Data processing: structural design – modeling – simulation – and em – Simulating electronic device or electrical system – Circuit simulation
Reexamination Certificate
1998-07-29
2001-04-10
Teska, Kevin J. (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Simulating electronic device or electrical system
Circuit simulation
C703S004000, C703S005000, C703S014000
Reexamination Certificate
active
06216100
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to the field of the simulation of signal responses of nonlinear amplifiers. An object of the invention is a system for the simulation of the response signal of a nonlinear amplifier having a memory effect.
A system of this kind can be applied to the simulation of high efficiency microwave amplification, especially in the AB, B or C class of amplification and more particularly to the simulation of the response of solid state power amplifiers (SSPA) and travelling wave tube amplifiers (TWT) used in land or satellite transmission radio links.
At high frequencies or at high efficiency, amplifier devices of this kind have a nonlinear characteristic response curve.
2. Description of the Prior Art
FIG. 1
illustrates an exemplary input/output response curve of a nonlinear amplifier ANL. The curve giving the output signal level g of the amplifier ANL as a function of the input signal level x is typically inflected at the high amplitudes A of the input signal x because of saturation phenomena. When the amplifier is used in conditions such that the gain is not constant as a function of the input signal level x, it is said to be an amplifier working in nonlinear mode or more simply the amplification is called nonlinear amplification.
Nonlinear devices can be divided into memoryless devices, quasi-memoryless devices and devices with memory.
Memoryless amplifiers have high nonlinearity in amplitude and a lower phase distortion. The input/output response characteristic of a memoryless nonlinear amplifier ANL can then be reduced, as shown in
FIG. 1
, to a single curve g(x).
It is possible to model and simulate the response, as a function of the time t, of an memoryless amplifier ANL to a sinusoidal input signal x, with a frequency f
0
, that is amplitude modulated A and phase modulated &phgr;, the signal having the following form:
x(t)=A(t).cos(2.f
0
.t+&phgr;(t)) (1)
A(t) represents the envelope of the input signal, which is defined by the amplitude limits in which the sine signal x evolves, the envelope varying as a function of time.
FIG. 3
illustrates a timing diagram of a signal x(t) having a constant envelope A.
The output signal g of the memoryless amplifier then has the following form:
g(t)=C(A(t)).cos(2&pgr;.f
0
.t+&phgr;(t)) (2)
It is useful to give a complex envelope to these signals x and g in abandoning any reference to the time t since the memoryless amplifiers have an instantaneous response.
The input signal x of the equation (1) has a complex envelope X with the following form:
X=A.exp(j.&phgr;) (3)
All the useful information pertaining to the amplitude modulation A(t) and phase modulation &phgr;(t) is recorded in this complex envelope X.
The output signal g of equation (2) similarly has a complex envelope G with the following form:
G=C(A).exp(j.&phgr;) (4)
For a memoryless nonlinear amplifier ANL, it is shown that C(A) is the Chebyshev transform of the input/output response curve g(x).
The response of a :memoryless nonlinear amplifier ANL to a modulated signal x can therefore be modeled and simulated simply by a single curve C(A), whose example is shown in an unbroken line in
FIG. 6A. A
curve of this kind giving the output amplitude C as a function of the input amplitude A is called a curve of nonlinearity in amplitude and is referenced in abbreviated form as an AM/AM curve.
FIG. 2
illustrates a response characteristic of a nonlinear amplifier with memory ANLAM on which there appears a phenomenon of hysteresis prompted by a memorizing effect. It can be seen that the rising hysteresis curves m and m′ are not superimposed on each other when the respective amplitudes A and A′ of the input signal x are different. The variation in memorizing time related to the variation in amplitude prevents the curves m and m′ from getting superimposed on each other.
When the memorizing time of the amplifier ANLAM is negligible in comparison to the period of the amplitude variation A(t), it can furthermore be considered that the amplitude A is stable and the amplifier is called a quasi-memoryless amplifier.
FIG. 4
shows a timing diagram of an output signal y of a quasi-memoryless amplifier to which there is applied the input signal x illustrated by the timing diagram of
FIG. 3
whose formula is recalled here below:
x(t)=A(t).cos(2&pgr;.f
0
.t+&phgr;(t)) (1)
For a quasi-memoryless nonlinear amplifier to which the signal x of equation (1) is applied, the output signal y takes the following form:
y(t)=C(A).cos(2&pgr;.f
0
.t−&PHgr;(A)+&phgr;(t)) (5)
where C(A) is the amplitude of the output signal y,
and &PHgr;(A) is the phase shift of the output signal y,
which depends on the amplitude A(t) of the input signal x.
Thus, at a given instant t, the amplitude C(A) and the phase shift &PHgr;(A) of the output signal y depend solely on the amplitude A of the input signal x at this instant t. It is thus possible to overlook the amplitude variations A(t) as a function of time and consider that the amplitude A is almost constant as can be seen in FIG.
3
.
It is also useful to write in a complex form the envelopes of the signals x and y expressed here above, namely as the envelopes X and Y which take the following respective forms:
X=A.exp(j.&phgr;) (3)
(the envelope A considered as being constant in time)
Y=C(A).exp(j.&phgr;−&PHgr;(A)) (6)
The response of a quasi-memoryless nonlinear amplifier can therefore be modeled and simulated simply on the basis of knowledge of the following two characteristic curves:
1. A curve C(A) wherein the amplitude C of the output signal y is a function of the amplitude A of the input signal, illustrated for example by the curve AM/AM, in an unbroken line, of
FIG. 6A
(amplitude/amplitude conversion curve);
2. A curve &PHgr;(A) wherein the phase shift &PHgr; of the output signal y with respect to the input signal x is a function of the amplitude A of the signal x, called an amplitude/phase conversion curve, abbreviated as AM/PM, an example of which is shown in an unbroken line in FIG.
6
B.
It can be shown that, similarly, the curve C(A) is the norm of the complex Chebyshev transform of the response characteristic y(x), the curve &PHgr;(A) being the argument of the complex transform.
The complex envelope Y of the output signal can also be written in the form of two parts, namely a real part and an imaginary part, corresponding to an in-phase component P and a quadrature component Q, these components P and Q having the following forms:
P(A)=C(A).cos(&PHgr;(A)) (7′)
Q(A)=C(A).sin(&PHgr;(A)) (7″)
FIG. 7
shows an example of curves P(A) and Q(A) equivalent to the curves C(A) and &PHgr;(A) of
FIGS. 6A and 6B
.
The known models of simulation of the response of quasi-memoryless amplifiers generally prefer to use characteristics in the form of pairs of curves P(A) and Q(A) rather than in the form of pairs of curves C(A) and &PHgr;(A), although these pairs of curves are strictly equivalent.
According to a known principle of the simulation of nonlinear amplifiers, the amplifier that is made is precharacterized on the test bench. The precharacterizing is done with a signal having a specified frequency and amplitude in order to then simulate the response to a signal of any frequency and amplitude.
As shown schematically in
FIG. 5
, a signal with a single-frequency f
0
taking different amplitudes A′, A″, A′″ is applied to the amplifier tested to obtain its characteristics, illustrated for example in
FIG. 6
or
7
.
However, for amplifiers having a certain quantity of memory, it is observed that the characteristics vary to a major degree depending on the frequency f
0
−
, f
0
or f
0
+
of the signal to be amplified.
A known system for the simulation of such amplifiers has been explained by H. B. Poza in an article entitled
Cances Jean-Pierre
Chevallier François-René
Dumas Jean-Michel
Meghdadi Vahid
France Telecom (SA)
Jones Hugh
Nilles & Nilles S.C.
Teska Kevin J.
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