CA1208709A - Device for linearizing a high frequency amplifier with complex non linearity coefficients - Google Patents
Device for linearizing a high frequency amplifier with complex non linearity coefficientsInfo
- Publication number
- CA1208709A CA1208709A CA000447114A CA447114A CA1208709A CA 1208709 A CA1208709 A CA 1208709A CA 000447114 A CA000447114 A CA 000447114A CA 447114 A CA447114 A CA 447114A CA 1208709 A CA1208709 A CA 1208709A
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- Canada
- Prior art keywords
- signal
- amplified
- cos
- amplitude
- amplifier
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- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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Classifications
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03F—AMPLIFIERS
- H03F1/00—Details of amplifiers with only discharge tubes, only semiconductor devices or only unspecified devices as amplifying elements
- H03F1/32—Modifications of amplifiers to reduce non-linear distortion
- H03F1/3241—Modifications of amplifiers to reduce non-linear distortion using predistortion circuits
- H03F1/3247—Modifications of amplifiers to reduce non-linear distortion using predistortion circuits using feedback acting on predistortion circuits
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03F—AMPLIFIERS
- H03F1/00—Details of amplifiers with only discharge tubes, only semiconductor devices or only unspecified devices as amplifying elements
- H03F1/32—Modifications of amplifiers to reduce non-linear distortion
- H03F1/3241—Modifications of amplifiers to reduce non-linear distortion using predistortion circuits
- H03F1/3258—Modifications of amplifiers to reduce non-linear distortion using predistortion circuits based on polynomial terms
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03F—AMPLIFIERS
- H03F1/00—Details of amplifiers with only discharge tubes, only semiconductor devices or only unspecified devices as amplifying elements
- H03F1/32—Modifications of amplifiers to reduce non-linear distortion
- H03F1/3241—Modifications of amplifiers to reduce non-linear distortion using predistortion circuits
- H03F1/3282—Acting on the phase and the amplitude of the input signal
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03F—AMPLIFIERS
- H03F1/00—Details of amplifiers with only discharge tubes, only semiconductor devices or only unspecified devices as amplifying elements
- H03F1/32—Modifications of amplifiers to reduce non-linear distortion
- H03F1/3241—Modifications of amplifiers to reduce non-linear distortion using predistortion circuits
- H03F1/3294—Acting on the real and imaginary components of the input signal
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- Physics & Mathematics (AREA)
- Nonlinear Science (AREA)
- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Algebra (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Amplifiers (AREA)
Abstract
ABSTRACT OF THE DISCLOSURE
The present invention provides a linearization device comprising a predistorsion device (1) for predistorting the signal to be amplified e(t), itself comprising a modulator (2) for modulating the amplitude of the signal to be amplified by a first correction signal q(t) and a modulator (3) for modulating, with carrier suppression, the amplitude of the signal to be amplified, phase shifted by ? by a second correction signal q'(t), the signals q(t) and q'(t) being more especially obtained by making two feed back information signals XS and YS, reflections of the amplitudes of the amplified signal S(t) with respect to two real orthogonal components coming respectively from the real part and from the imaginary part of the transfer function of the amplifier (12) to be linearized, dependent on two similar information signals , reflections of the signal to be amplified e(t).
The present invention provides a linearization device comprising a predistorsion device (1) for predistorting the signal to be amplified e(t), itself comprising a modulator (2) for modulating the amplitude of the signal to be amplified by a first correction signal q(t) and a modulator (3) for modulating, with carrier suppression, the amplitude of the signal to be amplified, phase shifted by ? by a second correction signal q'(t), the signals q(t) and q'(t) being more especially obtained by making two feed back information signals XS and YS, reflections of the amplitudes of the amplified signal S(t) with respect to two real orthogonal components coming respectively from the real part and from the imaginary part of the transfer function of the amplifier (12) to be linearized, dependent on two similar information signals , reflections of the signal to be amplified e(t).
Description
r~ / l I M
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.
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
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(~
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
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(~
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~
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
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~
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~
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) ~ 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~
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:
.
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 ~ 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~
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 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~
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+
eVI V2 cos(3wl-2w2)t + ~eV2 Vl CS(3W2-2Wl)t + 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 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).
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~
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) ~ 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~
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:
.
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 ~ 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~
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 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~
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+
eVI V2 cos(3wl-2w2)t + ~eV2 Vl CS(3W2-2Wl)t + 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 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).
