t) obtained from
the signal to be amplified and whose spectrum comprises,
besides the high frequency spectral lines of the signal
to be amplified,correcting lines situated at the frequencies
of the intermodulation products to be eliminated.
When the non linearity coefficients of the amplifier
are complex, it is known to obtain the correcting lines
3~
v~
by acting separately on the modulus and the phase of the
output signal s(t) of the amplifier. It is for example
known to slave the envelope (attenuator) and the phase
of the signal s(t) independently and separately to the
envelope and to the phase of the signal e(t).
It is further known, according to French patent
no. 2,520,957, filed in the name of the applicant, to
obtain the correcting lines by precorrection by acting
independently and separately on two separate parameters
of the signal s(t).
The linearization device described in this
patent application in fact comprises means for elabora-
ting by precorrection, from the high frequency signal to
be amplified, a first and second correction signal whose
spectrum comprises adjustable amplitude spectral lines
situated at frequencies corresponding to the harmonics
of the di-fferences of tones of the high frequency signal
to be amplified, acting separately on two separate para-
meters of the amplified signal, and a predistortion de-
vice for elaborating, from the high frequency signal to
be amplified and from the first and second correction
signals, an inpu-t signal of the amplifier whose spectrum
comprises, besides high frequency spectrum lines of the
signal to be amplified, correcting lines, at the frequen-
cies of the intermodulation products of uneven orders,
and of adjustable amplitude by joint action on the ampli-
tude adjustments of the spectral lines of the first and
of the second correction signal, these adjustments being
carried out so as to obtain cancelling of the intermodu-
lation products of ineven orders situated in the vicinity
of the transmission band in the amplified signal.
Furthermore, in the above mentioned French pa-
tent, a special predistortion device has been described
comprisin~ a phase modulator and an amplitude modulator
intended respec-tively for modulating the signal to be
amplified by the first and the second correction signal.
:~2~8~
SUMMARY OF TIJE INV[NTION
The present patent application provides a new pre-
distortion device having intrinsica]ly easier implementation
with respect to the one described in the above mentioned
5 patent application and, in association with means for
obtaining the signals q(t) and q'(t) in accordance with the
second object of the invention, simplified use of the
linearization device.
According to the invention, the device for linearizing-
lO a i1igh frequency signal amplifier having complex non
linearity coefficients and intended to amplify a multitone
signal e(t), comprising means for elaborating, from the
high frequency signal to be amplified, a first and a
second correction signal q(t) and q'(t) whose spectrum
15 comprises adjustable amplitude spectral lines situated
at frequencies corresponding to the harrnonics of the tone
differences of the high frequency signal to be amplified,
acting separately on two separate parameters of the
- amplified signal, and a predistortion device for
20 elaborating from the high frequency signal to be amplified
and from the first and second correction signals an input
signal h(t) of the amplifier whose spectrum comprises,
besides the high frequency spectral lines of the s:ignal
to be amplified, correcting lines at the frequencies of the
25 intermodulation products of uneven orders, and of adjustable
am~litude by joir.t action on the amplitude adjustments
of the spectral lines of the spectrum of the first and
second correction signal q(t) and q'(t), these adjustments
being carried out so as to obtain cancelling of the
30 intermodulation products of uneven orders situated in the
vicinity of the transmission band in the amplified signal,
~nd the predistortion deyice ~omprisin~ an amplitude modulator for
modulating the amplitude of the signal to be amplified e(t)
by the first correction signal q(t), an amplitude modulator
35 with carrier suppression ~or ~odulating the amplitude of
the signal ~o be arnpli~ied e(t),phase shirted by 2~ by
tlle second correction signal q'(t) and a summator summing
the signals from these two modulators, supplying the input
signal of the ampli~ier.
In accordance with another object of the present
invention, the first and second correction signals are
obtained respectively by slaving two particular parameters
of the signal s(t)7 which are its cornponent coming from the
real part of the transfer function of the amplifier and
its component coming from the imaginary part of the transfer
Function of the amplifier (also called hereafter reflections
of the amplitude of two real orthogonal components of the
amplified signal, or more simply components X and Y of the
signal s(t)), tD the corresponding components of the
signal to be amplified.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention will be better understood from the foll-
owing description and accompanying Figures which are
given solely by way of indication and in no wise limiting
oF the characteristics of the invention; they show:
Figures la to ld, the diagrams of the transfer function
of an ~IF amplifier to be linearized;
Figure 2, the trend of the inrnt sinnal of this
amplifier and of its envelope for an energization with tw~
e4ual tones;
Figures 3a and 3b, the total spectrum and the filtered
spectrum of the output signal of the amplifier;
Figure 4a, a functional diagram of the predistortion
device in accordance with the invention, Figures 4b, 4c and
4d representing variants thereof;
Figure 5, a functional diagram of a precorrection
linearization device oi~tained by applying to the predistortion
device in accordance ~ith~the invention, corrrection signals
obtained by processing the envelope of the signal to be
amplified ;
,, . . _ , .... .
