Jarry / Beneat Passive and Active RF-Microwave Circuits

Course and Exercises with Solutions
1. Auflage 2015
ISBN: 978-0-08-100472-2
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 280 Seiten

Microwave and radiofrequency (RF) circuits play an important role in communication systems. Due to the proliferation of radar, satellite, and mobile wireless systems, there is a need for design methods that can satisfy the ever increasing demand for accuracy, reliability, and fast development times. This book explores the principal elements for receiving and emitting signals between Earth stations, satellites, and RF (mobile phones) in four parts; the theory and realization of couplers, computation and realization of microwave and RF filters, amplifiers and microwave and RF oscillators. Passive and Active RF-Microwave Circuits provides basic knowledge for microwave and RF range; each chapter provides a complete analysis and modelling of the microwave structure used for emission or reception technology, providing the reader with a set of approaches to use for current and future RF and microwave circuits designs. - Each chapter provides a complete analysis and modeling of the microwave structure used for emission or reception technology. - Contains step-by-step summaries of each chapter with analysis, - Provides numerous examples of problems with practical exercises

Autoren/Hrsg.

Jarry, Pierre

Beneat, Jacques N.

Leseproben

1 Microwave Coupled Lines
Abstract
We consider the lines of propagation in which length and coupling are about the wavelength ?. We use to say that the effect is distributed. The electromagnetic (EM) field of the line (1) induces an EM field of the line (2) and reciprocally. The phenomenon is induced on a wavelength ? that is around some Giga Hertz = GHz = 109 Hz in microwaves. =cf=300,000km/s109=3×108109=0.3m Keywords Coupled and non-coupled differential system Guide coupler Hybrid ring Magnetic and capacitive coefficients Mesh law Notch law Proximity coupler Sinusoidal excitation Transversal electromagnetic (TEM) waves Voltage standing waves ratio (VSWR) 1.1 Introduction
We consider the lines of propagation in which length and coupling are about the wavelength ?. We use to say that the effect is distributed. The electromagnetic (EM) field of the line (1) induces an EM field of the line (2) and reciprocally. Figure 1.1 Two coupling microstrip lines 1.2 Description
The phenomenon is induced on a wavelength ? that is around some Giga Hertz = GHz = 109 Hz in microwaves. =cf=300,000km/s109=3×108109=0.3m 1 GHz ? ? = 30 cm decimeter waves 10 GHz ? ? = 3 cm centimeter waves 100 GHz ? ? = 3 mm millimeter waves 1.2.1 Proximity coupler
We like to say that going from 1 to 2 is the direct way and going from 3 to 4 is the coupling way. Then, we define: – coupling : (db)=20log1|S13| – insertion losses : (db)=20log1|S12| – isolation : (db)=20log1|S14| – adaptation : Voltage Standing Waves Ratio (VSWR) of all the lines Figure 1.2 Proximity coupler The same definitions occur to the other type of coupler as the hybrid ring or the guide coupler. Figure 1.3 Hybrid ring 1.2.2 Hybrid ring
Suppose that 1 is the input of the waves. From 1 to 3, there is a path of ?/4. Through the other way, 1, 4, 2, 3, there is a path of 5?/4. And a difference of way of: l=5?4-?4=? Then, 3 is in phase with 1 and this recombines two waves in 3. Now, consider 1 as the input and 2 as the output. The way 1, 3, 2 is 4?/4 and the way 1, 4, 2 is 2?/4. This induces a difference in way of: l=4?4-2?4=?2 And nothing appears in 2. We have constructed a coupler. 1.2.3 Guide coupler
