RU2696207C1 - Tunable oscillator with connected microstrip lines - Google Patents

Abstract

FIELD: radio equipment.

SUBSTANCE: invention relates to the field of radio equipment. For this purpose, a tunable oscillator with connected microstrip lines, in particular, is made using an inductive three-point circuit on a bipolar transistor which is connected in a circuit with a common emitter. It includes basic resistive voltage divider and emitter resistor, by means of which transistor operation mode is set by direct current. Decoupling inductance and interlocking capacitors are used to isolate microwave circuits by control and power supply. For positive voltage supply to varicap and transistor bias voltages positive power sources are used. Remained elements of the circuit are frequency-setting, they form basic, collector circuits and emitter circuit.

EFFECT: technical result is reduction of phase noise level of tunable oscillators with resonant systems on three-wire connected microstrip transmission lines differing from each other by an optimum value.

1 cl, 12 dwg

Description

The proposed device relates to the field of radio engineering and can be used in modern frequency synthesizers, which are part of various transceiver radio equipment operating up to the microwave range. In particular, this device relates to voltage-controlled microwave generators (VCOs), in which either two-, three-, or multi-wire coupled strip transmission lines are used to improve frequency characteristics.

, на двух диагональных концах которых реализован режим работы «холостого хода». При помощи отрезков МПЛ 5 и 6 на входе транзистора 1 создается необходимое для генерации колебаний отрицательное сопротивление. Управляющее напряжение и напряжения питания через клеммы 7-9 подаются на варикап и электроды транзистора, используя следующие элементы развязки: резисторы 10, 11, блокировочные конденсаторы 12-16, а также четвертьволновые отрезки МПЛ 17 и 18. Конденсатор 19 на выходе устройства является разделительным. В ≈8%-ном диапазоне перестраиваемых частот (от 20.4 до 22 ГГц) типовые уровни фазовых шумов ГУН на данном полевом транзисторе находятся в пределах от -71.3 до -80.3 дБ/Гц на частотах отстройки 100 кГц. Для этого ГУН установлено также, что по сравнению с однопроводной микрополосковой линией длиной

применение двух связанных линий приводит к снижению спектральной плотности мощности фазовых шумов на 3-4 дБ/Гц. Подобный вывод сделан и в работе [1], где на основе аналитических выражений показано, что крутизна реактивного сопротивления параллельного резонанса одиночной линии ниже аналогичной величины, соответствующей двухпроводной связанной линии.VCO is known (See Sevimli, O. GaAs HEMT monolithic voltage-controlled oscillators at 20 and 30 GHz incorporating Schottky-varactor frequency tuning / O. Sevimli, JW Archer and GJ Griffiths // IEEE Trans. On Microwave Theory and Techniques. - 1998 . - Vol. 46. - N. 10. - P. 1572-1576). This device, a circuit diagram of which is shown in FIG. 1, is performed on a GaAs HEMT field effect transistor 1, connected according to a common drain circuit. This VCO employs a resonator containing varicap 2 and associated microstrip lines (MPL) of gears 3 and 4 in length

, at the two diagonal ends of which the idle operation mode is implemented. Using segments of the MPL 5 and 6 at the input of the transistor 1 creates the necessary negative resistance to generate oscillations. The control voltage and supply voltage through the terminals 7-9 are applied to the varicap and electrodes of the transistor using the following isolation elements: resistors 10, 11, blocking capacitors 12-16, and also quarter-wave segments of the MPL 17 and 18. The capacitor 19 at the output of the device is a separation. In the ≈8% range of tunable frequencies (from 20.4 to 22 GHz), typical VCO phase noise levels on a given field effect transistor are in the range from -71.3 to -80.3 dB / Hz at 100 kHz detuning frequencies. For this, the VCO also found that, compared with a single-wire microstrip line of length

the use of two coupled lines leads to a decrease in the spectral power density of phase noise by 3-4 dB / Hz. A similar conclusion was made in [1], where on the basis of analytical expressions it was shown that the steepness of the reactance of parallel resonance of a single line is lower than a similar value corresponding to a two-wire coupled line.

The disadvantage of an analogue is the relatively high level of phase noise.

, на двух диагональных концах которых реализован короткозамкнутый режим. Необходимое для генерации колебаний отрицательное сопротивление на входе транзистора 20 создается при помощи емкости связи 26, индуктивности 27, а также RC-цепи из элементов 28 и 29. Используя клеммы 30-32, управляющее напряжение и напряжения питания подаются на варикап и транзистор через элементы развязки: индуктивности 33-35 и блокировочные конденсаторы 36-38. Выходной сигнал ГУН снимается с коллекторного отрезка МПЛ 39. Использование в связанных отрезках МПЛ вместо холостого хода режимы короткого замыкания, а также применение вместо полевого GaAs НЕМТ-транзистора кремниевого биполярного транзистора приводят к улучшению частотных характеристик ГУН, в частности, к расширению полосы перестройки и уменьшению уровня фазовых шумов. Так, в 25%-ном диапазоне перестройки частоты от 4.9 до 6.3 ГГц спектральная плотность мощности фазовых шумов ГУН не превышает -105 дБ/Гц на частоте анализа 100 кГц.A VCO is known (See Merenda, JL Varactor tuned strip line resonator and VCO using same / JL Merenda // USA Patent US 5942950 A. - 24 august 1999). A schematic diagram of this device is shown in FIG. 2. The VCO is made on a bipolar transistor 20 and a resonator, which contains a varicap 21, capacitors 22, 23 and associated segments of the MPL gears 24 and 25 in length

, at the two diagonal ends of which a short-circuited mode is realized. The negative resistance required to generate oscillations at the input of transistor 20 is created using a coupling capacitance 26, inductance 27, and an RC circuit from elements 28 and 29. Using terminals 30-32, the control voltage and supply voltage are supplied to the varicap and transistor through isolation elements : inductances 33-35 and blocking capacitors 36-38. The output signal of the VCO is removed from the collector segment of the MPL 39. The use of short-circuit modes instead of idling in the connected segments of the MPL, as well as the use of a silicon bipolar transistor instead of a GaAs field-effect transistor, leads to an improvement in the frequency characteristics of the VCO, in particular, to an expansion of the tuning band and a decrease level of phase noise. So, in the 25% range of frequency tuning from 4.9 to 6.3 GHz, the spectral power density of the phase noise of a VCO does not exceed -105 dB / Hz at an analysis frequency of 100 kHz.

