EP2034550A1 - Integrated active phase shifter - Google Patents

Abstract

The shifter has a constant phase-shifting element (4), variable gain and analog control amplifiers (5, 6), digital-analog converters (7, 8) and a summation element (9), which are provided on a semiconductor substrate, where the substrate is silicon-germanium substrate, gallium arsenide substrate or silicon substrate. The digital-analog converters digitally control the amplifiers to vary the phase-shifting. The amplifiers are digitally controlled by a processor. Serial-parallel conversion registers are provided between the converters.

Description

The present invention relates to an integrated vector sum phase shifter on the same semiconductor substrate. It applies for example in the field of electronic scanning antennas.

The electronic scanning antennas are mainly used in the field of detection and listening systems, such as radars for example. They allow to orient an electromagnetic wave beam by refraction or reflection of the beam by an array of radiating elements. The refraction angle of the beam varies with the relative phase shift of the field radiated by the elements arranged in a network. To achieve this, it is necessary to precisely control the phase and the amplitude of the signals received or emitted by each of the radiating elements. The radiating elements may be waveguides incorporating in particular phase shifters for adjusting the phase of the signal emitted from the received signal. There are different possibilities for making phase shifters. The passive phase shifters comprise a number of elementary passive elements whose characteristics are constant, of the type delay lines or filters, which are switched according to the desired phase shift. Active phase shifters are based on the direct control of the signal phase, thanks to an active element such as a varactor or a transistor. The present invention relates more particularly to another type of active phase shifter, based on the vector sum of the received signal and one or more signals obtained by phase shift of the received signal. The principle of the vector sum will be explained later.
The US patent US 4,398,161 discloses an active phase shifter based on the vector sum of the received signal and a phase-shifted signal. In this patent, the phase shift is obtained by analogically adjusting the amplitude of the signal. However, since the control laws of the electronic scanning are calculated by digital processors, it may be convenient to control the phase shift digitally. This is what the patent suggests US 4,398,161 without, however, describing a mode of production. However, if we consider the very high level of integration required for this type of phase shifter, its realization with numerical control is not without posing many difficulties. Indeed, the semiconductor processes for producing integrated circuits, commonly called "Microwave Monolithic Integrated Circuits" or "MMIC" according to the English terminology, are suitable for the integration on the same substrate of active microwave elements such as amplifiers and passive microwave elements such as delay lines or filters. But these methods are not suitable for the integration of digital or analog control circuits, such as digital-to-analog converters, for working frequencies greater than a few gigahertz. For example, Gallium Arsenide substrate GaAs technology does not allow economically integrating on the same substrate amplifiers, delay lines, filters and especially complex digital control circuits, as would require a controlled active phase shifter digital. This is a technical problem which the present invention proposes to answer.
Solutions exist to try to achieve as integrated as possible active phase shifters vector sum, especially variable gain amplifiers. One solution consists in producing a phase-shifter in the form of discretized elements, such as several current sources discharging in a fixed load or a fixed current source discharging in several loads, switchable with digital control to obtain the desired gain. In this case, it is difficult to integrate more than a few discretized elements on the same substrate. However, the smaller the discretization step, the greater the deviation from the ideal analog law phase shift control is high. Another solution is to achieve direct analog control, for example of the current source, with a digital-to-analog conversion performed by an external component. In this case, the integration level is not sufficient, since it is necessary to have an external digital-to-analog converter for each of the phase shifters.

The aim of the invention is in particular to integrate on the same MMIC-type substrate an active phase-shifter using analog-controlled variable gain amplifiers as well as digital-to-analog converters making it possible to vary the gain of the amplifiers numerically and thus to control numerically the phase shift. For this purpose, the invention relates to a vector sum phase shifter. It comprises, on the same semiconductor substrate, a constant phase shift element, two amplifiers variable gain and analog control, two digital-to-analog converters and a summing element. The digital-to-analog converters enable the amplifiers to be digitally controlled in order to vary the phase shift.
In one embodiment, it may comprise serial-parallel conversion registers at the input of the digital-to-analog converters.
Advantageously, the amplifiers can be digitally controlled by a processor.
For example, the substrate may be a III-V semiconductor substrate, such as Gallium Arsenide (GaAs). The substrate may also be a semiconductor type IV substrate, such as silicon-germanium (SiGe). The substrate may also be a silicon substrate.
For example, the phase shifter can be used in a scanning antenna.