Coupling is made by the two irises I1 and I2 upon a length of ?g/4. Figure 1.4 Guide coupler On iris I1, a small part of the energy (10-3) goes through the secondary guide and induces B'4 and B'3. On iris I2, a small part of the energy (10-3) goes through the secondary guide and induces B?4 and B?3. – In branch 3, if waves B'3 and B?3 have the same phase, then B3 ? 0. – But in branch 4, if waves B'4 and B?4 are in opposition, then B4 ? 0. The difference in way is 2l = ?g/2. Then, we have a diphase of p. Figure 1.5 Use of coupler 1.2.4 Use of couplers
This system is used to take a previous small part of the microwave energy. It can be used: – to measure the frequency, power, etc. – to make a feedback technique and then equalize the output power. 1.3 Lossless equivalent circuit
1.3.1 Mesh law
We give the lossless equivalent circuit on a dz length. We know the equivalent circuit in the case of alone line and we suppose two lines are coupled by: – a magnetic coupling M; and – a capacitive coupling Cm. Figure 1.6 Equivalent circuit of two coupled lines on a dz length The mesh law of the equivalent circuit is now: 1(z)=Ldz?I1?t+Mdz?I2?t+V1(z+dz)V2(z)=Ldz?I2?t+Mdz?I1?t+V2(z+dz) But by definition: 1(z)-V1(z+dz)=-?V1?zdzV2(z)-V2(z+dz)=-?V2?zdz And we get: ?V1?z=L?I1?t+M?I2?t-?V2?z=M?I1?t+L?I2?t 1.3.2 Notch law
Now, for the notch law, we have to consider the currents: 1(z)=C0dz?V1?t+Cmdz?(V1-V2)?t+I1(z+dz)I2(z)=C0dz?V2?t+Cmdz?(V2-V1)?t+I2(z+dz) Using: 1(z)-I1(z+dz)=-?I1?zdzI2(z)-I2(z+dz)=-?I2?zdz We also get: ?I1?z=(C0+Cm)?V1?t-Cm?V2?t-?I2?z=-Cm?V1?t+(C0+Cm)?V2?t 1.3.3 Coupled differential system of the first order
Considering the whole capacity: =C0+Cm We have to find a solution of the coupled differential system of four equations: ?I1?z=C?V1?t-Cm?V2?t[1.1]-?I2?z=-Cm?V1?t+C?V2?t[1.2]-?V1?z=L?I1?t+M?I2?t[1.3]-?V2?z=M?I1?t+L?I2?t[1.4] 1.3.4 Non-coupled differential system of the second order
The resolution of these four coupled equations [1.1] – [1.4] is easy. First, we transform to non-coupled equations. We consider the sums of equations [1.1] + [1.2] and [1.3]+ [1.4] and have: ?Ie?z=(C-Cm)?Ve?t-?Ve?z=(L+M)?Ie?t With the even (sum) voltages and currents: e=I1+I2Ve=V1+V2 It is the same as if there is only one line of capacity (C - Cm) and inductance (L + M). We also consider the differences of equations [1.1] – [1.2] and [1.3] – [1.4] and then we have: ?Io?z=(C+Cm)?Vo?t-?Vo?z=(L-M)?Io?t With the odd (differences) voltages and currents: o=I1-I2Vo=V1-V2 It is the same as if there is only one line of capacity (C + Cm) and inductance (L - M). Combining these two groups of two equations, we obtain equations on the even modes and on the odd modes (non-coupled telegraph equations). 2?z2|IeVe-LC(1+kL)(1-kC)?2?t2|IeVe=0?2?z2|IoVo-LC(1-kL)(1+kC)?2?t2|IoVo=0 where we have defined the magnetic and capacitive coefficients and the even and odd speed of propagation: L=MLandkC=CmCve=1LC(1+kL)(1-kC)vo=1LC(1-kL)(1+kC) EM state on the two lines results from the superposition of two Transversal Electro Magnetic (TEM) modes. These two modes are orthogonal and they are the normal modes of the coupler. 1.4 Homogeneous medium of permittivity e
If the medium is homogeneous with a permittivity e (this is not the case of the microstrip) and the TEM waves are propagating with the speed of the light in this medium, then: =ve=vo=1µe And the coupling coefficient k will be: =kL=kC=CmC=ML We also have: =1/LC1-k2 where /LC is the propagation speed without coupling. Now it is possible to have an expression of the coupling coefficient: =1-µeLC 1.5 Sinusoidal excitation, even and odd modes
In the case of a sinusoidal excitation (i = e and o): i(z,t)=ReVi(z)ej?tIi(z,t)=ReIi(z)ej?t The equations to be satisfied are: 2dz2|IeVe+?2LC(1-k2)|IeVe=0?2dz2|IoVo+?2LC(1-k2)|IoVo=0 The propagation constant is: =?LC(1-k2) The general solutions of these two last equations with...