The analogue has the same drawback - a relatively high level of phase noise.

A VCO is known (See Grebennikov, A. RF and microwave transistor oscillator design / A. Grebennikov. - Chichester, England: John Wiley & Sons, Ltd, 2007. - 441 p.) Its circuit diagram is shown in FIG. 3. The VCO is made on a bipolar transistor 40 and an external feedback circuit, which includes varicaps 41, 42, capacitors 43, 44, connected segments of the MPL gears 45 and 46, as well as capacitors 47, 48. Through the corresponding terminals 49-51, the control voltage and the supply voltage is supplied to the varicaps and electrodes of the transistor using the following elements: decoupling inductors 52-56 and blocking capacitors 57-60. The current of the transistor is set using a resistor 61. The output signal of the VCO is removed from the capacitive voltage divider formed by elements 47, 48. A distinctive feature of this analogue is that due to the possibility of excitation in connected lines of different types of waves, two operating modes are simultaneously implemented here that correspond to Capacitive three-point circuits of the Clapp and Seiler generators. In the first case, the inductive element between the collector and the base of the transistor is connected in series, and in the second, the additional capacitance of the varicap is connected in parallel, and the type of three-ton in both cases remains capacitive. The implementation of a dual mode of operation provides minimal changes in the amplitude of oscillations in a wide range of frequency tuning. So, when the control voltage changes from 1 to 25 V, the frequency changes from 2.2 to 4 GHz. It can be assumed that when choosing the same types of bipolar transistors, the phase noise level of this VCO, taking into account the difference in frequencies, can be estimated at the same value as the previous analogue.

The disadvantage of this analogue is also an increased level of phase noise.

Closest to the proposed technical solution is a voltage-controlled microwave generator (See Rohde, UL Low noise, hybrid tuned wideband voltage controlled oscillator / UL Rohde, AK Poddar, R. Rebel, P. Patel, KJ Schoepf // USA Patent US 7365612 B2 - April 29, 2008). In FIG. 4 is a simplified diagram of the device shown in fig. 7 patent descriptions. This VCO is made on a bipolar transistor 62, included in the scheme with a common emitter. The operation mode of the DC transistor is set using the active stabilization circuit 63 and resistors 64-66. The device contains a communication capacitance 67, the capacitance of an emitter RC circuit 68, a first 69 and a second resonant system on varicaps and multi-wire connected microstrip lines, a coarse circuit 70 and an accurate 71 adjustment of the first and second resonant systems, respectively. At the output of the VCO, along with capacitors 72, 73, a tunable filter 74 with an integrated buffer amplifier is used, the supply voltage of which is supplied through a resistor 75. In addition to resistors 64 and 65, the fine tuning circuit 71 also includes a second resonant system formed by capacitors of capacitors 76, 77 and varicaps 78, 79 and three-wire coupled microstrip lines 80-82, as well as decoupling inductors 83, 84 and blocking capacitors 85, 86. The total parallel capacitance of the circuit is also included in the second resonant system of circuit 71 capacitors 87, 88 and varicap 89, which, in turn, are also used in the operation of the first resonant system 69. Resistors 90-92, inductive elements 93-95, and blocking capacitors 96 are used for decoupling microwave circuits for power and control in the VCO -99. The capacitor 100 is a separation, and the segments of the MPL 101 and 102 are connecting. To supply the locking voltage to the varicaps, terminals 103 are used, and to enter the supply voltage to the transistor and the buffer amplifier, terminals 104 are used. To implement the frequency tuning range from 1200 to 3600 MHz, in this device, when adjusting the resonant systems, coarse and fine tune circuits are used, in which 10 different varicaps come in. Four more varicaps are part of an active tunable filter to reduce harmonics. In the operating frequency band from 1600 to 3600 MHz, the phase noise level of the VCO reaches values slightly lower than -90 dB / Hz at a detuning frequency of 10 kHz [2]. To reduce phase noise, in addition to two resonant systems based on coupled microstrip lines, an RC noise filter in the emitter circuit is used here, and an active stabilization circuit is used in the collector circuit by which negative feedback on low-frequency noise is implemented.

Despite all the measures taken in the prototype device to reduce phase noise, the disadvantage of the prototype is their relatively high level.

The technical effect to which the proposed solution is aimed is to reduce the phase noise level of tunable generators with resonant systems on three-wire coupled microstrip transmission lines that differ from each other by an optimal length.

или при длине волны в диэлектрике λ отличаются на физическую длину

в области электромагнитной связи, при этом величины основных элементов перестраиваемого генератора удовлетворяют уравнению:This effect is achieved by the fact that in a tunable generator with coupled microstrip lines containing a transistor 105 connected in a circuit with a common emitter, the collector of which is connected via series-connected capacitors 121 and 122 with a common bus, and the base of the transistor 105 is connected to a common connection point of the first capacitor leads 118 and 119, the second terminal of the capacitor 119 being connected to the first common terminal of the parallel RC circuit, consisting of a resistor 108 and the capacitor 120, electromagnetically connected microstrip lines ne the driver 112, 113 and 114 with the first terminals connected together, a resistor 107 connected to a common bus, the other terminal of which is connected to a resistor 106, a varicap 116, the anode of which is connected to a common bus, and the cathode to a common connection point of the first isolation inductance terminals 109 and a capacitor 117, the second terminal of which is connected to the second terminal of the capacitor 118, a capacitor 124 connected to a common bus, the second terminal of which is an output of the device, microstrip transmission lines 115, 123 and capacitors 110 and 111 connected to the common bus, other terminals which are connected to the positive terminals 126 and 125 of the power supply and control voltage sources, respectively, whose negative terminals are the contacts of the device common bus, according to the invention, the microstrip transmission line 115 is connected between the collector and the positive power supply terminal 126, line 123 between the device output and the common point of the capacitors 121 and 122, the emitter of the transistor is connected to the connection point of the capacitor 119 with a parallel RC circuit, the second common output of the elements of which is connected to a common the bus, the base of the transistor is connected to a common connection point of the resistors 106 and 107, and the second terminal of the resistor 106 is connected to the positive terminal 126 of the supply voltage, the second terminal of the inductance inductance 109 is connected to the positive terminal 125 of the control voltage source, the first combined conclusions of the connected microstrip transmission lines 112 , 113 and 114 are connected to a common bus, idle mode is implemented on the second terminals of transmission lines 112 and 114, and the second terminal of transmission line 113 is connected to a common connection point of capacitors 117 and 118, with than line 113 with respect to line 112, as well as line 114 in comparison with line 113 differ by phase shift

or at a wavelength in the dielectric λ differ by the physical length

in the field of electromagnetic coupling, while the values of the main elements of the tunable generator satisfy the equation:

