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The real frequency technique (RFT) is an optimum solution to broadband amplifier equalization problems. This chapter provides a complete description of the RFT for the case of multistage microwave amplifier design for the simultaneous optimization of transducer gain and voltage standing wave ratio (VSWR). The simple formalism of the RFT allows optimizing many performance parameters of single- or multistage microwave amplifiers. There exist many optimization routines but one that was found to work well in the case of microwave amplifier design is to use a single-valued error function based on a sum of squares and an optimization algorithm based on a Levenberg-Marquardt-More technique for solving least-squares problems. At low frequencies, microwave GaAs MESFETs are unstable and are virtually impossible to match over large bandwidths. It is thus necessary to use either a lossy matching or RL feedback technique to reduce terminal impedances and stabilize the transistor.

This chapter proposes to design multistage power amplifiers, based on the real frequency technique (RFT) and the use of large-signal scattering parameter data generated from a few reference points. The optimization of added power usually used in oscillator design is found to be well suited for power amplifier design because their nonlinear properties have a common nature and common description. The chapter provides the new formulas for the multistage transducer power gain when starting from the load. In the classic RFT technique, the input and output voltage standing wave ratio (VSWR) were computed using a stage-by-stage approach that started from the source. The chapter provides the new formulas for the multistage input and output VSWR when starting from the load. The optimization algorithm is used to define polynomial coefficients of an equalizer that minimize a least mean square error function that includes desired target functions with different weight factors.

This chapter presents a new idea that is to optimize the lossy junctions as part of the optimization of the equalizers used in a multistage amplifier. The lossy junctions are introduced between lossless unit elements (UEs) composing an equalizer so that the equalizers can be used to offset power gain issues at low frequencies. In this resistive matching case, the real frequency technique (RFT) is used to directly synthesize the resistors and the UEs to satisfy both gain flatness and stability. The distributed multistage amplifier RFT is successfully modified to introduce the lossy elements and incorporated into a CAD program called SYNTARD. The chapter first validates the new concept by designing a single-stage 0.1-5??GHz microwave amplifier. Then, it uses the modified multistage RFT to design a two-stage 0.1-9??GHz broadband amplifier. In order to realize the equalizers, the chapter gives a lossy UE network synthesis method.

Microwave filters are commonly located in the front end of the telecommunication system. This chapter shows that the real frequency method (RFT) can be modified to successfully design active filters. It presents simulation results for two broadband microwave active filters: a low-pass case from 0 to 5??GHz with two transmission zeros and a bandpass case from 3 to 7??GHz with four transmission zeros. The chapter also gives a bandpass active filter from 7.7 to 8.1??GHz with two transmission zeros realized in monolithic microwave integrated circuit (MMIC) technology. The optimization algorithm is used to define polynomial coefficients for an equalizer that minimize a least mean square error function that includes desired target functions with different weight factors. For the active filters of the chapter, the error function consists of the transducer gain, the voltage standing wave ratio (VSWR), and the group delay.

This chapter presents how the real frequency technique (RFT) is used in the design of multistage distributed amplifiers. The equalizers are made of transmission lines. The chapter introduces a new variable and formalism better suited for the distributed medium. The modified RFT is able to optimize and synthesize the transmission lines. The chapter provides a method for optimizing the multistage amplifier noise figure. It gives a technique to solve the problem of too high or too low characteristic impedance requirements for the microstrip realizations. The chapter provides a possible transistor bias circuit and shows how it can be used during the optimization process to provide more accurate results. It concludes with realizations of a 1.15-1.5??GHz, a 2-8??GHz, and a 5.925-6.425??GHz distributed amplifiers. For the distributed amplifiers of the chapter, the error function consists of the transducer gain, the voltage standing wave ratio (VSWR), and the noise figure.

We have to transmit an analog wave that is coded. Then we introduce an error that can be considered as a noise: the quantization noise. If the quantization samples are of equal amplitude, then the smaller the signal, the more significant the relative error.

In the previous chapter, we said that the equivalent circuit of the different iris formed by diaphragms, coupling holes, self bars, etc., is a parallel and imaginary admittance. As an example, we will show that the equivalent circuit of the diaphragm is given by an inductance j X ¯ .

We consider the ring modulator that allows us to modulate the numerical tension V MN formed of “0” and “1” by a sinusoidal carrier of pulsation ω C . We want to determine this modulated voltage V S .

This section describes different channels such as radio beams, satellites, optic fibers and radars. L0 is the distance of regeneration between two repeaters that also regenerate the signal (R.R. is a repeater regenerator). In the case of telephone, we have L0 = 1,830 m.

The transmission’s supports are the radio beams, the satellites, the optic fibers, and the radar. We give some quick information on these support elements.