12f~7~g
Eiqure 6, a furlctional diagrarn of a slavir)g lineari -
zation devicr,? obtained by applying to the predistortion device
in accordance with the invention, correction signals comming from the
comparisons of the amplitude and of the phase of the
amplified signal s(t) witll the amplitude and the phase of
5 the signal to be amplified e(t);
Figure 7, a functional diagram of a slaving lineariz-
aLion devicr? ohtained hy applyinrl to the predistortion
,evice in accordance with the invention, correction signals obtained in
accordance with the invention, by comparison of two
1~ parameters which are the reflections of the amplitude of
two real orthogonal components of the amplified signal, to
the corresponding components of the signal to be amplified.
Identical elements in the separate Figures bear the
same references.
DESCRIPTION OF THE PREFERRED EMBODIMENT
A high frequency amplifier is considered receiving a
signal e(t) at the input and,delivering a signal s(t) at
20 the output. S(t) may be written:
S(t) = X(e(t))~ j Y(e(t))
in which X and Y are real functions and j is the irnaginary
nurnber such that j2 = -1.
Figures la and lb show that the high frequency
amplifier is not linear; in particular X(e(t)) is not
proportional to e(t), and has a slight saturation for
example. The modulus of the output signal may be
represented by:
¦S(t)¦ = ~ + Y2.e(t)
The diagram of this modulus appears in Figure lc. The
phase shift of the output signal with respect to the input
signal,
~ (S/e) = Arctg(Y/X)
7~3
is showrl in Figure ld. The transfer characteristics of an
ideal amplifier are shown with broken lines in these
diagrams. The signal e(t), amplified by such an amplifier,
will then undergo deformations during amplification.
These deformations may be explained by breaking down the
signal S(t) according to the transfer polynomial. According
to such breaking down S(t) is written:
S(t) = A e(t) + B e (t) + C e3(t) ~
in which A, B, C are complex numbers such that:
10 ¦A¦= a + ja' with A =~a + al2
¦B¦= b ~ jb' with B =lb + b'
¦C¦= c + jc' with C =~c2 + c,2
........
A, B, C... characterizing the linearity defects of the
15 amplifier. It should be noted that generally their modulus
decreases when they weight the high input signal e(t> to
a higher and higher power. It will be stated herea-fter
how this breaking up shows that the linearity defect oF
the amplifier causes the appearance of troublesome
20 intermodulation products. But, in addition, the study will
show that it is not necessary to know the transfer function
of the amplifier which it is desired to correct and that
therefore a device according to the present invention has
for this purpose a universal character. In fact, after
25 processing by the linearization device of the invention,
the characteristic terms X, Y, A, B, C of the amplifier
will have disappeared to be replaced by a characteristic
of the form S(t) = X'(e(t)) + jY'(e(t)), Xi and Y' being
linear, i.e X (ee(tt))) = constant and Y'(e(~t!) = constant.
30 Then ~ S/e = constant. e~t)
In actual fact, if the amplifier has at its output a harmonic
filter, the action of this latter is incorporated in the
preceding expression of S(t).
When the signal e(t) only comprises one high frequency
35 tone, the non linearity only causes harmonic spectral lines
7(~9
whose amplitude according to the r~nk is related to the value of
the coefficients A, B, C... They may be readily elirninated by
filtering. On the other hand, if the signal e(t) comprises
at least two tones, it is quite different and some parasite
spectral lines fall in frequency zones intermediate to
5 the two tones It the two tones are close to one another,
the filtering of these parasite intermodulation products
will not be able to be easily carried out.
The following study is made for an input signal e(t)
comprising two equal tones according to the method
10 recommended by the CCIR but the principle remains valid
for two unequal tones or for n tones of any kind, even
emitted at different amplitudes. The signal e(t), with
two equal tones for example, applied to the input of the
amplifier to be corrected will have the form~
e(t) = V(cos wlt + cos w2t)
which may also be written
w2-wl w2+wl .
e(t) = 2V cos ( 2 ) t cos ( 2 -)t
In this expression wl and w2 are the pulsations of
20 each of the two tones.
In one example, the amplifier~to be corrected will be
an amplifier for BLU signals emi-tted in the 1.5 to 30 MHz
band. The pulsations wl, w2, corresponding to the two
zones mentioned, will correspond to frequencies situated
25 in this band and separated from each other by about three
KHz for example. These magnitudes are of course in no
wise restrictive of the field of application of the invention.
5uch a signal e(t) is shown in Figure 2. In this
Figure can be seen the signal e(t) properly speaking
30 formed by the tightly spaced half waves shown with continuous
lines. According to the second part of the expression
e(t) mentioned above it is apparent that e(t) is equivalent
to the product of a first pulsation signal 1 W2 multiplied
by a second pulsation signal W2 Wl (of low frequency).
.. .. . . -- -- . . - -- - .
