Lecturer Note. Lecturer-29

Transcription

1 Lecturer Note Sub: MWE Subject code: PCEC 4402 Sem: 8 th Prepared by: Mr. M. R. Jena Lecturer-29 Reflex klystron- The tube was the first practical source of microwaves and its invention initiated a search for increasingly more powerful sources, which continues to this day. Klystron designers have always maintained a close relationship to physicists, and the Plasma Physics community in particular. High-power CW klystrons at C-band and X- band have been in use for low hybrid heating in tokamacs for some time. In High Energy Physics, experimental physicists using particle accelerators rely on klystrons for increasingly higher power and frequency,1 since the limit has yet to be reached for the energy density attainable in e+e- linear colliders. Proton colliders, such as the APT, currently under study at Los Alamos to transmute isotopes of helium and lithium into tritium, require hundreds of huge megawatt CW klystrons. There are also connections of a second and third kind with plasma physics: The study of plasmas has given rise to an intense computer code development activity and klystron engineers have been among the beneficiaries. Cold testing of cavities and other klystron components, which a decade ago required expensive model building, is now carried out on computers, with better accuracy and flexibility. Even more importantly, 2-D and 3-D particle-in-cell codes are now available to predict klystron performance without actually building them.3 The codes are becoming increasingly accurate as computer capacity increases and programming is improved. They have been a very significant new tool in designing the state-of-theart klystrons that will be described later. The third connection results from a migration of plasma physicists into the microwave engineering profession, which has been taking place over the last fifteen years.

2 It has been a consequence of the Star Wars programs and has created a more or less separate community of experimenters, with an agenda that includes the generation of gigawatt microwave pulses and the study of plasmas in microwave tubes. The new community has taken the name High Power Microwaves or HPM. At this writing, microwave tube engineers and HPM physicists have yet to join forces, or reconcile differences in their respective methods. Velocity modulation- Velocity-modulated tubes are microwave tubes using transit time in the conversion of dc power to radio-frequency power. The interchange of power is accomplished by using the principle of electron velocity modulation and low-loss resonant cavities in (or near the electron beam of) the microwave tube. Velocity modulation is then defined as that variation in the velocity of a beam of electrons caused by the alternate speeding up and slowing down of the electrons in the beam. This variation is usually caused by a voltage signal applied between the grids through which the beam must pass. The direction of the electron beam and the static electrical field goes to each other parallelly (linearly) into linear beam tubes. Against this the fields influencing the electron beam stand vertically by the electron beam at the cross field tubes. Klystrons make use of the transit-time effect by varying the velocity of an electron beam. A klystron uses special resonant cavities which modulate the electric field around the axis of the tube modulating the electric field around the axis the tube. In the middle of these cavities, there is a grid allowing the electrons to pass the cavity. Due to the number of the resonant cavities klystrons are divided up into Two- or Multicavity klystrons Reflex or Repeller Klystrons Another tube based on velocity modulation, and used to generate microwave energy, is the reflex klystron (repeller klystron).

3 The reflex klystron contains a reflector plate, referred to as the repeller, instead of the output cavity used in other types of klystrons. The electron beam is modulated as it was in the other types of klystrons by passing it through an oscillating resonant cavity, but here the similarity ends. The feedback required to maintain oscillations within the cavity is obtained by reversing the beam and sending it back through the cavity. The electrons in the beam are velocity-modulated before the beam passes through the cavity the second time and will give up the energy required to maintain oscillations. The electron beam is turned around by a negatively charged electrode that repels the beam ( repeller ). This type of klystron oscillator is called a reflex klystron because of the reflex action of the electron beam. Repeller klystrons are often used in older radar sets as local oscillators or as oscillators in measurement sets. If the voltage feed is keyed, then the repeller klystron can be used for RF-pulse generation too, but as self-oscillating tube it provides a non-coherent oscillation only.