In addition to providing a fully integrated digital phase shifter, the present invention also has the main advantages that the use of digital technologies brings a high level of accuracy and allows to approach very close the ideal law of control of the phase shift. The error with respect to the ideal law can be very small, since it is limited only by the resolution of the digital-to-analog converters, which can easily reach 8 or 10 bits whereas the current embodiments of discretized phase shifters reach at best resolutions from 5 to 6 bits. This high resolution also makes it possible to finely correct the drifts of the phase shift as a function of external conditions such as temperature. It suffices to record these drifts at in advance and deduce a digital compensation law that can be stored in an external or internal memory. This compensation law is then used to send digital commands.

• la figure 1, une illustration par un synoptique du principe des déphaseurs à somme vectorielle ;
• la figure 2, une illustration par un synoptique d'un exemple de circuit mettant en oeuvre un déphaseur à somme vectorielle selon la présente invention ;
• la figure 3, une illustration géométrique du signal obtenu en sortie d'un déphaseur à somme vectorielle selon l'invention.

Other characteristics and advantages of the invention will become apparent with the aid of the following description made with reference to appended drawings which represent:

• the figure 1 , an illustration by a synoptic of the principle of phase shifters with vector sum;
• the figure 2 an illustration by a block diagram of an exemplary circuit implementing a vector sum phase shifter according to the present invention;
• the figure 3 , a geometric illustration of the signal obtained at the output of a vector sum phase shifter according to the invention.

The figure 1 illustrates by a synoptic the principle of phase shifters with vector sum. A signal E is received at the input of a phase shifter. A module 1 makes it possible to phase out the signal E by a value Φ to obtain at the output of the module 1 a phase-shifted signal E '. A variable gain amplifier 2 receives the signal E 'as input. At a given moment, the gain of the amplifier 2 is equal to B where B is a real coefficient between -1 and 1. A variable gain amplifier 3 receives the signal E at the input. At a given moment, the gain of the amplifier 3 is equal to A where A is a coefficient between -1 and 1. For example, if Φ is equal to 90 degrees and if A and B vary between -1 and 1 while respecting the condition A ² + B ² = 1, then a signal S = A.E + BE 'obtained by summing the outputs of the amplifiers 2 and 3 corresponds to the signal E shifted by a value varying from -90 degrees to +90 degrees respectively. As explained above, it is often desirable to control the phase shift digitally, since the control laws of the electronic scanning are calculated by digital processors. It is very difficult to integrate on the same substrate amplifiers such as amplifiers 2 and 3 when they are digitally controlled, respecting the condition A ² + B ² = 1 and ensuring minimum distances from the ideal law.

$${\mathrm{E}}_2\mathrm{=}{\mathrm{r}}_2\mathrm{.}\mathrm{E}\mathrm{.}\exp \left({\mathrm{j\varphi }}_2\right)$$

Les signaux E₁ et E₂ sont appliqués respectivement en entrée des amplificateurs 5 et 6. En supposant que les amplificateurs 5 et 6 à gains variables génèrent des déphasages Φ_A et Φ_B lorsque leurs gains valent A et B respectivement, alors des signaux S₁ et S₂ en sortie des amplificateurs 5 et 6 respectivement vérifient les égalités (3) et (4) suivantes : $${\mathrm{S}}_{\mathrm{1}}\mathrm{=}\mathrm{A}\mathrm{.}{\mathrm{E}}_{\mathrm{1}}\mathrm{.}\exp \left({\mathrm{j\varphi }}_{\mathrm{A}}\right)\mathrm{=}\mathrm{A}\mathrm{.}{\mathrm{r}}_{\mathrm{1}}\mathrm{.}\mathrm{E}\mathrm{.}\exp \left(\mathrm{j}\left({\mathrm{\varphi }}_{\mathrm{1}}\mathrm{+}{\mathrm{\varphi }}_{\mathrm{A}}\right)\right)$$

$${\mathrm{S}}_2\mathrm{=}\mathrm{B}\mathrm{.}{\mathrm{E}}_{\mathrm{2}}\mathrm{.}\exp \left({\mathrm{j\varphi }}_{\mathrm{B}}\right)\mathrm{=}\mathrm{B}\mathrm{.}{\mathrm{r}}_{\mathrm{2}}\mathrm{.}\mathrm{E}\mathrm{.}\exp \left(\mathrm{j}\left({\mathrm{\varphi }}_{\mathrm{2}}\mathrm{+}{\mathrm{\varphi }}_{\mathrm{B}}\right)\right)$$