1~il37()9
By replacing, in the polynomial breakup of S(t), e(t)
by the conventional two tone value which has just been
determined, S(t) is written, once all the calculations
have been made,
S(t) = B + B(cos(wl-w2)t + cos(wl+w2)t)
+(A+4 ) (cos wl.t+cos w2.t)
+(4C) (cos(2wl~w2)t + cos (2w2-wl)t)
(B) (cos 2wl~t +, cos 2W2
+4C(cos(2wl + w2)t + coS(2W2 + Wl)t)
C (cos 3Wl.t + .cos 3W2
+....
To simplify the calculations, we stopped at non
linearities of order 3, but the enumeration of these
20 calculations remains valid for any higher order.
A spectral representation of S(t) is given in Figure
3a. This Figure shows the total spectrum of S(t). Since
wl~w2 is very much greater than w2-wl it can be seen
that this spectrum presents groups of spectral lines
25 about pulsations having the value of:
Wl +W2
w = n(- ), n being a whole number between O and
infinity. 2
The amplitudes of the different spectral lines,
30 appearing in this total spectrum, are those given as a
function of the parameters A, B, C of the polynomial
breakdown of S(t). Only the modulus of the coefficients
appearing as ordinates is to be taken into account. It
will be noted that only the group situated about pulsation
wl-~W2
~ interests us~ It is troublesome, for it comprises
:12~37~)~
spectral lines at pulsations 2wl-w2 or 2w2-wl. With a prior
art device, the harmonics situated outside this useflJl
band will moreover be easily eliminated. In fact, a convent-
ional transmitting equipment has at its output harmonic
filters letting through neither the continuous components
5 nor the low frequency (w2-wl).
The spectrum of the amplified signal in the useful
band is shown in Figure 3b. It can be seen that it comprises
spectral lines at pulsations wl and w2 each weighted by
the same coefficient A ~4C thus signifying that each
10 spectral line has undergone equal amplif`ication. It also
comprises two intermodulation parasite spectral lines
2wl-w2, 2w2-wl, to each of which is assigned the coefficient
4C It will be noted that the amplitudes of the intermod-
ulation spectral lines of the fifth order of the form
15 3wl-2w2 and 3w2-2wl have not been shown in-Figure 3b. On
the one hand, the coefficients afFecting each oF these
spectral lines are in general less than the coeFficients
affecting the intermodulation spectral lines of the third
order and, on the other hand, it will be seen hereafter
20 that these intermodulation spectral lines will undergo the
same treatment as the first and will also be cancelled out.
Representation thereof would have encumbered the
representations of Figure 3.
It has been seen that the even terms had no incidence
25 on the intermodulation products which concern us. To
continue the calculations, we will therefore not bother
about non linearities of even order, and we will go as
far as the order 5 for non linearities of uneven order:
S(t) = A e(t) +C e (t) + Ee (t)
By giving to the polynomial the complex character
mentioned above (A = a + ja', C = c + jc' and E = e + je'),
with all calculations made, S(t) takes on the following
form after harmonic filtering:
17~9
(t) = (aV ~4c V3 + 5 8V ) (cos wlt + cos w2t)
+(a'V + 94 V3 ~ 50B U ) (cos(wlt + 72r) ~ cos(w2t+ 2))
~(- cV3 +~5 eV5) (cos(2wl-w2)t ~ cos(2w2-wl)t)
(l) +(4c'V3 + 25 e'V5) (cos((2wl-w2)t + ~-)+ cos((2w2-wl)t+72r))
+(8 V ) (cos(3wl-2w2)t + cos (3w2-2wl)t)
+(5e V5) (cos((3wl-2w2)t+~2)+cos((3w2-2wl)t~
This way of writing causes each spectral line of the
spectrum of S(t) to appear with.harmonic filtering,
according to two real orthogonal components 9 one-coming
15 from the real part of the non linearity coefficients,
the other, phase shifted by ~2 radians, coming from the
imaginary part of tlle ~seme coefficients.
These CQmpOnentS a~e cQn~p~m, on the one hand, to an
amplitude modulation of e(t) als~ letting through the
20 main spectral lines and, ~n the other hand, to a sec~nd
modulation of e(t) , either of phase with small index , or
of amplitude without carrier (DBL, balanced modulation),
phase shifted by 2~ radians, and added to the first one.
~rom this observation, ~t is then possible to create
spectral lines opposed to the intermodulation spèctral
lines , by ~d~ing ~an amplitude modulation of e(t) by
a first adequate cvrrectiQn signal q(t) and an
amplitude m~dulat~on ~ithout carrier , of e(t) previously
phase shilted by ~ radians, by a second adequate
30 correction signal q'(t), This is why the predistortion
device l in accordance w~th the invention, shown in
Figure 4a, compris-es an amplitude modu]ator 2 which receiyes
the signa~s e(t) and q(t?,.. an amplitude modulator with
carrier suppression 3, which receives the signal e(t) pha$e
35 shifted by 12r by means of a phase shifter 4, and a summer
.....