, который соответствует физической длине

линии 112, входное сопротивление базового контура генератора Z_К(θ₀,Δ) определяется следующим выражением:where ƒ ₀ is the main generation frequency of the device, С _Э is the equivalent capacitance of the emitter circuit, and L _К , L _Б are the equivalent inductances of the collector and base loops, in addition, for the selected value of the phase shift

which corresponds to the physical length

line 112, the input resistance of the base loop of the generator Z _K (θ ₀ , Δ) is determined by the following expression:

moreover, this resistance is inductive in nature, reaching its maximum at the optimum value of the phase shift Δ _opt , if the equality holds:

отличаются от набегов фаз в линии 113 в n-раз, а аналогичные характеристики двухпроводной линии передач длиной

, которая является продолжением отрезков 113 и 114 трехпроводной линии передач, имеют при условии

равные величины, то комплексное сопротивление Z(θ₀,Δ) находится следующим образом:where C ₁ is the capacitance of capacitor 118, C _Σ is the total capacitance of varicap 116 and capacitor 117, and Z (θ ₀ , Δ) is the input complex resistance of a three-wire line formed by three connected microstrip lines 112, 113 and 114 short-circuited on one side, on at the other ends in lines 112 and 114 of which the idle mode is set, if we assume that the widths of lines 112 and 114 are the same and the gaps of their electromagnetic connections with line 113 too, and also assume that the phase shifts corresponding to the propagation of waves of even and odd types in a line 112 and 114 long gears

differ from phase incursions in line 113 by an order of magnitude, and similar characteristics of a two-wire transmission line in length

, which is a continuation of the segments 113 and 114 of a three-wire transmission line, are provided

equal values, then the complex resistance Z (θ ₀ , Δ) is found as follows:

Where

, который является продолжением линии 114,

, где

и

- проводимости, устанавливающие связи между нормированными амплитудами токов и напряжений в отрезках длиной

двухпроводной линии передач и определяемые выражениями:

и

, в которых

, γ - постоянная распространения, а

,

- элементы матрицы проводимости и произведения матриц сопротивления и проводимости. В выражение Z(θ₀,Δ) входят также числовые коэффициенты σ₂, σ₃, σ₄ и проводимость Y₂, определяющая связь между нормированными амплитудами токов и напряжений в отрезке трехпроводной линии длиной

, которые вычисляются так:Here ρ is the wave impedance of a single-wire segment of length

, which is a continuation of line 114,

where

and

- conductivity, establishing relationships between the normalized amplitudes of currents and voltages in segments of length

two-wire transmission line and defined by the expressions:

and

, in which

, γ is the propagation constant, and

,

- elements of the conductivity matrix and the product of the resistance and conductivity matrices. The expression Z (θ ₀ , Δ) also includes the numerical coefficients σ ₂ , σ ₃ , σ ₄ and the conductivity Y ₂ , which determines the relationship between the normalized amplitudes of currents and voltages in a three-wire line length

which are calculated as follows:

,

,

,

,

,

,

,

,

,

,

,

,

where Y _ij , α _ij are the elements of the conductivity matrix and the product of the resistance and conductivity matrices, det is the determinant of the product of the resistance and conductivity matrices.

(или соответствующую ей оптимальную фазовую величину Δ). При этом ширины w линий Л1 и Л3 одинаковы и их зазоры s связи с линией Л2 тоже. С одной стороны данной трехпроводной линии реализованы режимы короткого замыкания с общей шиной, а с другой, на входах первой и третьей линиях - режимы холостого хода. Свободный вывод линии Л2 является входом трехпроводной линии передач, которая вместе с емкостями варикапа 116 и конденсаторов 117, 118 образует базовый контур. Кроме того в модели трехпроводной линии на фиг 6 предполагается, что фазовые сдвиги, соответствующие распространению волн четного и нечетного типов в линиях Л1 и Л3 длиной

отличаются от набегов фаз линии Л2 в n-раз. Вместе с тем, здесь аналогичные характеристики двухпроводной линии передач длиной

, которая является продолжением первого Л1 и второго Л2 отрезков трехпроводной линии передач, считаются равными по величине при условии, что

. Поскольку импедансы коллекторной и базовой цепей предложенного генератора носят индуктивный характер, а эмиттерной цепи - емкостной, в качестве модели такого автогенератора используем индуктивную эквивалентную трехточечную схему с последовательной обратной связью, которая приведена на фиг. 7. Данная звездообразная схема получена в работе [3] из типовой треугольной схемы индуктивной трехтонки на основе общих взаимных условий эквивалентных преобразований треугольника сопротивлений в звезду и наоборот - преобразования сопротивлений звезды в треугольник. В рассматриваемой на фиг. 7 модели автогенератора точки отмечены буквами а, b и с, а в качестве центральной точки звезды используется корпус прибора. Кроме транзистора 127 эквивалентная схема содержит два индуктивных 128, 129 и один емкостной 130 элементы. Указанным на фиг. 7 элементам модели в ГУН соответствуют эквивалентные индуктивности коллекторного L_K и базового L_Б контуров и эквивалентная емкость С_Э эмиттерной цепи. Эмиттерная цепь образована конденсатором 120 и конденсатором связи 119 с базовым контуром, а в состав коллекторного контура входят микрополосковые линии 115, 123 и конденсаторы 121, 122, 124.In FIG. 5 is a schematic diagram of a tunable generator with coupled microstrip lines. The device is made according to a three-point circuit on a bipolar transistor 105, which is included in the circuit with a common emitter. Using resistors 106-108, the dc transistor operation mode is set. To decouple the microwave circuits for power, an inductance 109 and capacitors 110, 111 are used. The remaining elements of the circuit are frequency-setting. To a greater extent, this function is performed by microstrip lines 112-115, varicap 116, and capacitors 117-122. To a lesser extent, microstrip line 123 and capacitor 124, which mainly serve to suppress the higher harmonics of the fundamental frequency at the 50-Ohm output. A positive terminal 125 is used to supply a blocking voltage to the varicap 116, and a terminal 126 is used to enter the supply voltage to the transistor. The magnetically coupled microstrip lines 112-114 (see Fig. 6) are a three-wire transmission line in which the second line L2 from the first L1 , and the third L3 from the second L2 line differ by the optimal physical length