Les signaux S₁ et S₂ sont appliqués en entrée de l'élément 9 de sommation de sorte à additionner les sorties S₁ et S₂ des amplificateurs 5 et 6 à gains variables. Si des valeurs angulaires Φ₁ et Φ₂ permettent de représenter le déphasage généré par l'élément 9, alors idéalement Φ'₂-Φ'₁=0. Des coefficients r'₁ et r'₂ permettant de représenter les pertes dues au déphasage par l'élément 9 des signaux S₁ et S₂ d'un angle de Φ'₂-Φ'₁ degrés, un signal S en sortie de l'élément 9 de sommation vérifie les égalités (5) et (6) suivantes : $$\mathrm{S}\mathrm{=}{\mathrm{rʹ}}_{\mathrm{1}}\mathrm{.}{\mathrm{S}}_{\mathrm{1}}\mathrm{.}\exp \mathrm{\left(}{\mathrm{j\varphi ʹ}}_{\mathrm{1}}\mathrm{\right)}\mathrm{+}{\mathrm{rʹ}}_{\mathrm{2}}\mathrm{.}{\mathrm{S}}_{\mathrm{2}}\mathrm{.}\exp \left({\mathrm{j\varphi ʹ}}_{\mathrm{2}}\right)$$

$$\mathrm{S}\mathrm{=}\mathrm{E}\mathrm{.}\mathrm{[}\mathrm{A}\mathrm{.}{\mathrm{r}}_{\mathrm{1}}\mathrm{.}{\mathrm{rʹ}}_{\mathrm{1}}\mathrm{.}\exp \mathrm{\left(}\mathrm{j}\mathrm{\right(}{{\mathrm{\varphi }}_{\mathrm{1}}\mathrm{+}\mathrm{\varphi ʹ}}_{\mathrm{1}}\mathrm{+}{\mathrm{\varphi }}_{\mathrm{A}}\mathrm{\left)}\mathrm{\right)}\mathrm{+}\mathrm{B}\mathrm{.}{\mathrm{r}}_{\mathrm{2}}\mathrm{.}{\mathrm{rʹ}}_{\mathrm{2}}\mathrm{.}\exp \mathrm{\left(}\mathrm{j}\mathrm{\right(}{{\mathrm{\varphi }}_{\mathrm{2}}\mathrm{+}\mathrm{\varphi ʹ}}_{\mathrm{2}}\mathrm{+}{\mathrm{\varphi }}_{\mathrm{B}}\mathrm{\left)}\mathrm{\right)}\mathrm{]}$$

The figure 2 illustrates by a block diagram an example of a circuit implementing a vector sum phase shifter according to the present invention. The circuit groups, on the same substrate MMIC, a phase shift element 4, two amplifiers 5 and 6, two digital-to-analog converters 7 and 8 and a summing element 9. Element 4 provides a constant phase shift. Advantageously, the two amplifiers 5 and 6 can be variable gain and analog control. The MMIC substrate may be of the III-V semiconductor type or more advantageously of the IV semiconductor type. In order to reduce the number of digital inputs of the circuit of the figure 2 , the parallel inputs of the digital-to-analog converters 7 and 8 can advantageously again be transformed into serial inputs by adding serial-parallel conversion registers to the input of the digital-to-analog converters 7 and 8. These registers are not represented on the figure 2 .
Angular values Φ ₁ and Φ ₂ make it possible to represent the constant phase shift generated by element 4. For example, a signal E applied to the input of element 4 is phase shifted by 90 degrees by adjusting Φ ₁ and Φ ₂ of so that Φ ₂ -Φ ₁ = 90. Coefficients r ₁ and r ₂ making it possible to represent the losses due to the phase shift by the element 4, signals E ₁ and E ₂ at the output of the element 4 respectively verify the equalities ( 1) and (2): $${\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">E</figure-callout>}}_{\mathrm{1}}\mathrm{=}{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{1}}\mathrm{.}\mathrm{E}\mathrm{.}\exp \left({\mathrm{j\phi }}_{\mathrm{1}}\right)$$

$${\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E</figure-callout>}}_2\mathrm{=}{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\mathrm{.}\mathrm{E}\mathrm{.}\exp \left({\mathrm{j\phi }}_2\right)$$

The signals E ₁ and E ₂ are applied respectively to the input of the amplifiers 5 and 6. Assuming that the amplifiers 5 and 6 with variable gains generate phase shifts Φ _A and Φ _B when their gains are equal to A and B respectively, then S signals ₁ and S ₂ at the output of the amplifiers 5 and 6 respectively verify the following equalities (3) and (4): $${\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">S</figure-callout>}}_{\mathrm{1}}\mathrm{=}\mathrm{AT}\mathrm{.}{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">E</figure-callout>}}_{\mathrm{1}}\mathrm{.}\exp \left({\mathrm{j\phi }}_{\mathrm{AT}}\right)\mathrm{=}\mathrm{AT}\mathrm{.}{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{1}}\mathrm{.}\mathrm{E}\mathrm{.}\exp \left(\mathrm{j}\left({\mathrm{\phi }}_{\mathrm{1}}\mathrm{+}{\mathrm{\phi }}_{\mathrm{AT}}\right)\right)$$

$${\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="imgf0002.png"\; state="\{\{state\}\}">S</figure-callout>}}_2\mathrm{=}\mathrm{B}\mathrm{.}{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E</figure-callout>}}_{\mathrm{2}}\mathrm{.}\exp \left({\mathrm{j\phi }}_{\mathrm{B}}\right)\mathrm{=}\mathrm{B}\mathrm{.}{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{2}}\mathrm{.}\mathrm{E}\mathrm{.}\exp \left(\mathrm{j}\left({\mathrm{\phi }}_{\mathrm{2}}\mathrm{+}{\mathrm{\phi }}_{\mathrm{B}}\right)\right)$$