4 Lecturer-30 Reflex Klystron Operation- The klystron was the first embodiment of the velocity modulation principle. The so-called Applegate diagram best illustrates this.5 After being accelerated by a DC voltage, electrons from the cathode initially drift with constant velocity. When they traverse a pair of closely spaced grids, their velocity is modulated by a sinusoidal rf signal. (The illustration actually shows gridless gaps, which are used in all high-power tubes.) Following that, the electrons drift and form bunches, centered at the electrons which transited the grids at the time the rf field was zero and was increasing. The electron bunches constitute an rf current, which induces a voltage across a second pair of grids downstream. That voltage can impart additional velocity modulation to the beam. The process can be repeated by including more cavities, until considerable amplification takes place, or until the increased space charge within the bunches prevents tighter bunching. This places an upper limit on the efficiency of the device. (See Klystron Tutorial) The beam designed so that the voltage induced across it slows the beam down. In the process, the electrons give up their kinetic energy to the cavity rf fields. Klystrons are the most efficient of linear beam microwave tubes. Their efficiency increases as the space charge in the beam decreases. Beam space charge is measured by a quantity called perveance, useful in the design of electron guns, and defined as the ratio of the beam current to the 3/2-power of the voltage. For most klystrons, the perveance chosen is between 0.5X10-6 and 2.5x10-6, but in certain cases, lower perveances may be useful, despite the higher beam voltages that they imply. The gain of multi-cavity klystrons is very high. Gains of 60 db, or even higher, are not unusual. On the other hand, klystrons are narrow-band devices, compared with travelling-wave tubes.6 For most applications, including communications, this is not a

5 serious disadvantage because some klystron broadbanding is possible, at the expense of gain. However, for many radar applications and for electronic countermeasures (against radar), only TWTs are suitable. In addition to the TWT competition, low-power klystrons, particularly reflex oscillators, lost the battle to solid-state replacements in radar and communication equipment some time ago. The rf current produced by the bunched beam, moving from left to right, causes the output cavity (the extended interaction circuit to the right of the illustration above) to ring at its fundamental frequency. The current induced at the output circuit produces a voltage across it, which slows the beam down, converting its kinetic energy to rf energy in the cavity, and dispersing the bunches. Power is taken out by a waveguide (not shown). The electrons shown between bunches detract from good efficiency. More electrons can be directed toward the bunches by inductively tuned cavities placed before the output circuit (as the single TM01 resonator shown above), or by one or more 2nd harmonic cavities upstream. Space charge forces prevent tighter bunches from being formed. These forces increase with beam perveance, which is defined as: K = / Hence, the lower the perveance, the tighter the bunching and the conversion efficiency. A gap resistance Rg must be chosen to optimize the gap voltage for good conversion efficiency. Its value depends on the coupling coefficient M between beam and circuit, and on the ratio of rf to dc current, I1/I0. M and I1/Io are usually determined by simulation. An empirical formula for the gap resistance Rg is: Rg = 1 0

6 The required gap resistance and the cavity R/Q determine how tightly the output cavity is to be coupled to the output waveguide (or how low the Qe can be). R/Q is proportional to the ratio of the square of the gap voltage to the energy stored in the cavity. Q e = A low Qe implies better circuit efficiency and wider bandwidth for the klystron. Good design calls for a high coupling coefficient and R/Q, either of which results in a low Qe. Low-perveance klystrons have good efficiency, but because of a higher Rg, have narrower bandwidth and lower output circuit efficiency. η 0 = In pulsed, high-peak power klystrons, it is essential to minimize the surface gradients at the output circuit to avoid rf breakdown. A single cavity is often unsuitable and extended circuits must be employed. Their function is to develop the required interaction voltage over a longer distance to reduce surface gradients.

7 Traveling Wave Tube Lecturer-31 Traveling wave tubes (TWT) are wideband amplifiers. They take therefore a special position under the velocity-modulated tubes. On reason of the special low-noise characteristic often they are in use as an active RF amplifier element in receivers additional. There are two different groups of TWT: low-power TWT for receivers occurs as a highly sensitive, low-noise and wideband amplifier in radar equipments high-power TWT for transmitters these are in use as a pre-amplifier or final stage for high-power transmitters. Physical construction and functional describing The Traveling Wave Tube (TWT) is a high-gain, low-noise, wide-bandwidth microwave amplifier. It is capable of gains greater than 40 db with bandwidths exceeding an octave. (A bandwidth of one octave is one in which the upper frequency is twice the lower frequency.) Traveling-wave tubes have been designed for frequencies as low as 300 megahertz and as high as 50 gigahertz. The TWT is primarily a voltage amplifier. The wide-bandwidth and low-noise characteristics make the TWT ideal for use as an RF amplifier in microwave equipment. The TWT contains an electron gun which produces and then accelerates an electron beam along the axis of the tube. The surrounding magnet provides a magnetic field along the axis of the tube to focus the electrons into a tight beam. The helix, at the center of the tube, is a coiled wire that provides a low-impedance transmission line for the RF energy within the tube. The RF input and output are coupled onto and removed from the helix by waveguide directional couplers that have no physical connection to the helix.