(or the corresponding optimal phase value Δ). Moreover, the widths w of the lines L1 and L3 are the same, and their gaps s of the connection with the line L2, too. On the one hand of this three-wire line, short circuit modes with a common bus are implemented, and on the other, at the inputs of the first and third lines - idle modes. The free output of the L2 line is the input of a three-wire transmission line, which, together with the capacitors of the varicap 116 and capacitors 117, 118 forms a basic circuit. In addition, in the three-wire line model of FIG. 6, it is assumed that phase shifts corresponding to the propagation of even and odd waves in lines L1 and L3 of length

differ from the phase incursions of the L2 line n-times. However, here are similar characteristics of a two-wire transmission line with a length of

, which is a continuation of the first L1 and second L2 segments of a three-wire transmission line, are considered equal in magnitude, provided that

. Since the impedances of the collector and base circuits of the proposed generator are inductive, and the emitter circuit is capacitive, we use an inductive equivalent three-point circuit with series feedback, which is shown in FIG. 7. This star-shaped circuit was obtained in [3] from a typical triangular circuit of an inductive three-tone circuit based on general mutual conditions of equivalent transformations of a resistance triangle into a star and vice versa - conversion of a star’s resistance into a triangle. In the case of FIG. 7 models of the point auto-generator are marked with letters a , b and c, and the instrument case is used as the center point of the star. In addition to the transistor 127, the equivalent circuit contains two inductive 128, 129 and one capacitive 130 elements. Referring to FIG. The 7 elements of the model in the VCO correspond to the equivalent inductances of the collector L _K and the base L _B circuits and the equivalent capacitance C _{E of the} emitter circuit. The emitter circuit is formed by a capacitor 120 and a coupling capacitor 119 with a base circuit, and the collector circuit includes microstrip lines 115, 123 and capacitors 121, 122, 124.

Taking into account all the comments, the proposed device operates as follows.

,

,

и равна:For the device in question, which is described by the model in FIG. 7, the generation frequency ƒ ₀ is found from the condition: X _K X _E + X _E X _B + X _K X _B = 0 [4], where

,

,

and is equal to:

That is, when selecting the circuit elements of this device, calculated using formula (1), an inductive equivalent three-point circuit of the oscillator with sequential feedback is implemented, which is shown in FIG. 7.

We calculate the input resistance Z _K (θ ₀ , Δ) of the base circuit, at which it is in accordance with the one shown in FIG. 7 model is inductive. We write this impedance in the following form:

- фазовый сдвиг, соответствующий физической длине

линии Л3,

- фазовый сдвиг, соответствующий физической длине

, λ - длина волны в диэлектрике, Z(θ₀,Δ) - входное комплексное сопротивление связанных микрополосковых линий на фиг. 6. Для выбранного значения θ₀ и оптимальной величины Δ_опт сопротивление Z_K(θ₀,Δ) носит индуктивный характер и достигает максимума при выполнении равенства:where C ₁ is the capacity of the capacitor 118, C _Σ is the total capacity of the varicap 116 and the capacitor 117,

- phase shift corresponding to the physical length

L3 lines,

- phase shift corresponding to the physical length

, λ is the wavelength in the dielectric, Z (θ ₀ , Δ) is the input complex resistance of the coupled microstrip lines in FIG. 6. For the selected value θ ₀ and the optimal value Δ _{opt, the} resistance Z _K (θ ₀ , Δ) is inductive and reaches its maximum when the equality holds:

, а также короткими отрезками двухпроводной и однопроводной линий с длинами

, где можно считать диэлектрик однородным. Такой переход (от связанных полосковьгх линий с разной физической длиной в области электромагнитной связи к связанным полосковым линиям с неоднородным в поперечном сечении диэлектриком) правомерен с точки зрения одинаковых возможностей реализации неуравновешенных связей между матрицами первичных параметров, например, между матрицами сопротивлений [Z] и проводимостей [Y], когда [Z]≠[Y]^-1 [5]. Отмеченные составные части исходной трехпроводной линии являются двенадцатиполюсным, восьмиполюсным и четырехполюсным элементами, которые соединены между собой последовательно. Опишем каждый из этих элементов соответствующими матрицами передач. Используя с учетом граничных условий элементы суммарной матрицы, полученной в результате перемножения матриц передач трех каскадно-соединенных двенадцати-, восьми- и четырехполюсника, найдем выражение для входного сопротивления Z(θ₀,Δ) представленной на фиг. 6 микрополосковой структуры:For considered in FIG. 6 of the associated microstrip structure, we calculate the resistance Z (θ ₀ , Δ), which is included in expressions (2) and (3). To do this, imagine a three-wire line of segments of different lengths in FIG. 6 in the form of three series-connected parts: a three-wire line made on a dielectric inhomogeneous in cross section, but with the same length of segments

as well as short segments of two-wire and single-wire lines with lengths

where the dielectric can be considered homogeneous. Such a transition (from coupled strip lines with different physical lengths in the field of electromagnetic coupling to coupled strip lines with a dielectric inhomogeneous in the cross section) is valid from the point of view of equal possibilities for implementing unbalanced bonds between matrices of primary parameters, for example, between matrices of resistance [Z] and conductivities [Y] when [Z] ≠ [Y] ^-1 [5]. The marked components of the original three-wire line are twelve-pole, eight-pole and four-pole elements that are connected together in series. We describe each of these elements with the corresponding gear matrices. Using, taking into account the boundary conditions, the elements of the total matrix obtained by multiplying the transmission matrices of three cascade-connected twelve-, eight- and four-terminal devices, we find the expression for the input resistance Z (θ ₀ , Δ) shown in FIG. 6 microstrip structure:

, который является продолжением входящего в состав линии Л1 первого отрезка двухпроводной линии длиной

, a _ij,

- элементы матриц передачи двенадцати- и восьмиполюсников.where ρ is the wave impedance of a single-wire line segment of length

, which is a continuation of the first segment of a two-wire line that is part of the line L1

, a _ij ,

- elements of transmission matrices of twelve- and eight-terminal devices.