The signals S ₁ and S ₂ are applied at the input of the summing element 9 so as to add the outputs S ₁ and S ₂ of the amplifiers 5 and 6 with variable gains. If angular values Φ ₁ and Φ ₂ make it possible to represent the phase shift generated by the element 9, then ideally Φ ' ₂ -Φ' ₁ = 0. Coefficients r ' ₁ and r' ₂ making it possible to represent the losses due to the phase shift by the element 9 of the signals S ₁ and S ₂ by an angle of Φ ' ₂ -Φ ₁ degrees, a signal S at the output of the summation element 9 satisfies the following equalities (5) and (6): $$\mathrm{S}\mathrm{=}{\mathrm{r\text{'}}}_{\mathrm{1}}\mathrm{.}{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">S</figure-callout>}}_{\mathrm{1}}\mathrm{.}\exp \mathrm{\left(}{\mathrm{j\phi \text{'}}}_{\mathrm{1}}\mathrm{\right)}\mathrm{+}{\mathrm{r\text{'}}}_{\mathrm{2}}\mathrm{.}{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="imgf0002.png"\; state="\{\{state\}\}">S</figure-callout>}}_{\mathrm{2}}\mathrm{.}\exp \left({\mathrm{j\phi \text{'}}}_{\mathrm{2}}\right)$$

$$\mathrm{S}\mathrm{=}\mathrm{E}\mathrm{.}\mathrm{[}\mathrm{AT}\mathrm{.}{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{1}}\mathrm{.}{\mathrm{r\text{'}}}_{\mathrm{1}}\mathrm{.}\exp \mathrm{\left(}\mathrm{j}\mathrm{\right(}{{\mathrm{<figure-callout\; id="1"\; label="\phi "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_{\mathrm{1}}\mathrm{+}\mathrm{\phi \text{'}}}_{\mathrm{1}}\mathrm{+}{\mathrm{\phi }}_{\mathrm{AT}}\mathrm{\left)}\mathrm{\right)}\mathrm{+}\mathrm{B}\mathrm{.}{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{2}}\mathrm{.}{\mathrm{r\text{'}}}_{\mathrm{2}}\mathrm{.}\exp \mathrm{\left(}\mathrm{j}\mathrm{\right(}{{\mathrm{<figure-callout\; id="2"\; label="\phi "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_{\mathrm{2}}\mathrm{+}\mathrm{\phi \text{'}}}_{\mathrm{2}}\mathrm{+}{\mathrm{\phi }}_{\mathrm{B}}\mathrm{\left)}\mathrm{\right)}\mathrm{]}$$

$$\mathrm{tg\varphi }=\left[\mathrm{A}\mathrm{.}{\mathrm{r}}_{\mathrm{1}}\mathrm{.}{\mathrm{rʹ}}_{\mathrm{1}}\mathrm{.}\sin \left({\mathrm{\varphi }}_{\mathrm{1}}+{\mathrm{\varphi ʹ}}_{\mathrm{1}}+{\mathrm{\varphi }}_{\mathrm{A}}\right)\mathrm{+}\mathrm{B}\mathrm{.}{\mathrm{r}}_{\mathrm{2}}\mathrm{.}{\mathrm{rʹ}}_{\mathrm{2}}\mathrm{.}\sin \left({\mathrm{\varphi }}_{\mathrm{2}}+{\mathrm{\varphi ʹ}}_2+{\mathrm{\varphi }}_{\mathrm{B}}\right)\right]/[\mathrm{A}\mathrm{.}{\mathrm{r}}_{\mathrm{1}}\mathrm{.}{\mathrm{rʹ}}_1\mathrm{.}\cos \left({\mathrm{\varphi }}_1+{\mathrm{\varphi ʹ}}_1\mathrm{+}{\mathrm{\varphi }}_{\mathrm{A}}\right)+\mathrm{B}\mathrm{.}{\mathrm{r}}_{\mathrm{2}}\mathrm{.}{\mathrm{rʹ}}_{\mathrm{2}}\mathrm{.}\cos \left({\mathrm{\varphi }}_{\mathrm{2}}+{\mathrm{\varphi ʹ}}_2+{\mathrm{\varphi }}_{\mathrm{B}}\right)]$$