8 The attenuator prevents any reflected waves from traveling back down the helix. The electron- beam bunching already starts at the beginning of the helix and reaches its highest expression on the end of the helix. If the electrons of the beam were accelerated to travel faster than the waves traveling on the wire, bunching would occur through the effect of velocity modulation. Velocity modulation would be caused by the interaction between the traveling-wave fields and the electron beam. Bunching would cause the electrons to give up energy to the traveling wave if the fields were of the correct polarity to slow down the bunches. The energy from the bunches would increase the amplitude of the traveling wave in a progressive action that would take place all along the length of the TWT. Slow-wave structure model To achieve strong interaction between electric wave and electrons, both must propagate at roughly the same velocity. One uses a slow-wave structure (SWS) made of a cylindrical metallic tube which contains a metallic helix as sketched in Fig.1. As the electric wave travels along the helix, its axial velocity nears the electrons velocity. Figure: sketch of a travelling-wave tube

9 Figure: dispersion curves In the above figures sketch of a travelling-wave tube & its dispersion curves are given. One notices that the equivalent circuit is able to propagate direct waves as well as backward waves, and to present a gap when one dissymmetrizes its parameters. One also see that both dispersion curves matches for low phase velocities. Time evolution of the equivalent circuit is obtained by solving Kirhoff s equations of the cicuit.

10 Lecturer-32 We propose to modelise the SWS using an equivalent circuit approach in time domain. As seen in Fig. each point on the helix is coupled inductively with two neighbouring points on the helix, and capacitively with a point on the metalic sheath and two points that lie on the helix one turn foreward and one turn backward. The lowest degree of descretisation is to take two points per helix turn. It gives the equivalent circuit seen in Fig. The metallic sheath is taken as zero potential. The dispersion curve of this equivalent circuit is shown in Fig. together with the dispersion curve of an actual TWT. One notices that the equivalent circuit is able to propagate direct waves as well as backward waves, and to present a gap when one dissymmetrizes its parameters. One also see that both dispersion curves matches for low phase velocities. Time evolution of the equivalent circuit is obtained by solving Kirhoff s equations of the cicuit. Hence one obtains a differential system of the form: U& = M.U, where U contains capacitance voltages and inductance currents of the equivalent circuit. The solution of this system is given by: (υ ) (0).U t e U= M t. Electron beam dynamics We assume a one-dimensional beam. The phase space is assumed to be a set of discrete points ( u ) i j x v, and the beam is described by a distribution function ( u) i j f x v. Time evolution of the electron beam is given by one-dimensional Vlasov equation: ( υ) = 0 where q is the electron charge, m is the electron mass, ( υ) SWS i E x is the electrical field due to the SWS and (υ ) SC i E x is the space-charge field. The solution of Vlasov equation is made with the Piecewise Parabolic Method [7] that is based on time splitting of Vlasov equation into two advective equations [8], and on

11 solving successively both equations. This method is fast and conserves positivity and monotonicity of ( u ) i j f x v. Interaction between the beam and the slow-wave structure ( υ) SWS i E x is calculated at each time step as a function of the voltages of the equivalent circuit. (υ ) SC i E x is obtained by solving Poisson s equation. We use an analytical solution for a one-dimensional discretized beam in a metallic cylinder. While the electron beam is submitted to electric fields, it induces current in the SWS. This current is induced in the inter-turn capacitances, which are the only parts of the equivalent circuit that are acting on the beam. Shockly-Ramo s theorem is used to calculate at each time step the variation of the voltage of inter-turn capacitances. Characteristics of a TWT The attainable power-amplification is essentially dependent on the following factors: constructive details (e.g. length of the helix) electron beam diameter (adjustable by the density of the focussing magnetic field) power input voltage UA2 on the helix The gain of the TWT has got a linear characteristic of about 26 db at small input power. If you increase the input power, the output power doesn't increase for the same gain. So you can prevent an oversteer of e.g the following mixer stage. The relatively low efficiency of the TWT partially offsets the advantages of high gain and wide bandwidth. Given that the gain of an TWT effect by the electrons of the beam that interact with the electric fields on the delay structure, the frequency behaviour of the helix is responsible for the gain. The bandwidth of commonly used TWT can achieve values of many giga hertzes. The noise figure of recently used TWT is db.