в выражении (4) имеют вид:

,

,

,

,

, где

,

и

, а

,

- элементы матрицы проводимости и произведения матриц сопротивления и проводимости. Указанные значения

получены после раскрытия неопределенностей вида

в формулах элементов матрицы передачи

для двухпроводной связанной полосковой линии, рассмотренной в работе [5].For the case of two unequal coupled lines with a homogeneous dielectric, when the wave propagation coefficients of the two types of excitation are equal to each other, γ,

in the expression (4) have the form:

,

,

,

,

where

,

and

, but

,

- elements of the conductivity matrix and the product of the resistance and conductivity matrices. Indicated Values

obtained after disclosing uncertainties of the form

in the formulas of the elements of the transfer matrix

for a two-wire coupled strip line considered in [5].

, которые после применения в двенадцатиполюснике граничных условий остались в уравнении (4) ненулевыми, находятся из выражений:

- коэффициент распространения i-ой моды (i=1, 2, 3). Здесь используются принятые в работе [5] обозначения параметров трехпроводной связанной полосковой линии, описываемой матрицами нормированных амплитуд напряжения [A_U] и тока [A_I]:Element Values

which, after applying the boundary conditions in the twelve-port terminal, remained non-zero in equation (4), are found from the expressions:

is the propagation coefficient of the i-th mode (i = 1, 2, 3). Here, the designations of the parameters of a three-wire coupled strip line, described by matrices of normalized amplitudes of the voltage [A _U ] and current [A _I ], are used [5]:

as well as their invertible matrices [A _U ] ^-1 , [A _I ] ^-1 , whose elements are c _ij and d _ij . Elements of the matrices combined in expression (5) are calculated by the formulas:

,

,

,

,

,

,

в процессе распространения разных типов волн.where Y _ij , a _ij are the elements of the conductivity matrix and the product of the resistance and conductivity matrices, det is the determinant of the product of the resistance and conductivity matrices. The matrix elements in (5) k _ij and m _ij are the proportionality coefficients between the propagating along the lines voltages and currents of waves of different types. Using the conductivities Y ₁ , Y _2, and Y ₃ used in (5), relationships are established between the normalized amplitudes of currents and voltages in the corresponding segments of a three-wire transmission line with a length

in the process of propagation of different types of waves.

одинаковы, то есть, если k₃₁=1 и m₃₁=1. В результате, значения элементов матрицы a _ij равны следующим величинам

,

,

- фазовый сдвиг, соответствующий физической длине

отрезка третьей микрополосковой линии.The calculation of the quantities a _{ij is} greatly simplified for the same width w of the line segments L1, L3 and their gaps s with the line L2, when γ ₁ = γ ₃ = γ and γ ₂ = nγ; k ₂₁ = k ₂₃ , k ₃₁ = k ₃₃ , m ₂₁ = m ₂₃ , m ₃₁ = m ₃₃ ; Y ₁ = Y ₃ , as well as when two conditions are simultaneously fulfilled under which the normalized amplitudes of voltage and current in the first and third lengths of lines

are the same, that is, if k ₃₁ = 1 and m ₃₁ = 1. As a result, the values of the elements of the matrix a _ij are equal to the following quantities

,

,

- phase shift corresponding to the physical length

segment of the third microstrip line.

в уравнении (4) и поделив его числитель и знаменатель на cosΔ и на величину

(или

), запишем выражение для входного сопротивления Z(θ₀,Δ) структуры на фиг. 6 в новом виде:Having grouped the obtained products of matrix elements a _ij ,

in equation (4) and dividing its numerator and denominator by cosΔ and by

(or

), we write the expression for the input resistance Z (θ ₀ , Δ) of the structure in FIG. 6 in a new form:

Where

moreover, the dimensionless values of the numbers σ ₁ , σ ₂ , σ ₃ , σ _{4 are} calculated as follows:

,

,

,

,

,

,

.

.

. Затем сравним полученные характеристики с аналогичными зависимостями для подобной фиг. 6 микрополосковой структуры с нулевой добавкой длины

. Кроме того, сравним их с характеристиками аналога [1], в котором используется двухпроводная структура полосковых линий, короткозамкнутых с одной стороны и с режимом холостого хода на одной из них с другой стороны. При этом выберем величину

, равной волновому сопротивлению линий Л1 (или ρ), а значения 1/|Y_2Δ| и 1/|Y₂| такими же, как и значение волнового сопротивления линии Л2 микрополосковой структуры на фиг. 6. Другими словами, когда значения θ₀ равны или π/5 или π/3 (или в относительных длинах -

или 1/6), коэффициент n выбран 1.3 или 2, а величины модулей 1/Y₂ соответствуют 65 и 85 Омам, рассмотрим примеры резонансных систем, описываемых уравнениями (2) и (6), в которых ρ=130 Ом, σ₁=0.5, а σ₂=σ₃=σ₄=1.Substituting the resulting expression (6) into equation (2) with predetermined values of C _Σ , C ₁ , ƒ ₀ , we evaluate for the chosen values of n, θ ₀ , as well as σ _i , Y _1Δ , Y _2Δ , Y _{2 the} behavior of the imaginary part and input resistance module Z _K (θ ₀ , Δ) of the base circuit, depending on the change in a small value

. Then, we compare the obtained characteristics with similar dependences for a similar FIG. 6 microstrip structures with zero addition of length

. In addition, we compare them with the characteristics of the analogue [1], which uses a two-wire structure of strip lines, short-circuited on one side and with idle on one of them on the other side. In this case, we choose the value

equal to the wave impedance of the lines L1 (or ρ), and the values 1 / | Y _2Δ | and 1 / | Y ₂ | the same as the value of the wave impedance of the line L2 of the microstrip structure in FIG. 6. In other words, when the values of θ ₀ are either π / 5 or π / 3 (or in relative lengths -

or 1/6), the coefficient n is chosen to be 1.3 or 2, and the magnitudes of the modules 1 / Y ₂ correspond to 65 and 85 Ohms, we consider examples of resonant systems described by equations (2) and (6), in which ρ = 130 Ohm, σ ₁ = 0.5, and σ ₂ = σ ₃ = σ ₄ = 1.