1~8~7(~
11
5 which receives signals hl(t) and h2(t) coming respectively
from the modulators 2 and 3 and which supplies the signal
h(t) supplied to the input of the ampliFier.
The amplitude modulator with carrier suppression 3 is
formed for example by a balanced modulator, a ring modul-
5 ator, a multiplier, a variable gain amplifier or any otherequivalent circuit.
In practice, if it is desired to operate over a fairly
wide band, instead of the ~2 phas~ shifter 4, a circuit
4' known from the prior art will be used,as shown in
Figure 4b, using pass-all quadripoles delivering at two
outputs signals el(t) and e2(t) phase shifted by ~
radians with respect to each other butoE variable phase
with respect to the input. The variable character of the
phase is absolutely secondary within the scope of the
15 invention since this phase shift remains constant over the
narrow spectrum to be transmitted ( a few kilohertz).
The accuracy and the constancy of the phase difference
of ~ radians between el(t) and e2(t) depends on the order
of the pass-all circuits.
20 ~or e(t) = ~2V (cos(wlt - ~(f)) + cos (w2t - ~(f)))
el(t) = V(cos wl-t~ cos w2t)
we have
e~(t) = V(cos(wlt + ~) + cos(w2t + ~))
Also in practical operation, since the main spectral
lines must be transitted by the amplitude modulator 2
(or variable gain amplifier) passage into this branch will
be promoted by using an asymmetrical phase-shifter promoting the zero
degree output and leaving the ~ output at -10 or -15 dB.
305imilarly1 the summing may be achieved by means of a
summer which is also asymmetrical~ for exarnple a 10 or 15
dB wide band coupler 9 using the coupled channel as input
of the ~ phase shifted branch. In fact, by heavily
modulating the phase shifted channel, that allows modulat-
35ion spectral lines to be obtained equivalent to lû or 30dBof the main spectral lines, which in most cases is largely
37 Ll~
12
sufficient.
Figure 4c shows a variant of Figures 4a and 4b, in
which modulators 2 and 3 both receive the signal e(t)
to be amplified~ the 2 phase shift between the spectral
lines coming respectively from modulators 2 and 3 being
5 then obtained by means of a quadrature coupler 5' which
replaces the summer 5. Since coupler 5' provides a phase
shift (variable with the frequency) for the spectral lines
from modulators 2 and 3, it is necessary to take this
pha5e shift into account in the case where the si~nals
q(t) and q'(t) are obtained by feed back.
Another variant is also sllown in Figure 4d where the
amplitude modulator 2 is placed after the summer 59 which
adds to the modulation spectral lines phase shifted by
15 7~ a slight modulation which is perFectly negligible.
The predistortion device shown in Figure`s 4a, 4b, 4c
and 4d is simpler to implement because of the exclusive
use of amplitude modulators. Its operation will be
described at the same time as that of the means for
obtaining the correction signal q(t) and q'(t), accord-
ing to the different embodiments shown in Figures 5, 6 and
. 7.
The correction signals q(t) and q'(t) may be obtained
either by precorrection or by parametered slaved operation.
In Figure 5, the predistortion device 1 of the
invention has beèn shown (for example in accordance with
the diagram of Figure 4b) to which are applied signals
q(t) and q'(t) obtained by processing the envelope of the
- signal to be amplified, in accordance with the device
described in patent application n 82 01 454 filed in the
name of the applicant, reducing the intermodulation by
precorrection of the signal to be amplified.
The signal q(t) is obtained by means of N multipliers
61, 62, 63...6N, the first of which 61 has two inputs
connected to the output of a detector 7 of the envelope of
the signal e(t), the second 62 of which has two inputs
~LZ~'76~
13
connected to the output of the First one and of which the
nth 6n (n being a whole number between 3 and N) has two
inputsconnected respectively to the output of the First one
and of the (n-l)th.of N linear amplifiers Bn with adjust-
able amplitude and sign gain, each having an input connected
5 to the output of one of the N multipliers 6 , and a
summer 9 having N inpu-ts connected to the outputs of the N
adjustable gain amplifiers 8n and an output which supplies
the signal q(t).
Similarly, the signal q'(t) is obtained by means of N
'lO multipliers 6n, N linear amplifiers 10n with adjustable
amplitude and sign gain, each having an input connected
to the output of one of the N multipliers 6n and a summer
ll having N inputs connected to the outputs of the N
adjustable amplifiers 10n and an output which supplies the
15 signal q'(t).
In Figure 5 has also been shown the high frequency
amplifier 12 to be linearized, to which the signal h(t)
from the predistortion device l is supplied.