12 The helix may be replaced by some other slow wave structure such as a ring-bar, ring loop, or coupled cavity structure. The structure is chosen to give the characteristic appropriate to the desired gain/bandwidth and power characteristics. Multi-cavity Magnetron In 1921 Albert Wallace Hull invented the magnetron as a microwave tube. During World War II it was developed by John Randall and Henry Boot to a powerful microwave generator for Radar applications. Magnetrons function as self-excited microwave oscillators. Crossed electron and magnetic fields are used in the magnetron to produce the high-power output required in radar equipment. These multicavity devices may be used in radar transmitters as either pulsed or cw oscillators at frequencies ranging from approximately 600 to 96,000 megahertz. The relatively simple construction has the disadvantage, that the Magnetron usually can work only on a constructively fixed frequency. A magnetron is a high power microwave oscillator in which the potential energy of an electron cloud near the cathode is converted into r.f. energy in a series of cavity resonators similar to the one shown in Figure. As depicted by the low frequency analog, the rear wall of the structure may be considered the inductive portion, and the vane tip region the capacitor portion of the equivalent resonant circuit. The resonant frequency of a microwave cavity is thereby determined by the physical dimension of the resonator together with the reactive effect of any perturbations to the inductive or capacitive portion of the equivalent circuit. This is an important point and will be recalled later. In order to sustain oscillations in a resonant circuit, it is necessary to continuously input energy in the correct phase. Referring to Figure, if the instantaneous r.f. field, due to steady state oscillations in the resonator, is in the direction shown, and, an electron with velocity was to travel through

13 the r.f. field such that the r.f. field retarded the electron velocity by an amount, the decrease in electron energy will be exactly offset by an increase in the r.f. field strength. In a magnetron, the source of electrons is a heated cathode located on the axis of an anode structure containing a number of microwave resonators. Electrons leave the cathode and are accelerated toward the anode, due to the dc field established by the voltage source E. The presence of a strong magnetic field B in the region between cathode and anode produces a force on each electron which is mutually perpendicular to the dc field and the electron velocity vectors, thereby causing the electrons to spiral away from the cathode in paths of varying curvature, depending upon the initial electron velocity a the time it leaves the cathode. As this cloud of electrons approaches the anode, it falls under the influence of the r.f. fields at the vane tips, and electrons will either be retarded in velocity, if they happen to face an opposing r.f. field, or accelerated if they are in the vicinity of an aiding r.f. field. Since the force on an electron due to the magnetic field B is proportional to the electron velocity through the field, the retarded velocity electrons will experience less "curling force" and will therefore drift toward the anode, while the accelerated velocity electrons will curl back away from the anode. The result is an automatic collection of electron "spokes" as the cloud nears the anode, with each spoke located at a resonator having an opposing r.f. field. On the next half cycle of r.f. oscillation, the r.f. field pattern will have reversed polarity and the spoke pattern will rotate to maintain its presence in an opposing field. The "automatic" synchronism between the electron spoke pattern and the r.f. field polarity in a crossed field device allows a magnetron to maintain relatively stable operation over a wide range of applied input parameters. For example, a magnetron designed for an output power of 200 kw peak will operate quite well at 100 kw peak output by simply reducing the modulator drive level. The mode controlling techniques in a conventional magnetron, e.g., electrically connecting alternate vane tips together to assure identical potential, employing geometrical similarities between alternate resonators to favor mode oscillation, will adequately maintain mode control in conventional magnetron anodes.