Les valeurs A et B sont alors calculées en fonction du déphasage recherché Φ, elles sont données par les relations (9) et (10) suivantes : $$\mathrm{A}\mathrm{=}\mathrm{\left|}\mathrm{S}\mathrm{\right|}\mathrm{/}\left[\mathrm{\left|}\mathrm{E}\mathrm{\right|}\mathrm{.}{\mathrm{r}}_{\mathrm{1}}\mathrm{.}{\mathrm{rʹ}}_{\mathrm{1}}\mathrm{.}\mathrm{(}\mathrm{1}\mathrm{+}{\sin }^{\mathrm{2}}\left(\mathrm{\varphi }\mathrm{-}{\mathrm{\varphi }}_{\mathrm{1}}\mathrm{-}{\mathrm{\varphi ʹ}}_{\mathrm{1}}\mathrm{-}{\mathrm{\varphi }}_{\mathrm{A}}\right)\mathrm{/}{\sin }^{\mathrm{2}}\left(\mathrm{\varphi }\mathrm{-}{\mathrm{\varphi }}_{\mathrm{2}}\mathrm{-}{\mathrm{\varphi ʹ}}_{\mathrm{2}}\mathrm{-}{\mathrm{\varphi }}_{\mathrm{B}}\right)\mathrm{-}\mathrm{2}\mathrm{\cdot }\sin \left(\mathrm{\varphi }\mathrm{-}{\mathrm{\varphi }}_{\mathrm{1}}\mathrm{-}{\mathrm{\varphi ʹ}}_{\mathrm{1}}\mathrm{-}{\mathrm{\varphi }}_{\mathrm{A}}\right)\mathrm{/}\sin \left(\mathrm{\varphi }\mathrm{-}{\mathrm{\varphi }}_{\mathrm{2}}\mathrm{-}{\mathrm{\varphi ʹ}}_{\mathrm{2}}\mathrm{-}{\mathrm{\varphi }}_{\mathrm{B}}\right)\mathrm{.}\cos {\left({\mathrm{\varphi }}_{\mathrm{2}}\mathrm{+}{\mathrm{\varphi ʹ}}_{\mathrm{2}}\mathrm{+}{\mathrm{\varphi }}_{\mathrm{B}}\mathrm{-}{\mathrm{\varphi }}_{\mathrm{1}}\mathrm{-}{\mathrm{\varphi ʹ}}_{\mathrm{1}}\mathrm{+}{\mathrm{\varphi }}_{\mathrm{A}}\mathrm{)}\right)}^{\mathrm{1}\mathrm{/}\mathrm{2}}\right]$$

$$\mathrm{B}\mathrm{=}\mathrm{-}\mathrm{\left|}\mathrm{S}\mathrm{\right|}/\left[\mathrm{\left|}\mathrm{E}\mathrm{\right|}\mathrm{.}{\mathrm{r}}_{\mathrm{2}}\mathrm{.}{\mathrm{rʹ}}_{\mathrm{2}}\mathrm{.}\mathrm{(}\mathrm{1}\mathrm{+}{\sin }^{\mathrm{2}}\left(\mathrm{\varphi }\mathrm{-}{\mathrm{\varphi }}_{\mathrm{2}}\mathrm{-}{\mathrm{\varphi ʹ}}_{\mathrm{2}}\mathrm{-}{\mathrm{\varphi }}_{\mathrm{B}}\right)\mathrm{/}{\sin }^{\mathrm{2}}\left(\mathrm{\varphi }\mathrm{-}{\mathrm{\varphi }}_{\mathrm{1}}\mathrm{-}{\mathrm{\varphi ʹ}}_{\mathrm{1}}\mathrm{-}{\mathrm{\varphi }}_{\mathrm{A}}\right)\mathrm{-}\mathrm{2}\mathrm{\cdot }\sin \left(\mathrm{\varphi }\mathrm{-}{\mathrm{\varphi }}_{\mathrm{2}}\mathrm{-}{\mathrm{\varphi ʹ}}_{\mathrm{2}}\mathrm{-}{\mathrm{\varphi }}_{\mathrm{B}}\right)\mathrm{/}\sin \left(\mathrm{\varphi }\mathrm{-}{\mathrm{\varphi }}_{\mathrm{1}}\mathrm{-}{\mathrm{\varphi ʹ}}_{\mathrm{1}}\mathrm{-}{\mathrm{\varphi }}_{\mathrm{A}}\right)\mathrm{.}\cos {\left({\mathrm{\varphi }}_{\mathrm{2}}\mathrm{-}{\mathrm{\varphi ʹ}}_{\mathrm{2}}\mathrm{+}{\mathrm{\varphi }}_{\mathrm{B}}\mathrm{-}{\mathrm{\varphi }}_{\mathrm{1}}\mathrm{-}{\mathrm{\varphi ʹ}}_{\mathrm{1}}\mathrm{+}{\mathrm{\varphi }}_{\mathrm{A}}\mathrm{)}\right)}^{\mathrm{1}\mathrm{/}\mathrm{2}}\right]$$