Claims (11)
1. A device (12) for linearizing a high frequency signal amplifier, with complex non linearity coefficients, and intended for amplifying 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 comprises spectral lines of adjustable amplitude situated at frequencies corresponding to the harmonics of the tone differences of the high frequency signal to be amplified, acting separately on two separate parameters of the signal to be amplified, a predistortion device (1) for 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 signal to be amplified, correcting spectral lines, at the frequencies of the intermodulation products of uneven orders, of adjustable amplitude by joint action on the amplitude adjustments of the spectral lines of the spectrum of the first and of the second correction signal q(t) and q'(t), these adjustments being effected so as to obtain cancelling out of the intermodulation products of uneven order situated in the vicinity of the transmission band in the amplified signal, and the predistortion device (1) comprising a modulator (2) for modulating the amplitude of the signal to be amplified e(t) by the first correction signal q(t), a modulator (3) for modulating the amplitude, with carrier suppression, of the signal to be amplified e(t), phase shifted by ? by the second correction signal q'(t), and a summer (5) of the signals from these two modulators, supplying the input signal of the amplifier (12) .
2. The device as claimed in claim 1, wherein said predistortion device (1) comprises a modulator (2) for modulating the amplitude of the signal to be amplified e(t) by the first correction signal q(t), a modulator (3) for modulating, with carrier suppression, the amplitude of the signal to be amplified e(t) by the second correction signal q'(t) and a quadrature coupler (5') of the signals from these two modulators, supplying the input signal of the amplifier (12).
3. The device as claimed in claim 1, wherein the first and the second correction signals, q(t) and q'(t), are obtained respectively by making the amplitude of two orthogonal components X and Y of the amplified signal (attenuated), coming respectively from the real part and from the imaginary part of the transfer function of the amplifier to be linearized, dependent on the corresponding components of the signal to be amplified.
4. The linearization device as claimed in claim 3, wherein the reference information Xe relative to providing dependence on parameter X is obtained by means of a multiplier (24) which receives at its two inputs the signal to be amplified e(t), followed by a low pass filter (25).
5. The linearization device as claimed in claim 3, wherein the feed back information XS relative to providing dependence on parameter X is obtained by means of a multiplier (25) which receives a signal to be amplified e(t) and the attenuated amplified signal .beta. s(t), followed by a low pass filter (28).
6. The device as claimed in claim 3, wherein the reference information Ye relative to providing dependence on parameter Y is zero.
7. The device according to claim 3, wherein the feed back information Ys relative to providing dependence on parameter Y is obtained by means of a multiplier (30) which receives the signal to be amplified e(t), phase shifted by ?, and the attenuated amplified signal .beta. S(t), followed by a low pass filter (31).
8. The device as claimed in claim 3, wherein the means for obtaining the correction signals q(t) and q'(t) comprise delay lines (32, 33) for compensating the phase shift of the amplified signal (attenuated) with respect to the signal to be amplified.
9. The device as claimed in claim 3, wherein the attenuation .beta. of the output signal of the amplifier (12), prior to elaboration of the feed back information, is controlled so as to maintain the operating point of the predistortion device constant.
10. The device as claimed in claim 9, wherein said control is provided by means of a programmed memory (38) controlling a variable attenuator (37).