Synthesis is a method of identification between a prototype and a physical structure. The filter is formed of n successive cavities. The space between two irises is approximate to λ G 0 /2. The iris are formed by diaphragms, coupling holes, self bars and all have an equivalent circuit given by a parallel and imaginary admittance j X ¯ .

The propagation structure is made up of three conductors in a homogeneous medium (only one dielectric). We can see that two modes can propagate: the symmetrical mode (even mode) and the non-symmetrical mode (odd mode). These are called the normal modes of the coupler.

We begin to give a very simple “filter” made of only one guide-resonator and two irises. This chapter will give a description and the method of filtering of this system.

Couplers can also be used to characterize the return loss of a structure. There are two methods: – first, a zero method where we compare the unknown reflection coefficient to this of an etalon load; – second, a reflectometric method where we separate and compare the incident and reflected waves. In this chapter, we will discuss only about the zero methods.

We have to transmit the signal s ( t ) at the discreet times t i , and s ( t i ) are the samples. If these samples s ( t i ) are quite numerous, then it is possible to recover the signal s ( t ). This is a consequence of Shannon's theorem.

Suppose we have to transmit a binary element “1” through the support of transfer function HS(f)=e−α−j2πlvf and that this support is dispersive α=kf+k′f.

The classification of microwave oscillators is based on three parameters: – the power; – the possibility of electric tuning; – spectral purity. The above three parameters are not compatible because: – a low power with a good spectra oscillator is difficult to tune; – a power oscillator has no pure spectra; – A tuned oscillator has an output, which of low power. But it is possible to obtain two of the three properties with a cascade of two particular oscillators (for example a tuned oscillator and a power oscillator give a tuned power oscillator).

Coherent modulation requires: – the exact knowledge of the phase at reception; – the recovery of the carrier at reception. These operations are delicate, especially at reception. However, the differential coding determines the jumps of the carrier's phase. And we need to use a particular code to obtain the bonds of the phase, which is called transcoding.

We consider the lines of propagation in which length and coupling are about the wavelength λ . 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 λ that is around some Giga Hertz = GHz = 10 9 Hz in microwaves. λ = c f = 300 , 000 km / s 10 9 = 3 × 10 8 10 9 = 0 . 3 m

In order to bring more and more information, we need efficient transmission systems such as: – radio beams (with numerical rate ranging from 50 to 100 Mbits/s)

A dielectric resonator (DR) is a ceramic microwave resonator with equivalent characteristics as a microwave cavity but with weak dimensions. TE 01 δ is the fundamental mode and then the DR is equivalent to a magnetic dipole.

In many applications of communications, we require amplification of the signals. To avoid obstacles, the communications very often go through a satellite and the conception of reception microwave amplifiers is different from these emission microwave amplifiers. At the emission, the amplitude of the signals is powerful but at reception the amplitude is small. The characteristics of a microwave amplifier are gain, stability, noise, power, linearity, etc. We will deal with only the first three properties and give only a measure of the latter two. The choice of the active element will be given by the central frequency f 0 , the passband Δf , the gain G and the noise factor F . In the microwave domain, we use generally field effect transistor (FET) made up of gallium arsenide (GaAs).

We will discuss the spectral power density in the cases of the coherent and differential modulations. We will also discuss the effect of the noise.

In this chapter, we show how to synchronize an oscillator, compute the variation in the frequency of the oscillation by varying the load (the pulling) and give the equivalent sinusoids in the cases of frequency-modulated (FM) and amplitude-modulated (AM) noises by considering the different spectrum.

Summary This chapter evaluates the currents in the sides of the conductors. The lossy conductors are equivalent to perfect conductors with a skin effect. Double vectorial product of transverse electric (TE) and transverse magnetic (TM) waves is derived in the chapter. It defines attenuation losses in the cases of TM and TM waves. The chapter discusses solution of some problems related to waves between two parallel metallic and lossy planes.

Summary This chapter presents two methods for the determination of the characteristics of transverse electromagnetic (TEM) lines. These methods are conform transformations and finite differences. Finite differences method can be used for lines with complicated geometry, but it takes a lot of computation. The chapter discusses solutions of some problems related to conform transformations method.

The analysis and design of miniaturized fractal filters is presented in this article. It is shown that fractal resonators can be significantly smaller than conventional planar resonators for the same resonant frequency requirements. It is observed that when increasing the number of fractal iterations (typically 3), the size of the resonators decreases and the quality factor increases. The filter design method is based on the synthesis of an inline prototype with symmetrical or asymmetrical pseudo-elliptic characteristics and coupling factor simulations using a commercial electromagnetic simulator. The fractal filters were designed using suspended substrate technology and fabricated in-house and with the services of a regular printed circuit board company. Keywords: microwave filters; fractal filters; meandered line filters; Hilbert filters; Minkowski filters