A et B prenant des valeurs quantifiées, l'erreur de quantification est évidemment d'autant plus faible que la résolution de A et B est élevée, d'où l'intérêt de l'approche avec commande analogique et convertisseur numérique-analogique intégré.
Dans le cas idéal où :

• r₁=r₂=½,
• r'₁=r'₂,
• Φ'₁=Φ'₂,
• Φ_A=Φ_B,
• Φ₂-Φ₁=90 degrés,

il vient simplement les relations (11) et (12) suivantes : $${\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="imgf0002.png"\; state="\{\{state\}\}">S</figure-callout>}}^{\mathrm{2}}\mathrm{=}{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E</figure-callout>}}^{\mathrm{2}}\mathrm{.}\left[{\mathrm{A}}^{\mathrm{2}}+{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="imgf0002.png"\; state="\{\{state\}\}">B</figure-callout>}}^{\mathrm{2}}\right]\mathrm{/}\mathrm{2}$$

$$\mathrm{tg\varphi }=\mathrm{B}\mathrm{/}\mathrm{A}$$

Et si les commandes A et B sont telles que A=cosα et B=sinα, il vient alors les relations (13) et (14) suivantes : $${\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="imgf0002.png"\; state="\{\{state\}\}">S</figure-callout>}}^{\mathrm{2}}\mathrm{=}{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E</figure-callout>}}^{\mathrm{2}}\mathrm{/}\mathrm{2}$$

$$\mathrm{\varphi }\mathrm{=}\mathrm{\alpha }$$

The figure 3 geometrically illustrates the signal S given by the relation (6) and obtained at the output of the phase shifter of the figure 2 . According to the parallelogram rule, the following relations (7) and (8) come: $${\left|\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="imgf0002.png"\; state="\{\{state\}\}">S</figure-callout>}\right|}^{\mathrm{2}}\mathrm{=}{\left|\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E</figure-callout>}\right|}^{\mathrm{2}}\mathrm{.}\left[{\mathrm{AT}}^{\mathrm{2}}\mathrm{.}{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{1}}}^{\mathrm{2}}\mathrm{.}{{\mathrm{r\text{'}}}_{\mathrm{1}}}^{\mathrm{2}}\mathrm{+}{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="imgf0002.png"\; state="\{\{state\}\}">B</figure-callout>}}^{\mathrm{2}}\mathrm{.}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{2}}}^{\mathrm{2}}\mathrm{.}{{\mathrm{r\text{'}}}_{\mathrm{2}}}^{\mathrm{2}}\mathrm{+}\mathrm{2.}\mathrm{AT}\mathrm{.}{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{1}}\mathrm{.}{\mathrm{r\text{'}}}_1\mathrm{.}\mathrm{B}\mathrm{.}{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{2}}\mathrm{.}{\mathrm{r\text{'}}}_{\mathrm{2}}\mathrm{.}\cos \left({\mathrm{\phi }}_{\mathrm{2}}\mathrm{-}{\mathrm{<figure-callout\; id="1"\; label="\phi "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_{\mathrm{1}}\mathrm{+}{\mathrm{\phi \text{'}}}_{\mathrm{2}}\mathrm{-}{\mathrm{\phi \text{'}}}_{\mathrm{1}}\mathrm{+}{\mathrm{\phi }}_{\mathrm{B}}\mathrm{-}{\mathrm{\phi }}_{\mathrm{AT}}\right)\right]$$