11. The device as claimed in claim 1, wherein the first and the second correction signal, q(t) and q'(t), are obtained respectively by making the amplitude of two orthogonal components X and Y of the amplified signal (attenuated), coming respectively from the real part and from the imaginary part of the transfer function of the amplifier to be linearized, dependent on the corresponding components of the signal to be amplified, wherein said feed back information Ys relative to providing a dependence on parameter Y is obtained by means of a multiplier (30) which receives the signal to be amplified e(t), phase shifted by ?, and the attenuated amplified signal S(t) followed by a low pass filter (31), and wherein said ? phase shifts are provided by the same element.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| FR8302253A FR2541058B1 (en) | 1983-02-11 | 1983-02-11 | HIGH FREQUENCY AMPLIFIER LINEARIZATION DEVICE WITH COMPLEX NON-LINEARITY COEFFICIENTS |
| FR8302253 | 1983-02-11 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1208709A true CA1208709A (en) | 1986-07-29 |
Family
ID=9285853
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000447114A Expired CA1208709A (en) | 1983-02-11 | 1984-02-09 | Device for linearizing a high frequency amplifier with complex non linearity coefficients |
Country Status (5)
| Country | Link |
|---|---|
| EP (1) | EP0121446B1 (en) |
| JP (1) | JPS59158113A (en) |
| CA (1) | CA1208709A (en) |
| DE (1) | DE3463992D1 (en) |
| FR (1) | FR2541058B1 (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5193224A (en) * | 1991-04-24 | 1993-03-09 | Northern Telecom Limited | Adaptive phase control for a power amplifier predistorter |
Families Citing this family (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| FR2713851B1 (en) * | 1993-12-14 | 1996-01-05 | Thomson Csf | Device for linearizing a high-frequency transmission element with complex non-linearity coefficients. |
| US6335767B1 (en) * | 1998-06-26 | 2002-01-01 | Harris Corporation | Broadcast transmission system with distributed correction |
| GB2339917A (en) * | 1998-07-21 | 2000-02-09 | Ifr Limited | Generating a multitone test signal |
| JP3570898B2 (en) * | 1998-08-24 | 2004-09-29 | 日本電気株式会社 | Pre-distortion circuit |
| US6501805B1 (en) * | 1999-05-14 | 2002-12-31 | Harris Corporation | Broadcast transmission system with single correction filter for correcting linear and non-linear distortion |
| DE19927952A1 (en) * | 1999-06-18 | 2001-01-04 | Fraunhofer Ges Forschung | Device and method for predistorting a transmission signal to be transmitted over a non-linear transmission path |
| GB2376581B (en) * | 2001-06-15 | 2005-03-09 | Wireless Systems Int Ltd | Control scheme for signal processing arrangement |
Family Cites Families (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE2306294A1 (en) * | 1973-02-08 | 1974-08-15 | Rohde & Schwarz | CIRCUIT TO COMPENSATE THE NON-LINEARITY OF AN AMPLIFIER, IN PARTICULAR THE POWER AMPLIFIER OF A TELEVISION TRANSMITTER |
| FR2275065A1 (en) * | 1974-06-11 | 1976-01-09 | Lgt Lab Gen Telecomm | LINEARIZED AMPLIFIER DEVICE BY AUTOMATIC CORRECTION |
| US4243955A (en) * | 1978-06-28 | 1981-01-06 | Motorola, Inc. | Regulated suppressed carrier modulation system |
| US4178557A (en) * | 1978-12-15 | 1979-12-11 | Bell Telephone Laboratories, Incorporated | Linear amplification with nonlinear devices |
| US4291277A (en) * | 1979-05-16 | 1981-09-22 | Harris Corporation | Adaptive predistortion technique for linearizing a power amplifier for digital data systems |
| FR2507026A1 (en) * | 1981-05-26 | 1982-12-03 | Thomson Csf | INTERMODULATION CORRECTION DEVICE PRODUCED BY A HIGH FREQUENCY SIGNAL AMPLIFIER |
| FR2520957A1 (en) * | 1982-01-29 | 1983-08-05 | Thomson Csf | DEVICE FOR CORRECTING INTERMODULATION PRODUCED BY A HIGH-FREQUENCY CONTROLLED SIGNAL AMPLIFIER |
-
1983
- 1983-02-11 FR FR8302253A patent/FR2541058B1/en not_active Expired
-
1984
- 1984-02-02 DE DE8484400226T patent/DE3463992D1/en not_active Expired
- 1984-02-02 EP EP19840400226 patent/EP0121446B1/en not_active Expired
- 1984-02-09 CA CA000447114A patent/CA1208709A/en not_active Expired
- 1984-02-10 JP JP2423284A patent/JPS59158113A/en active Pending
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5193224A (en) * | 1991-04-24 | 1993-03-09 | Northern Telecom Limited | Adaptive phase control for a power amplifier predistorter |
Also Published As
| Publication number | Publication date |
|---|---|
| EP0121446A1 (en) | 1984-10-10 |
| JPS59158113A (en) | 1984-09-07 |
| EP0121446B1 (en) | 1987-05-27 |
| DE3463992D1 (en) | 1987-07-02 |
| FR2541058B1 (en) | 1986-01-24 |
| FR2541058A1 (en) | 1984-08-17 |
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| Date | Code | Title | Description |
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| MKEX | Expiry |