The linearization device shown in Figure 5 operates
20 in the following way:
For el(t) = V(cos wlt + cos w2t), we have:
q(t) = 2KlV2 -~ 6K2V4 + l
~(2klV2+ 8K2V4) cos(w2-wl)t
-~2k2V4 cos 2(w2-wl)t
the coefficients kl, k2...etc representing the gain of
30 the amplifiers 8n with gain adjustable algebraically
by the operator and the term -~l characterizing the
amplitu,de modulation from a variable gain stage9 in which
case it is outside and the modulator stage only provides
a rnultiplication of e(t) by q(t) to give hl(t) = el(t).q(t)
,~,
12~ 7C~9
.~,
hl(t)= (V~3klV3-~lOk~V5)(coswlt+cos w2t)
~(k~V3~5k2V5)(cos(2wl-w2)t+cos(2w2-wl)t)
+ k2V5'(cos (3wl-2w2)t ~ cos (3w2-2wl)t)
Si~ilarly
5 q'(t)= ~kllv2+6kl2v4
+(2k'lV2+8k'2V4) cos(w2-wl)t
+2k'2V4 cos2(w2-wl)t
where k'l, k'2,.. etc re~resent the gain of the amplifiers
lU 10n with gain a~ljustable alge~raically by the operator (here
it is a question of modulation without transrnission of main
spectral lines, The term ~l does not then appear).
. . h2(t)=e2(t).q'(t) :
h2(t)= t3k'lV3+lOk'2Y~(cos(wlt+~)+cos(w2t+2)j
+(kllv3+5kl2v5)(cos((2wl-w2)t+~)~cos~(2w2-wl)t-~2)3
~(k'2V~(cos((3wl-2w2)t+ ~ +cos((3w2-2wl~t+~))
The signal h(t) = hl(t) -~ h2(t) passes through the
amplifier 12 whose non linearities aFfect practically solely
the main spectral lines, taking the levels into account.
Therefore, the output signal S(t) has as expression:
2Q S(tj=((aV +94V +508V )+a(3klV3+10k~V~)(cos wlt-~cosw2tj
+((a'V+_~-+5e8V )+a(3k'lV3+lOk'2V5))((cos(wlt~
+ coS (w2t ~ n2 )~
+u3c4V +~58eV )+a(klV3~5k2V5))(cos(2wl-w~t+cos(2w~-wl~t)
+ ((~ ~ ~5~ V .3 + a ~k' lV3 + 5 k~ V5)) (cos U2w w2) t + n )
+ cos ((?W2-wl)t + ~
+ ( 8V + a k2V5) (cos (3wl-2w2)t + cos (3w2-2wl)t)
~ (~ + a k'2V5) ~cos ((3wl-2w2)t ~ 2 ~ ~ cos U3w2-2wl)t
.
7(~9
8y beyinning the adjustrnent by the spectral lines of
the highest order, there is obtained for
~2 = -8 a' k'2 = -8 a kl = -4 a' and k'l = _ 4 c :
S(t) = aV (cos w t + cos w t)
1 2
~ a'V (cos (wlt + F ) + cos (w2t + 2))
In Figure 6, the pre~istortion device in accordance
with Figure 4b has been shown, to which signals q(t) and
10 q'(t) are appliedJ working by making the amplitude and the
phase of the amplified signal dependent on the amplitude
and the phase of the signal to be amplified. There are also
shown in this Figure the harmonic filters 13 disposed at the
output of the hioh frequency amplifier 12.
15 ~.. ccording to the prior art, the si~.nal q(t) is obtained at the
output of a comparator 14 which compares the envelope of
the signal S(t), attenuated by means of an attenuator 15
and of the signal el(t) 9 detected respectively by means o~
two envelope detectors 16 and 17.
2û Similarly, the signal q'(t) ls obtained at the output
of a phase comparator 18 which compares the phase of the
signals S(t) and el(t) fed respectively to choppers 19 and
20, the phase comparator 18 being followed by a low pass
filter 21, and a delay line 22 being disposed in the path
of el(t).
Since operation by dependence on the modulus and the
phase is well known~ it will not be described here in
greater detail.
In Figure 7 the predistortion device according to
30 Figure kh has been shown, to which are applied signals
~(t)and q'(t3 obtained, in accordance with the invention, by
comparison of the low frequency and continuous signals
(XS and Y5) representative of the amplitude of the
amplified signal according to two real orthogonal components
35~one of which is in phase with the signal to be amplified,
lZ~8~
16
with similar signals (Xe and Ye) representative of the signal
to be amplified.
The principle of this dependence will first of all be
described.
Let us take un input signal:
el~t) = V cos wt
After passing through a linear amplifier with gain G
providing a cnnstant phase shift ~, we obtain:
S(t) = GV cos (wt + ~)
The input signal is squared:
e21 (t) = V (1 + cos 2wt)
After low pass filtering eliminating the high
frequency terms,there remains:
v2
X = 2
Xe is in fact proportional to the square of the component
along the axis of the abscissa.