(кривые 2) и рассмотренную в работе [1] двухпроводную линию (кривые 3). Все характеристики рассчитаны на одной частоте ƒ₀=1.08 ГГц при одинаковых значениях С₁=1.8 пФ и С_Σ=2.35-2.5 пФ. При расчете зависимостей на фиг. 8 использовались величины n=1.3, θ₀=π/5 и 1/|Y₂|=85 Ом, характеристики на фиг. 9 получены при n=2, θ₀=π/5 и 1/|Y₂|=65 Ом, а на фиг. 10 параметры Z_K(θ₀,Δ) вычислялись при n=2, θ₀=π/3 и 1/|Y₂|=65 Ом. Анализ импедансных характеристик, полученных для резонансного контура с микрополосковыми линиями разной длины (кривые 1) показывает, что существуют оптимальные величины Δ_опт, которым соответствуют максимальные положительные значения мнимых частей и модулей входных сопротивлений. При выбранных параметрах контура оптимальные величины Δ_опт находится в пределах от 0.069 до 0.081, что соответствует оптимальным физическим длинам

мм. При построении кривых (2) и (3) в формулах для их вычисления Z_K(θ₀,Δ) кроме θ₀ использованы дополнительные фазовые сдвиги ϕ₀, с помощью которых максимальные значения мнимых частей и модулей входных сопротивлений для второй и третьей резонансных систем графически совмещаются с аналогичными характеристиками предлагаемого устройства с оптимальными величинами Δ_опт. В результате такого совмещения можно сделать следующие выводы. Первый вывод состоит в том, что импедансные характеристики (ImZ_K(θ₀,Δ) и модуль Z_K(θ₀,Δ)) ухудшаются при увеличении значений n и θ₀. Так, при увеличении θ₀ с π/5 до π/3 крутизна функции ImZ_K(θ₀,Δ) вблизи Δ_опт уменьшается до 2 раз, а ширина графика модуля Z_K(θ₀,Δ) по уровню 4×10⁴ Ом - до 4 раз. Приблизительно также ведут себя импедансные характеристики при увеличении n с 1.3 до 2. Основной же вывод заключается в том, что резонансный контур, использующий предлагаемую структуру микрополосковых линий разной длины, обладает существенно большими возможностями для увеличения нагруженной добротности колебательной системы автогенератора. Причем это увеличение достигается не за счет высокой собственной добротности ненагруженного контура, а схемотехническим путем, когда колебательная система превращается в эквивалентную многоконтурную структуру. Подтверждением тому в предлагаемом генераторе служат большие в 2-4 раза крутизны функций ImZ_K(θ₀,Δ), а также меньшие в 4-10 раз ширины графиков модулей Z_K(θ₀,Δ) по уровню 4×10⁴ Ом (см. фиг. 8, 9, 10 а) и б) вблизи Δ_опт). Такое поведение зависимостей на фиг. 8, 9 и 10 соответствует выводам работы [1] и приводит к повышению нагруженной добротности колебательной системы, по крайней мере, в q-раз (в 2-4 раза). Если в качестве оценки уровня фазовых шумов генератора использовать шумы его простой модели [6], то при прочих равных с другими генераторами условиях (одинаковых входных мощностях усилителей при согласовании с источниками, коэффициентах шума усилителей и собственных добротностей ненагруженных контуров) спектральная плотность мощности фазовых шумов предлагаемого устройства становится в q²-раз ниже. Другими словами, по сравнению с аналогами и прототипом уровень фазовых шумов предлагаемого устройства уменьшается на величину 6-12 дБ/Гц. Причем этот эффект практически не зависит от величин n и θ₀.In FIG. Figures 8, 9 and 10 show the dependences of the imaginary parts of the input resistances Z _K (θ ₀ , Δ) a) and their modules b) for three types of resonant circuits using the proposed structure (curves 1), the microstrip system in FIG. 6 with zero length

(curves 2) and the two-wire line considered in [1] (curves 3). All characteristics are calculated at the same frequency ƒ ₀ = 1.08 GHz with the same values of C ₁ = 1.8 pF and C _Σ = 2.35-2.5 pF. When calculating the dependencies in FIG. 8, the values n = 1.3, θ ₀ = π / 5 and 1 / | Y ₂ | = 85 Ohms were used, the characteristics in FIG. 9 are obtained for n = 2, θ ₀ = π / 5 and 1 / | Y ₂ | = 65 Ohms, and in FIG. 10, the parameters Z _K (θ ₀ , Δ) were calculated for n = 2, θ ₀ = π / 3 and 1 / | Y ₂ | = 65 Ohms. An analysis of the impedance characteristics obtained for a resonant circuit with microstrip lines of different lengths (curves 1) shows that there are optimal values of Δ _opt that correspond to the maximum positive values of imaginary parts and input resistance modules. With the selected parameters of the circuit, the optimal values of Δ _opt are in the range from 0.069 to 0.081, which corresponds to the optimal physical lengths

mm When constructing curves (2) and (3) in the formulas for their calculation Z _K (θ ₀ , Δ), in addition to θ ₀ , additional phase shifts ϕ _{0 were used} , with the help of which the maximum values of the imaginary parts and input resistance modules for the second and third resonance systems graphically combined with similar characteristics of the proposed device with optimal values Δ _opt . As a result of this combination, the following conclusions can be drawn. The first conclusion is that the impedance characteristics (ImZ _K (θ ₀ , Δ) and the modulus Z _K (θ ₀ , Δ)) deteriorate with increasing values of n and θ ₀ . So, with an increase in θ ₀ from π / 5 to π / 3, the steepness of the function ImZ _K (θ ₀ , Δ) near Δ _opt decreases to 2 times, and the width of the graph of the module Z _K (θ ₀ , Δ) at a level of 4 × 10 ⁴ Ohm - up to 4 times. The impedance characteristics behave approximately the same as n increases from 1.3 to 2. The main conclusion is that the resonant circuit using the proposed structure of microstrip lines of different lengths has significantly greater possibilities for increasing the loaded Q factor of the oscillator system of the oscillator. Moreover, this increase is achieved not due to the high intrinsic Q factor of the unloaded circuit, but by the circuitry when the oscillatory system turns into an equivalent multi-circuit structure. Confirmation of this in the proposed generator is the large 2-4 times the steepness of the functions ImZ _K (θ ₀ , Δ), as well as 4-10 times smaller widths of the graphs of the modules Z _K (θ ₀ , Δ) at a level of 4 × 10 ⁴ Ohms ( see Fig. 8, 9, 10 a) and b) near Δ _opt ). This dependency behavior in FIG. 8, 9 and 10 corresponds to the conclusions of [1] and leads to an increase in the loaded Q-factor of the oscillatory system, at least q-fold (2-4 times). If we use the noise of its simple model as an estimate of the phase noise level of the generator [6], then, ceteris paribus with other generators conditions (equal input power of the amplifiers in agreement with the sources, noise factors of the amplifiers and intrinsic Q factors of the unloaded circuits), the spectral power density of the phase noise of the proposed device becomes q ² times lower. In other words, compared with analogues and prototype, the phase noise level of the proposed device is reduced by 6-12 dB / Hz. Moreover, this effect is practically independent of the values of n and θ ₀ .