14 Due to mode separation parameters, the number of resonators in conventional magnetron anodes is limited and rarely exceeds 20 resonator vanes. Since the physical size of each resonator is fixed by the desired output frequency, the overall size of the anode is limited, thereby restricting cathode dimensions and heat dissipation capacity. The result is that at higher frequencies the conventional magnetron has reduced power output capability, lower reliability and a shorter operating lifetime than can be realized at the lower microwave frequencies. The distinguishing feature of the coaxial magnetron is the presence of a high Q stabilizing cavity between the anode and the output waveguide. The theory of operation presented for a conventional magnetron applies equally to the anode-cathode region of the coaxial structure. However, the coaxial stabilizing cavity affords very significant improvements in overall magnetron performance. Typical Magnetron Parameters The following is a discussion and explanation of typical magnetron specification parameters. Thermal Drift At the time high voltage is first applied to a magnetron, the thermal equilibrium of the device is suddenly altered. The anode vanes being to heat at the tips due to electron bombardment and the entire anode/cathode structure undergoes a transient change in thermal profile. During the time required for each part of the magnetron to stabilize at its normal operating temperature, the output frequency of the magnetron will "drift." The curve of output frequency vs. time during the period following initial turn on is called the "Thermal Drift" curve. Generally speaking, the maximum drift occurs during the first few minutes after turn on, and slowly approaches equilibrium over a period ranging from 10 to 30 minutes depending upon the structure mass, power output, type of cooling and basic magnetron design. Thermal drift curves across a variety of magnetron types operating at the same frequency and output power may differ radically from each other.

15 Each type is usually designed for a particular purpose and subtle differences in the internal magnetron configuration can produce radical differences in the thermal drift curve. It should be noted that a thermal drift effect will occur not only at initial turn-on, but whenever the peak or average input power to the magnetron is changed, e.g., a change of pulse duration, PRF or duty. Figure shows typical thermal drift curves for a particular magnetron plotted as a function of duty. The dotted line indicates the effect of a change in duty from.001 to.0005 after thermal equilibrium has been initially achieved. Temperature Coefficient After the thermal drift period has expired and a stable operating frequency has been achieved, changes to ambient conditions which cause a corresponding change in the magnetron temperature will produce a change in the output frequency. In this content ambient changes include cooling air temperature or pressure in air cooled magnetrons; mounting plate temperature in heat sink cooled magnetrons; and flow rate or temperature in liquid cooled magnetrons. The change in magnetron output frequency for each degree change in body temperature, as measured at a specified point on the outside surface of the magnetron body, is defined as the Temperature Coefficient for the magnetron and is usually expressed in MHz/oC. For most magnetrons the temperature coefficient is a negative (frequency decreases as temperature increases) and is essentially constant over the operating range of the magnetron. When estimating magnetron frequency change due to temperature coefficient, keep in mind that the temperature coefficient relates magnetron frequency to body temperature and there is not necessarily a 1:1 relation between body temperature and, for example, ambient air temperature. In addition, for airborne systems, the cooling effect of lower air temperature at altitude may offset by a corresponding reduction in air density. Pushing Figure

16 The pushing figure of a magnetron is defined as the change in magnetron frequency due to a change in the peak cathode current. Referring back to the earlier theory discussion, we noted that the resonant frequency of a vane resonator is determined by its mechanical dimensions plus the reactive effect of any perturbation. The presence of electrons in the vicinity of the vane tips affects the equivalent capacitance of the resonator by an amount proportional to the density of the electrons and, since electron density is similarly related to peak pulse current, changes in pulse current level will produce changes in output frequency. The pushing figure expressed in MHz/Amp is represented by the slope of a frequency vs. peak current curve plotted for a particular magnetron type From the curve of Figure, it can be seen that the slope is not a constant over the full range of operating current. It is therefore meaningless to talk about a specific value for the pushing figure unless one also specifies the range of peak current over which it applies. It should be noted that since power output is proportional to peak current in a magnetron, the pushing figure at peak current levels well below the normal operating point of the magnetron are usually unimportant because the power output at these current levels is low.