A phase shift of ~ is added to el(t) so as to obtain,
20 e2(t) and this new signal is multiplied by el(t):
' el(t~. e2(t) = v2 (ros wt. cos(wt + F))
= ~2(cos(2wt + T) + C09 2)
After low pass filtering, there remains:
Ye
By working out the same products on the output signal,
we obtain: '
S(t) . el(t) = GV (cos(2wt + ~) + cos ~)
that is to say, after filtering:
X5 = GV2 COS ~,
and:
S(t).e2(t) = GU2 (cos(2wt + ~ + ~) + cos (~
3S that is, after filtering:
.
17
G V 2
Except for the coefficient (2)~ it can be seen tl)at:
X = V , Y - o
X5 = GV cos ~ Y5 = GV sin ~
If we now apply this principle to the predistortion
device of Figures 4a, 4b, 4c and 4d, i.e. to signals:
el(t) = V(cos wlt + cos w2t)
and
e2(t) = V(cos(wlt ~ 2) + cos(w2t + F)),
with the output signal S(t) such as defined above by the
fDrmula (1), and attenuated by means of a ~ transfer function
attenuator, with all~calculations made, after multiplication
and low pass filtering, we obtain:
(2~Xe=V (l-~co~w2-wl)t)
)Ye=V2 (cos((w2-wl)t~ cos((wl-w2)t+~))=o
(4)X5=~V ~ (aV+ 4 + 8
~(aY+3cV3+758V )cos(w2-wl)t
~(4CV ~ 8 CV~ cos2(w2 Wl)t ¦ A
+58eV5 3(W2 Wl~t
(5)Ys=~V ~a'V~ 8 5)
(a'V+3c'Y3+758eV )cos(w2-wl)t
(43c'V3~38 e'V~ cos2(w2-wl)t
+ ~e'V5 cos3(w~-wl)t
On these signals can be observed continuous terms,
and harmonic low frequency terms of the frequency difference
between the two initial tones. These signals have
respectively amplitudes which are the combination,for XS,
35 of the diFferent real parts of the non linearity coefficie-
nts of the amplifier to be corrected and,for YS,of the
.
,, .
7~
different imaginary parts o~ the same non linearit~
coeFficients. These coefficients are shown here for non
linearities not exc~eding the order 5. In actual ~act,
they go beyond; consequently, the cut off frequency of the
low pass filters used after the multipliers may be
5 evalu~ted.
With the magnitudes Xe, Ye characterizing the input
signal and the corresponding magnitudes Xs, Y5 characterizing
the output signal, it will be possible to provide two
independent slaving loops. They will use respectively
10 Xe and Ye ( equal 0) as reference information and res~ecti-
vely Xs and Y5 as feed back information. Sinc~ the
dependence~ tend to cancel out the difference between X5
and Xe on the one hand and between Y5 and 0 on the other,
the out,out signal will be as much as possible similar to the
15 input &ignal. The comparative elements uf these two loops
are formed by differential amplifiers whose gains define
the accuracy of the correction whereas the two actiue
modulation elements are integrated in the predistortion
device. The error signals q(t) and q'(t) are a function of
20 the difference between the reference and feed back
information.
As shown in Figure 7, the error signal q(t~ is
obtained at the output of a~ differential amplifier 23
which receives at its two inputs the reference X and feed
25 back Xs information for making the component-of S~)
dependent, which comes from the real part of the transfer
function of the amplifier.
~ To obtain the reference information X 9 a multiplier
?4 is provided which receives at its two inputs the signal
30 el(t) obtained at the non phase shifted ~utput o~ circuit
4' and a l~w pass filter 25 disposed at the output ~f
amplifier 24. -
Similarly, so as to obtain feed back information XS,a multiplier 26 is provided which rece-iues at its t~o
35 inputs respectively the siynal el(t~ and the signal Stt~ ;
l9
attenuated through a ~ transfer function attenuator 27, and
a low pass filter 2~ disposed at the output of multiplier
26.
The error signal q'(t) is obtained at the output of
a differential amplifier 29 which receives at its two
5 inputs the reference Ye (equal to 0) and Feed back Y5
information for making the component of S(t) dependent,
which comes from the imaginary part of the transfer function
of the amplifier. To obtain the feed back information YS,
a multplier 30 is provided which receives at its two inputs
lû respectively the signal e(t) and the signal S(t), and a
low pass filter 31 disposed at the outpot of multiplier 30.
The low pass filters conserve the harmonics n(w2-wl), - ~-
with n being a whole number greater than or equal to 1. By
way oF example, in the case of amplification in the 1.5 - 30
15 MHz band, the cut off frequency of the low pass filters
may be chosen equal to 50 kHz.
Although the means for obtaining the correction signals
q(t) and q'(t) in accordance with the invsntion may be
. used with a predistortion device other than the one which
2û Forms the subject of the present invention9 it can be
seen in Figures 7 that in the case where they are associated
-with the predistortion device of the invention, the
phase shifter 4' may be common to the predistortion
device and to the means for obtaining the signals q(t) and
25 q'(t), which simplifies implementation of the linearization
device.