Thus, if the parameters of the elements in the proposed device in FIG. 5 to choose in accordance with formulas (1) - (3) and (6), then the claimed technical effect will be guaranteed. Its result is a decrease in the phase noise level of tunable generators with resonant systems on three-wire coupled microstrip transmission lines that differ from each other by an optimal length.

мм, Δ_опт=0.068,

мм. При помощи формул (1)-(3) предварительно рассчитаем значения элементов схемы, а затем уточним их величины, используя известный прием проектирования автогенераторов [7]. Его суть состоит в том, чтобы реализовать суммарную входную проводимость на базе транзистора 105 равной нулю. При этом параметры всех элементов схемы ГУН на фиг. 5 определяются вновь, используя справочные данные об [S]-параметрах для выбранного транзистора 2Т 682 А-2. Другими словами, на базовом порту с сопротивлением, равным общему сопротивлению резисторов 106 и 107, результатом оптимизации уточненных параметров элементов схемы ГУН является одновременное выполнение на расчетной частоте ~1.08 ГГц приблизительного равенства нулю и действительной и мнимой частей суммарной проводимости. Такой прием проектирования автогенераторов применяется для индуктивной трехточечной схемы генераторных устройств с параллельной обратной связью, которая эквивалентна их звездообразной схеме на фиг. 7 [3]. Минимальные величины суммарной проводимости имеют место при следующих уточненных параметрах элементов. Величины конденсаторов равны 3.9 пФ (для элементов 119 и 122), 2 пФ (для 121 элемента), 8.2 пФ (для 120 элемента), 1.8 пФ (для элементов 118 и 124). При этом длина отрезка МПЛ 115 составляет 5.8 мм, отрезок МПЛ 123 имеет длину 9.5 мм, а длины связанных отрезков 112, 113 и 114 равны 13.3, 14.9 и 16.5 мм, соответственно. Кроме того, основной полосок МПЛ 113 имеет ширину 0.7 мм при зазорах между отрезками МПЛ 112, 114 величиной 0.2 мм, а ширины всех остальных отрезков составляет 0.3 мм при толщине 0.8 мм стеклотекстолитовой подложки типа FR-4. Суммарная емкость конденсатора 117 и варикапа 2В 169 А9 меняется в пределах от 1.45 до 2.5 пФ. Развязывающий элемент 109 выбран величиной 82 нГн, а блокирующие конденсаторы 110 и 111 имеют величины 330 и 100 пФ. Величины резистивных элементов 106-108 составляют 1.5 кОм, 1 кОм и 75 Ом.An example of a specific implementation of the device. We will develop a mock generator with parameters of the resonance system close to those established in the calculations of the impedance characteristics in FIG. 9: n = 2, θ ₀ = π / 6,

mm, Δ _opt = 0.068,

mm Using formulas (1) - (3), we preliminarily calculate the values of the circuit elements, and then we refine their values using a well-known technique for designing oscillators [7]. Its essence is to realize the total input conductivity based on the transistor 105 equal to zero. Moreover, the parameters of all elements of the VCO circuit in FIG. 5 are determined again using the reference data on the [S] parameters for the selected 2T 682 A-2 transistor. In other words, at the base port with a resistance equal to the total resistance of the resistors 106 and 107, the optimization of the refined parameters of the elements of the VCO circuit results in the simultaneous execution of approximately equal to zero and the real and imaginary parts of the total conductivity at a calculated frequency of ~ 1.08 GHz. Such a design technique for self-oscillators is used for an inductive three-point circuit of generating devices with parallel feedback, which is equivalent to their star-shaped circuit in FIG. 7 [3]. The minimum values of the total conductivity occur with the following specified parameters of the elements. The capacitors are 3.9 pF (for elements 119 and 122), 2 pF (for 121 elements), 8.2 pF (for 120 elements), 1.8 pF (for elements 118 and 124). The length of the segment MPL 115 is 5.8 mm, the segment MPL 123 has a length of 9.5 mm, and the lengths of the connected segments 112, 113 and 114 are 13.3, 14.9 and 16.5 mm, respectively. In addition, the main strips of MPL 113 have a width of 0.7 mm with gaps between the segments of MPL 112, 114 of 0.2 mm, and the width of all other segments is 0.3 mm with a thickness of 0.8 mm of a FR-4 fiberglass substrate. The total capacitance of the capacitor 117 and the varicap 2B 169 A9 varies from 1.45 to 2.5 pF. The decoupling element 109 is selected to be 82 nH, and the blocking capacitors 110 and 111 are 330 and 100 pF. The values of the resistive elements 106-108 are 1.5 kOhm, 1 kOhm and 75 Ohm.

Thus, in accordance with the circuit of FIG. 5, a voltage-controlled oscillator with a resonant system is developed on three coupled microstrip transmission lines that differ from each other by an optimal length. A photograph of this device is shown in FIG. 11a). An embodiment of a three-wire coupled microstrip line using MPL segments of different lengths is shown in FIG. 11b). With a consumed current of 16 mA and a supply voltage of +5 V, the developed generator with an output power of (0.7-1.2) mW tunes in the frequency range from 1.03 to 1.09 GHz with a change in the control voltage from 0.5 to 12 V. In this frequency spectrum, the power spectral density phase noise at offsets of 10 and 100 kHz is -101 and-123 dB / Hz (see Fig. 12), which is 6-10 dB / Hz lower than the typical phase noise levels of the generator, which is made according to the same scheme and on the same a transistor with a resonant circuit using a single segment of the MPL. In this generator, components are used only domestic production. The location of the contact pads for the inputs of the supply and control voltages and the output signal, the overall dimensions of the housing in the generator are completely, and its typical characteristics mainly correspond to the imported analogue of ROS-1100V.