17 Lecturer-33 Physical construction of a magnetron The magnetron is classed as a diode because it has no grid. The anode of a magnetron is fabricated into a cylindrical solid copper block. The cathode and filament are at the center of the tube and are supported by the filament leads. The filament leads are large and rigid enough to keep the cathode and filament structure fixed in position. The cathode is indirectly heated and is constructed of a high-emission material. The 8 up to 20 cylindrical holes around its circumference are resonant cavities. The cavities control the output frequency. A narrow slot runs from each cavity into the central portion of the tube dividing the inner structure into as many segments as there are cavities. The open space between the plate and the cathode is called the interaction space. In this space the electric and magnetic fields interact to exert force upon the electrons. The magnetic field is usually provided by a strong, permanent magnet mounted around the magnetron so that the magnetic field is parallel with the axis of the cathode. The form of the cavities varies, as shown in Figure. The output lead is usually a probe or loop extending into one of the tuned cavities and coupled into a waveguide or coaxial line. a) slot- type b) vane- type c) rising sun- type d) hole-and-slot- type Basic Magnetron Operation As when all velocity-modulated tubes the electronic events at the production microwave frequencies at a Magnetron can be subdivided into four phases too: 1. phase: production and acceleration of an electron beam 2. phase: velocity-modulation of the electron beam

18 3. phase: bunching the electrons, forming of a Space-Charge Wheel 4. phase: dispense energy to the ac field 1. Phase: Production and acceleration of an electron beam When no magnetic field exists, heating the cathode results in a uniform and direct movement of the field from the cathode to the plate. The permanent magnetic field bends the electron path. If the electron flow reaches the plate, so a large amount of plate current is flowing. If the strength of the magnetic field is increased, the path of the electron will have a sharper bend. Likewise, if the velocity of the electron increases, the field around it increases and the path will bend more sharply. However, when the critical field value is reached, as shown in the figure as a red path, the electrons are deflected away from the plate and the plate current then drops quickly to a very small value. When the field strength is made still greater, the plate current drops to zero. When the magnetron is adjusted to the cutoff, or critical value of the plate current, and the electrons just fail to reach the plate in their circular motion, it can produce oscillations at microwave frequencies. 2. Phase: Velocity-modulation of the electron beam The electric field in the magnetron oscillator is a product of ac and dc fields. The dc field extends radially from adjacent anode segments to the cathode. The ac fields, extending between adjacent segments, are shown at an instant of maximum magnitude of one alternation of the rf oscillations occurring in the cavities. In the Figure is shown only the assumed high-frequency electrical ac field. This ac field work in addition to the to the permanently available dc field. The ac field of each individual cavity increases or decreases the dc field like shown in the figure. Well, the electrons which fly toward the anode segments loaded at the moment more positively are accelerated in addition.

19 These get a higher tangential speed. On the other hand the electrons which fly toward the segments loaded at the moment more negatively are slow down. These get consequently a smaller tangential speed. 3. Phase: Forming of a Space-Charge Wheel On reason the different speeds of the electron groups a velocity modulation appears therefore. The cumulative action of many electrons returning to the cathode while others are moving toward the anode forms a pattern resembling the moving spokes of a wheel known as a Space-Charge Wheel, as indicated in Figure. The space-charge wheel rotates about the cathode at an angular velocity of 2 poles (anode segments) per cycle of the ac field. This phase relationship enables the concentration of electrons to continuously deliver energy to sustain the rf oscillations. One of the spokes just is near an anode segment which is loaded a little more negatively. The electrons are slowed down and pass her energy on to the ac field. This state isn't static, because both the ac- field and the wire wheel permanently circulate. The tangential speed of the electron spokes and the cycle speed of the wave must be brought in agreement so. 4. Phase: Dispense energy to the ac field Recall that an electron moving against an E field is accelerated by the field and takes energy from the field. Also, an electron dispense energy to a field and slows down if it is moving in the same direction as the field (positive to negative). The electron spends energy to each cavity as it passes and eventually reaches the anode when its energy is expended. Thus, the electron has helped sustain oscillations because it has taken energy from the dc field and given it to the ac field. This electron describes the path shown in Figure over a longer time period looked. By the multiple breaking of the electron the energy of the electron is used optimally. The effectiveness reaches values up to 80%. Modes of Operation The operation frequency depends on the sizes of the cavities and the interaction space between anode and cathode.