- By taking the case again of a signal with a single
tone, for which:
X - ? Y = O
e e
X5 = ~ ros ~ yS =2V sin ~,
when the two loops are balanced we have:
Xe = Xs~ ~h~ is:to say
-~ ~ GV2 cos ~ , or else~
lZ~t7~
V ~ ~ GV cos ~
and Y = YS, that is to say:
0 ~ GV sin ~ or else:
sin ~ ~ 0
When the two loops are balanced we have, For a single
tone signal:
~ 1
O
In the case of a two tone signal, the balance of the
two loops results by the identity of the terms having the
same pulsation, on the one hand in the expressions X and
X5 (formulae (2) and (4) discussed above), and on the other
hand in the expressions of Y and Y5 (formulae(3) and (5)).
The equality Y = Y results in:
S e
9c'V3 50e'V5
4 8
~ V (a'V ~ 3c'V3 + 75eBV ) = 0
~ V (-4 c'V3 + 30 e'V5 ) = 0
~ V (-8 e'V5) = 0
Since ~ and V are non zero, the equivalent terms a', c',
d' may be deduced with dependence:
e' = 0, meaning that the intermodulation of order 5,
phase shifted by ~2~ of formula (1) is zero.
c' = 0, meaning that the intermodulation of order 3,
phase shiFted by 2~ of formula (1) is zero.
a' = 0 "neaning that the main components, phase
30 shifted by 2~ of the formula (1), are zero.
Similarly, the equality X = X results in:
S e
~ V (aV ~ 4c V3 + 50ev ) V2
~ V (aV + 3cV3 ~ 75eV ) = v2
~2C~
21
V (~ c~3 + 30 e~5) - o
~ V (~ eV5) = 0
As before, the equivalent terms a, c, e may be dedu~ed
with dependence:
e = 0, meaning that the intermodulation of order 5,
non phase shifted, o~ formula (1) is zero.
c = 0, ~eaning that the intermodulation of order 3,
not phase shifted of formula (1) is zero.
a ~ ~, representing the gain of the system on the
main spectral linesO
It is then apparent that the system behaves with
conventional dependence on the HF signal in which the
non linear amplifier of gain G would be fed back with a
linear rate (attenuator). Then the e~uivalent g~in is:
S(t) = 1
It is a conventional formula in the
dependences, providing that G.g is very much greater than
1 (9 representing the gain of the differential amplifiers).
It is indeed this assumption which has been chosen since,
at the input of the differential amplifier, we have
consid~red that when balanced the two signals presented a
zero difference; that supposes g is large so as to maintain
the error signal (q and q').
In practise, a certain transit time ~ may exist in
the different elements of the HF chain and produce a
phase shift ~ = W r which is variable with the pulsation w.
Therefore:
S(3 ( v+9C v3+50eV 3 (cos(w1t+ ~ +cos(w2t+4))
(a~Y+9C'y3+50e'V~ (cos(wlt~+~)+cos(w~t~2~e))
(6~ +(43cV3+28 eV~ (cos((2w1 w2)t~)+cos((2w2-w1~t~ ~)
~(43c'V3+28 e'Y5~(cos((2w1-w~t+~+~+cos((2w2-w1~t~ n~
~58V5 (cos((3wl-2w~t~e)~cos((3w~-2w1)t+B))
+5~eV5 (cos((3w1-2w~t+~+ ~ +cos~(3w2-2w1)t~n~3
'7~g
22
With el(t) = ~(cos wlt + cos w2t) we then have:
Xs=el(t)O~35(t)=
l (aV ~94 + 8- )cos~-(aY+ 4 -~ 8 )sin e
5 t7) + ((aV + 3cV3 ~ eV5)cos~-(a'V + 3c'V3 +~e'V~sinB)cos(w2-wl)t
i3V + ((43 cY3 + 38 eV5)cos ~ e'V3 + 30 e'V5)sin ~) cos 2(w2-w
_. + (~ eV5 cos e - ~ e'V5 sin 4) cos 3(w2-w l)t
And with e2(t) = ~(cos(wlt + ~2) + cos(w2(+~2))9 we have:
Ys=e2(t).~S(t)=
(aV+94V +-508eV )sin4~(a~v +9c'V +50e'V5)cOs~
(8) + ((aV ~ 3cV3 + ~eV5)sin4~ (a'V + 3c'V3 -i 75e'V~cos~)cos(w2-wl3t
gV + ((43 cV3 t 38 eV5)sin ~ e'V3 ~ 38 e'V5)cos ~) cos 2 (w2-wl)t
+ (g eV5 sin~ + 58 e'V5 cos ~) cos 3 (w2-wl)t
Each term is this time formed of two parts in which
the parasite term, weighted by the value of 9, is all the
20 rnore troublesome the greater ~is-
Thus the system is stabilized but there is inter-
dependence of the action of a loop on the correction of the
other and vice versa. This clifficulty will be avoidecl by
placing a delay circuit, for bringing ~ back to a zero
25 value, either at the outputs el(t) and e2(t) in the
direction of the multipliers, by placing two delay lines
32 and 33 of value ~ , or by placing in the p return a
delay line 34 (T - ~) but this latter varies with -the
frequency, which is l~ss convenient (the delay line 34
3U being shown with a broken line in Figure 7).