$$\mathrm{tg\phi }=\left[\mathrm{AT}\mathrm{.}{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{1}}\mathrm{.}{\mathrm{r\text{'}}}_{\mathrm{1}}\mathrm{.}\mathrm{<figure-callout\; id="1"\; label="sin\; \phi "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">sin\; </figure-callout>}\left({\mathrm{\phi }}_{}\right)\left({\mathrm{}}_{\mathrm{1}}+{\mathrm{\phi \text{'}}}_{\mathrm{1}}+{\mathrm{\phi }}_{\mathrm{AT}}\right)\mathrm{+}\mathrm{B}\mathrm{.}{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{2}}\mathrm{.}{\mathrm{r\text{'}}}_{\mathrm{2}}\mathrm{.}\mathrm{<figure-callout\; id="2"\; label="sin\; \phi "\; filenames="imgf0002.png"\; state="\{\{state\}\}">sin\; </figure-callout>}\left({\mathrm{\phi }}_{}\right)\left({\mathrm{}}_{\mathrm{2}}+{\mathrm{\phi \text{'}}}_2+{\mathrm{\phi }}_{\mathrm{B}}\right)\right]/[\mathrm{AT}\mathrm{.}{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{1}}\mathrm{.}{\mathrm{r\text{'}}}_1\mathrm{.}\cos \left({\mathrm{\phi }}_1+{\mathrm{\phi \text{'}}}_1\mathrm{+}{\mathrm{\phi }}_{\mathrm{AT}}\right)+\mathrm{B}\mathrm{.}{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{2}}\mathrm{.}{\mathrm{r\text{'}}}_{\mathrm{2}}\mathrm{.}\cos \left({\mathrm{\phi }}_{\mathrm{2}}+{\mathrm{\phi \text{'}}}_2+{\mathrm{\phi }}_{\mathrm{B}}\right)]$$

The values A and B are then calculated as a function of the desired phase shift Φ, they are given by the following relations (9) and (10): $$\mathrm{AT}\mathrm{=}\mathrm{\left|}\mathrm{S}\mathrm{\right|}\mathrm{/}\left[\mathrm{\left|}\mathrm{E}\mathrm{\right|}\mathrm{.}{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{1}}\mathrm{.}{\mathrm{r\text{'}}}_{\mathrm{1}}\mathrm{.}\mathrm{(}\mathrm{1}\mathrm{+}{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="imgf0002.png"\; state="\{\{state\}\}">sin</figure-callout>}}^{\mathrm{2}}\left(\mathrm{\phi }\mathrm{-}{\mathrm{\phi }}_{\mathrm{1}}\mathrm{-}{\mathrm{\phi \text{'}}}_{\mathrm{1}}\mathrm{-}{\mathrm{\phi }}_{\mathrm{AT}}\right)\mathrm{/}{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="imgf0002.png"\; state="\{\{state\}\}">sin</figure-callout>}}^{\mathrm{2}}\left(\mathrm{\phi }\mathrm{-}{\mathrm{\phi }}_{\mathrm{2}}\mathrm{-}{\mathrm{\phi \text{'}}}_{\mathrm{2}}\mathrm{-}{\mathrm{\phi }}_{\mathrm{B}}\right)\mathrm{-}\mathrm{2}\mathrm{\cdot }\sin \left(\mathrm{\phi }\mathrm{-}{\mathrm{\phi }}_{\mathrm{1}}\mathrm{-}{\mathrm{\phi \text{'}}}_{\mathrm{1}}\mathrm{-}{\mathrm{\phi }}_{\mathrm{AT}}\right)\mathrm{/}\sin \left(\mathrm{\phi }\mathrm{-}{\mathrm{\phi }}_{\mathrm{2}}\mathrm{-}{\mathrm{\phi \text{'}}}_{\mathrm{2}}\mathrm{-}{\mathrm{\phi }}_{\mathrm{B}}\right)\mathrm{.}\cos {\left({\mathrm{\phi }}_{\mathrm{2}}\mathrm{+}{\mathrm{\phi \text{'}}}_{\mathrm{2}}\mathrm{+}{\mathrm{\phi }}_{\mathrm{B}}\mathrm{-}{\mathrm{\phi }}_{\mathrm{1}}\mathrm{-}{\mathrm{\phi \text{'}}}_{\mathrm{1}}\mathrm{+}{\mathrm{\phi }}_{\mathrm{AT}}\mathrm{)}\right)}^{\mathrm{1}\mathrm{/}\mathrm{2}}\right]$$