20 But the single cavities are coupled over the interaction space with each other. Therefore several resonant frequencies exist for the complete system. Two of the four possible waveforms of a magnetron with 8 cavities are in the figure 8 represented. Several other modes of oscillation are possible (3/4π, 1/2 π, 1/4 π), but a magnetron operating in the π mode has greater power and output and is the most commonly used. So that a stable operational condition adapts in the optimal pi mode, two constructive measures are possible: Strapping rings: The frequency of the π mode is separated from the frequency of the other modes by strapping to ensure that the alternate segments have identical polarities. For the pi mode, all parts of each strapping ring are at the same potential; but the two rings have alternately opposing potentials. For other modes, however, a phase difference exists between the successive segments connected to a given strapping ring which causes current to flow in the straps. Use of cavities of different resonance frequency Magnetron coupling methods Energy (RF) can be removed from a magnetron by means of a coupling loop. At frequencies lower than 10,000 megahertz, the coupling loop is made by bending the inner conductor of a coaxial line into a loop. The loop is then soldered to the end of the outer conductor so that it projects into the cavity, as shown in Figure, view (A). Locating the loop at the end of the cavity, as shown in view (B), causes the magnetron to obtain sufficient pickup at higher frequencies. The segment-fed loop method is shown in view (C) of Figure 17. The loop intercepts the magnetic lines passing between cavities. The strap-fed loop method (view (D), intercepts the energy between the strap and the segment. On the output side, the coaxial line feeds another coaxial line directly or feeds a waveguide through a choke joint. The vacuum seal at the inner conductor helps to support the line. Aperture, or slot,

21 coupling is illustrated in view (E). Energy is coupled directly to a waveguide through an iris. Magnetron Tuning A tunable magnetron permits the system to be operated at a precise frequency anywhere within a band of frequencies, as determined by magnetron characteristics. The resonant frequency of a magnetron may be changed by varying the inductance or capacitance of the resonant cavities.

22 Lecturer-34 Crossed-Field Amplifier Also other names are used for the Crossed-Field Amplifier in the literature. Platinotron Amplitron2 Stabilotron The Crossed-Field Amplifier (CFA), is a broadband microwave amplifier that can also be used as an oscillator (Stabilotron). The CFA is similar in operation to the magnetron and is capable of providing relatively large amounts of power with high efficiency. The bandwidth of the cfa, at any given instant, is approximately plus or minus 5 percent of the rated center frequency. Any incoming signals within this bandwidth are amplified. Peak power levels of many megawatts and average power levels of tens of kilowatts average are, with efficiency ratings in excess of 70 percent, possible with crossed-field amplifiers. Because of the desirable characteristics of wide bandwidth, high efficiency, and the ability to handle large amounts of power, the CFA is used in many applications in microwave electronic systems. When used as the intermediate or final stage in highpower radar systems, all of the advantages of the CFA are used. The amplifiers in this type of power-amplifier transmitter must be broad-band microwave amplifiers that amplify the input signals without frequency distortion. Typically, the first stage and the second stage are traveling-wave tubes (TWT) and the final stage is a crossed-field amplifier. Recent technological advances in the field of solid-state microwave amplifiers have produced solid-state amplifiers with enough output power to be used as the first stage in some systems. Transmitters with more than three stages usually use crossed-field amplifiers in the third and any additional stages. Both traveling-wave tubes and crossed-field amplifiers have a very flat amplification response over a relatively wide frequency range.

23 Crossed-field amplifiers have another advantage when used as the final stages of a transmitter; that is, the design of the crossed-field amplifier allows rf energy to pass through the tube virtually unaffected when the tube is not pulsed. When no pulse is present, the tube acts as a section of waveguide. Therefore, if less than maximum output power is desired, the final and preceding cross-field amplifier stages can be shut off as needed. This feature also allows a transmitter to operate at reduced power, even when the final crossed-field amplifier is defective. Stabilotron is a crossed field amplifier using external resonant cavities as positive feed back loop. This is a kind of oscillating device like a magnetron, but, due to the higher accuracy of the external resonant cavities the stabilotron has got a more constant frequency. Table : Comparison of different microwave sources Klystron Traveling Magnetron Wave Tube frequency up to 35 GHz up to 95 GHz up to 95 GHz bandwidth 2-4 % % any megahertzes power up to 50 MW up to 1 MW up to 10 MW output amplification up to 60 db up to 50 db function as small-band power amplifier wide-band, lownoise voltage amplifier high power oscillator at one frequency Microwave Amplifier- Design of amplifiers with conjugately matched impedances This method of design is only applicable to transistors which are stable and give sufficient gain for our design aims. For other conditions we will have to use other design methods. This design procedure results in load and source reflection coefficients which provide a conjugate match for the actual output and input impedances of the transistor. However,