As has been shown with broken lines in Figure 7, the
at-tenuator 27 may be replacecl by a variable attentuator 37,
controlled for example by a programmed memory 38, so as to
compensate for the gain of the amplifier to be linearized,
35 in order to keep the operating point of the predistortion
- ~2~871~
23
deuic~ l constant.
In the case of Figure 7, the output information S(t)
is taken after harmonic filtering. S(t) may however be
taken be~ore filtering, for the harmonics multiplied by
el(t) and e2(t) (in multipliers 26 and 3û) give HF terms
which are eliminated by the low pass filter 28 and 31. If
the output information is taken afte~ the harmonic filter
13, this latter provides a very troublesome ph~se shift
which is added to the transit time. Tw~ filters 35 and 36
may then be formed with identical function and structure,
except for the power ( only the pha~e Chift function interests
us) and placed in seriPs with the d~lay lines 32 and 33.
There is thus good phase compensation between the signals
reaching multipliers 26 and 30.
It has been seen tha~, for an input signal having one
tone or two equal tones, the equivalent gain had as linear
value the inverse of the feed back coefficient ~ .
The case will now be taken of an input signal with
two unequal tones e(t) = Vl c~s wl t ~ V~ cos w2t.
We then have:
V12 V2~
Xe= 2 + 2 +vlv2cos(w2-wl~t
S(t)=
(aVl+~c(V13~2V1V22)~e(V15+6V13V22+3V1Y2~ coswlt
+ (a V2+ 43 c(V23+ 2V2V12~+ ~ e(V25+ 6Y23V12~ 3V2V14)) cos w2t
+ (a' Vl+ 43 c'(V13~ 2VlV;27)+ 5~, e'~V15+ 6V13V22+ 3VlY24)) cos(wlt ~ ~)
+ (al V2+ ~ c'(V23~ 2V;2V12)+ ~ e'(V~5~ 6V23Y12+ 3V7V14)~ cos(w2~ + i~
(43 c V12V2+ 58 e(2V14V;~ 3V12Y23~ cos(2wl-w2)t
(4 C V22Vl+ 58 e(2Y24V1~ 3V~2V133) coS(2w2-wl)t
+ (~ c' V12V2~ S, e'(2V~4V2+ 3Vl~V23~) cos ((2wl-w2)t +
24 ~ 7¢~
(43c'V22Yl~e'(2V24VI+3V22Yl~) cos((2w~ wl)t+
5 3 2
eVI V2 cos(3wl-2w2)t
S 3 2
+ ~eV2 Vl CS(3W2-2Wl)t
5 3 2
+ 8e'Vl V2 cos ((3wl-2w~+
+ 58e~v23vl2 cos ((3w2-2wl)t+ ~
The calculations of X5 and Y5 are not developed llcre
but, as before, the equality between Y5 and Ye (=)
cancels out the imaginary non linearity terms in a closed
loop. Similarly, the egality between X5 and X cancels out
the coefficients other than "a" in a closed loop.
The first terms of X~ may llowever be developed:
Xs =
2((aVl+43c(V13+2VlV22)+~e(V15-~6V13V22~3YlV24))Vl
+~(ay2+43c(v23+2v2vl2)+~e(v25+6v23vl2+3v2vl4))v2
~(aVl+43cV13+2VlV22)+5ge(V15+~V13V22+3VlV24)1
~2 I V~cos(w2 wl)t
3cV22V1~5~(2V24Vl~3Y22Vl~ J
f~av2+43cv23+2v2vl2)+~e(v~5+6v23vl2+3v2vl4)l
+ ~' I vlcos~w2-wl)t
3~ c Vl~V2+ 58 e(2V14V2+ 3V12V23) J
. . . etc . --
As has bccll seen, tile equivalent clo--ed loop terms
e, c, e', c', a' are cancelled out by the eguality at the
input of the comparators.
In a closed loop, X5 and X become:
7~9
X5 = ~2(aVl -~aV22) +2aVlV2 cos(w2-wl)t
1 2 2
Xe 2(Vl + V2 ) ~~ VlV2 Cos(w2-wl)t
By comparing X and X5 we finally have:
1 2 - 2 = P2 (aV12 ~ aV22)) for the continuous
terms and VlV2 = 2aVlV2 for the terms of pulsation
w2-wl , Whence(in a closed loop with balancing) a~ ~ .
The same solution appears if we take an input signal with
10 n tones. So, provided t`hat the phase condition between
e(t) and S(t) the closest possible to zero is respected, we
have in all cases:
S(t) ~ ~ e(t) (~ being the transfer function of a very
linear attenuator).