Thus, the given example of a specific implementation of a tunable generator with three connected microstrip lines of different lengths confirms the possibility of obtaining reduced levels of phase noise by choosing the optimal difference in these lengths. Theoretically and experimentally established a positive effect of reducing the phase noise level of 6-10 dB / Hz.

Information sources

1. Aristarchov, G.M. Frequency stabilization of microstrip microwave oscillators using coupled line systems with unequal phase velocities / G.M. Aristarchov, V.I. Panshin // Electronic Engineering. Ser. 10. Microelectronic devices. - 1984. -Vyp. 2 (44). - S. 5-11.

2. Poddar, A.K. Slow-Wave Resonator based Tunable Multi-Band Multi-Mode Injection-Locked Oscillators: Habilitationsschrift / Ajay Kumar Poddar. - Brandenburg University of Technology, Gottbus-Senftenberg. - 2014 .-- 250 p.

3. Baranov, A.B. Partial and generalized equivalent three-point circuits of microwave oscillators / A.V. Baranov // Electronic Engineering. Ser. 1. Microwave technology. - 2017. -Vyp. 1 (532). - S. 18-25.

4. Baranov, A.V. Voltage-controlled system of two mutually synchronized microwave oscillators / A.V. Baranov // Materials of the XIX coordination scientific and technical seminar on microwave technology, p. Khakhaly, Nizhny Novgorod region, (05-07) .09.2017. - Nizhny Novgorod, 2017 .-- S. 55 - 57.

5. Malyutin, N.D. Multiply connected strip structures and devices based on them. -Tomsk: Tomsk University Press, 1990. - 164 p.

6. Leeson, D. A simple model of feedback oscillator noise spectrum / D. Leeson // Proceedings of the IEEE. - 1966. - Vol. 54. - N 2. - P. 329-332.

- New Jersey, USA: John Wiley & Sons, Inc., 2005. - 543 p.7. Rohde, UL The design of modern microwave oscillators for wireless applications / UL Rohde, AK Poddar,

- New Jersey, USA: John Wiley & Sons, Inc., 2005 .-- 543 p.

Claims (15)

A tunable generator with coupled microstrip lines, comprising a transistor 105 connected in a circuit with a common emitter, the collector of which is connected via series-connected capacitors 121 and 122 with a common bus, and the base of the transistor 105 is connected to a common connection point of the first terminals of the capacitors 118 and 119, the second terminal the capacitor 119 is connected to the first common terminal of the parallel RC circuit, consisting of a resistor 108 and a capacitor 120, electromagnetically coupled microstrip transmission lines 112, 113 and 114 with combined the first terminals connected to the common bus resistor 107, the other terminal of which is connected to the resistor 106, varicap 116, the anode of which is connected to the common bus, and the cathode to the common connection point of the first outputs of the decoupling inductance 109 and the capacitor 117, the second terminal of which is connected to the second output of the capacitor 118, the capacitor 124 connected to the common bus, the second output of which is the output of the device, microstrip transmission lines 115, 123 and the capacitors 110 and 111 connected to the common bus, the other terminals of which are connected to the positive side to the terminal 126 and 125 of the power supply and control voltage sources, respectively, the negative terminals of which are the contacts of the device common bus, characterized in that the microstrip transmission line 115 is connected between the collector and the positive power supply terminal 126, line 123 is between the device output and the common point capacitors 121 and 122, the emitter of the transistor is connected to the connection point of the capacitor 119 with a parallel RC circuit, the second common output of the elements of which is connected to a common bus, the base of the transistor is connected a common connection point of the resistors 106 and 107, and the second terminal of the resistor 106 to the positive terminal 126 of the power supply source, the second terminal of the inductance inductance 109 is connected to the positive terminal 125 of the control voltage source, the first combined conclusions of the associated microstrip transmission lines 112, 113 and 114 are connected to common bus, at the second terminals of transmission lines 112 and 114, the idle mode is implemented, and the second terminal of transmission line 113 is connected to a common connection point of capacitors 117 and 118, and line 113 with respect to line 112, as well as line 114 in comparison with line 113 they differ by phase shift

or at a wavelength in the dielectric λ differ by the physical length

in the field of electromagnetic coupling, while the values of the main elements of the tunable generator satisfy the equation:

where ƒ ₀ is the main frequency of generation of the device, С _Э is the equivalent capacitance of the emitter circuit, a L _К , L _Б are the equivalent inductances of the collector and base loops, in addition, for the selected value of the phase shift

which corresponds to the physical length

line 112, the input resistance of the base loop of the generator Z _K (θ ₀ , Δ) is determined by the following expression:

moreover, this resistance is inductive in nature, reaching its maximum at the optimum value of the phase shift Δ _opt , if the equality holds:

where C ₁ is the capacitance of capacitor 118, C _Σ is the total capacitance of varicap 116 and capacitor 117, and Z (θ ₀ , Δ) is the input complex resistance of a three-wire line formed by three connected microstrip lines 112, 113 and 114 short-circuited on one side, on at the other ends in lines 112 and 114 of which the idle mode is set, if we assume that the widths of lines 112 and 114 are the same and the gaps of their electromagnetic connections with line 113 too, and also assume that the phase shifts corresponding to the propagation of waves of even and odd types in a line 112 and 114 long gears

differ from phase incursions in line 113 by an order of magnitude, and similar characteristics of a two-wire transmission line in length

, which is a continuation of the segments 113 and 114 of a three-wire transmission line, are provided

equal values, then the complex resistance Z (θ ₀ , Δ) is found as follows:

Where

Here ρ is the wave impedance of a single-wire segment of length

, which is a continuation of line 114,

where

and

- conductivity, establishing relationships between the normalized amplitudes of currents and voltages in segments of length

two-wire transmission line and defined by the expressions:

and

, in which

, γ is the propagation constant, and

,

- elements of the conductivity matrix and the product of the resistance and conductivity matrices. The expression Z (θ ₀ , Δ) also includes the numerical coefficients σ ₂ , σ ₃ , σ ₄ and the conductivity Y ₂ , which determines the relationship between the normalized amplitudes of currents and voltages in a three-wire line length

which are calculated as follows:

,

,

,

,

,

, where Y _ij , α _ij are the elements of the conductivity matrix and the product of the resistance and conductivity matrices, det is the determinant of the product of the resistance and conductivity matrices.

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