$$\mathrm{B}\mathrm{=}\mathrm{-}\mathrm{\left|}\mathrm{S}\mathrm{\right|}/\left[\mathrm{\left|}\mathrm{E}\mathrm{\right|}\mathrm{.}{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0002.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{2}}\mathrm{.}{\mathrm{r\text{'}}}_{\mathrm{2}}\mathrm{.}\mathrm{(}\mathrm{1}\mathrm{+}{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="imgf0002.png"\; state="\{\{state\}\}">sin</figure-callout>}}^{\mathrm{2}}\left(\mathrm{\phi }\mathrm{-}{\mathrm{\phi }}_{\mathrm{2}}\mathrm{-}{\mathrm{\phi \text{'}}}_{\mathrm{2}}\mathrm{-}{\mathrm{\phi }}_{\mathrm{B}}\right)\mathrm{/}{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="imgf0002.png"\; state="\{\{state\}\}">sin</figure-callout>}}^{\mathrm{2}}\left(\mathrm{\phi }\mathrm{-}{\mathrm{\phi }}_{\mathrm{1}}\mathrm{-}{\mathrm{\phi \text{'}}}_{\mathrm{1}}\mathrm{-}{\mathrm{\phi }}_{\mathrm{AT}}\right)\mathrm{-}\mathrm{2}\mathrm{\cdot }\sin \left(\mathrm{\phi }\mathrm{-}{\mathrm{\phi }}_{\mathrm{2}}\mathrm{-}{\mathrm{\phi \text{'}}}_{\mathrm{2}}\mathrm{-}{\mathrm{\phi }}_{\mathrm{B}}\right)\mathrm{/}\sin \left(\mathrm{\phi }\mathrm{-}{\mathrm{\phi }}_{\mathrm{1}}\mathrm{-}{\mathrm{\phi \text{'}}}_{\mathrm{1}}\mathrm{-}{\mathrm{\phi }}_{\mathrm{AT}}\right)\mathrm{.}\cos {\left({\mathrm{\phi }}_{\mathrm{2}}\mathrm{-}{\mathrm{\phi \text{'}}}_{\mathrm{2}}\mathrm{+}{\mathrm{\phi }}_{\mathrm{B}}\mathrm{-}{\mathrm{\phi }}_{\mathrm{1}}\mathrm{-}{\mathrm{\phi \text{'}}}_{\mathrm{1}}\mathrm{+}{\mathrm{\phi }}_{\mathrm{AT}}\mathrm{)}\right)}^{\mathrm{1}\mathrm{/}\mathrm{2}}\right]$$

A and B taking quantized values, the quantization error is obviously all the lower as the resolution of A and B is high, hence the interest of the approach with analog control and integrated digital-analog converter.
In the ideal case where:

• r ₁ = r ₂ = ½,
• r ' ₁ = r' ₂ ,
• Φ ' ₁ = Φ' ₂ ,
• Φ _A = Φ _B ,
• Φ ₂ -Φ ₁ = 90 degrees,

it simply comes the following relationships (11) and (12): $${\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="imgf0002.png"\; state="\{\{state\}\}">S</figure-callout>}}^{\mathrm{2}}\mathrm{=}{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E</figure-callout>}}^{\mathrm{2}}\mathrm{.}\left[{\mathrm{AT}}^{\mathrm{2}}+{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="imgf0002.png"\; state="\{\{state\}\}">B</figure-callout>}}^{\mathrm{2}}\right]\mathrm{/}\mathrm{2}$$

$$\mathrm{tg\phi }=\mathrm{B}\mathrm{/}\mathrm{AT}$$

And if the commands A and B are such that A = cosα and B = sinα, then it comes the following relations (13) and (14): $${\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="imgf0002.png"\; state="\{\{state\}\}">S</figure-callout>}}^{\mathrm{2}}\mathrm{=}{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="imgf0002.png"\; state="\{\{state\}\}">E</figure-callout>}}^{\mathrm{2}}\mathrm{/}\mathrm{2}$$

$$\mathrm{\phi }\mathrm{=}\mathrm{\alpha }$$

It should be noted that the circuit of the figure 2 can be implanted on a III-V semiconductor substrate of the GaAs type. But in this case, the circuit has a very large footprint, which initially poses difficulties of industrialization and integration difficulties. More advantageously, the circuit of the figure 2 can be implanted on a semiconductor substrate IV of silicon type or better SiGe, adapted to high frequencies. The use of a SiGe type substrate makes it possible in particular to reduce the cost of producing a numerically controlled phase shifter according to the invention.

Claims (8)

Vector sum phase shifter comprising, on the same semiconductor substrate: a constant phase shift element (4); - two amplifiers with variable gain and with analog control (5, 6); two digital-to-analog converters (7, 8); a summation element (9); digital-to-analog converters for digitally controlling the amplifiers to vary the phase shift, the phase shifter being characterized in that it comprises serial-parallel conversion registers at the input of the digital-to-analog converters. Phase shifter according to Claim 1, characterized in that the amplifiers (5, 6) are digitally controlled by a processor. Phase shifter according to Claim 1, characterized in that the substrate is a III-V semiconductor substrate. Phase shifter according to Claim 4, characterized in that the substrate is made of gallium arsenide (GaAs). Phase shifter according to claim 1 characterized in that the substrate is a semiconductor type IV substrate. Phase shifter according to Claim 6, characterized in that the substrate is made of silicon-germanium (SiGe). Phase shifter according to Claim 1, characterized in that the substrate is a silicon substrate. Phase shifter according to Claim 7, characterized in that it is used in an electronic scanning antenna.

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