24 remember that the actual output impedance of a transistor is dependent on its source impedance and vice-versa. This dependency is caused by the reverse gain (s12) of the transistor. If s12 was zero, then of course the load and source impedances would have no effect on the transistor s input and output impedances. Output reflection coefficient To find the desired load reflection coefficient for a conjugate match C2 = s22 (Dss11*) where the asterisk indicates the complex conjugate of s11 (same magnitude but opposite angle). The quantity Ds is the quantity calculated Next we calculate B2: B2 = 1 + s22 2 s11 2 Ds 2 The magnitude of the reflection coefficient is found from the equation ɼ L = The sign preceding the radical is opposite to the sign of B2 previously calculated. The angle of the load reflection coefficient is simply the negative of the angle of C2 calculated. After the desired load reflection coefficient is found, we can either (a) plot GL on a Smith chart to find the load impedance (Z) directly, or (b) substitute GL from the equation Γ v = Input reflection coefficient With the desired load reflection coefficient specified, the source reflection coefficient needed to terminate the transistor s input can now be calculated: Γ S = - Design of amplifiers for a specific gain In cases where a specific gain is required, it is normal practice to provide selective mismatching so that transistor gain can be reduced to the desired gain.

25 Selective mismatching is a relatively inexpensive method used to decrease gain by not matching a transistor to its conjugate load. One of the easiest ways of selective mismatching is through the use of a constant gain circle plotted on the Smith chart. A constant gain circle is merely a circle, the circumference of which represents a locus of points (load impedances) that will force the amplifier gain to a specific value. For instance, any of the infinite number of impedances located on the circumference of a 12 db constant gain circle would force the amplifier stage gain to 12 db. Once the circle is drawn on a Smith chart, you can see the load impedances that will provide a desired gain.

26 Microwave transistor- Lecturer-35 The word transistor is an abbreviation of two words transferring resistor. For explanation purposes, a transistor may be considered as two diodes connected back to back. This is the well known Ebers Moll model and it is shown in Figure 6.2 for the NPN transistor. In the Ebers Moll model, a current generator is included to show the relationship (Ic = aie) between the emitter current (Ie) and the collector current (Ic). In a good transistor, a ranges from 0.99 to about The action that takes place for an NPN transistor can be explained as followes. In this diagram, emitter, base and collector are diffused together and a base emitter depletion layer is set up between base and emitter, and a collector base depletion layer is set up between the collector and base. These depletion layers are set up in the same way as p n junctions. In normal transistor operation, the base emitter junction is forward biased and the base collector junction is reversed biased. This results in a narrow depletion (low resistance) at the base emitter junction and a wide depletion layer (high resistance) at the collector base junction. Electrons from the emitter (Ie) are attracted to the base by the positive potential Vbe. By the time these electrons arrive in the base region, they will have acquired relatively high mobility and momentum. Some of these electrons will be attracted towards the positive potential of Vbe but most of them (>99%) will keep moving across the base region which is extremely thin ( microns2) and will penetrate the collector base junction. The electrons (Ic) will be swept into the collector region where they will be attracted by the positive potential of Vcb. Relatively little d.c. energy is required to attract electrons into the base region because

27 it is forward biased (low resistance Rbe). Relatively larger amounts of d.c. energy will be required in the collector base region because the junction is reversed biased (high resistance Rcb). power in the collector base region power in the base emitter region Ic = collector current Ie = emitter current Rcb = resistance between collector and base Rbe = resistance between base and emitter Since by design, Ic Ie and since Rcb >> Rbe We have a power gain because Rcb >> Rbe. Hence if signal energy is placed between the base emitter junction, it will appear at a much higher energy level in the collector region and amplification has been achieved. The objectives of transistor biasing are: to select a suitable operating point for the transistor; to maintain the chosen operating point with changes in temperature; to maintain the chosen operating point with changes in transistor current gain with temperature; to maintain the chosen operating point to minimise changes in the a.c. parameters of the operating transistor; to prevent thermal runaway, where an increase in collector current with temperature causes overheating, burning and self-destruction; to try to maintain the chosen operating point with changes in supply voltages this is particularly true of battery operated equipment where the supply voltage changes

28 considerably as the battery discharges; to maintain the chosen operating point with changes in b when a transistor of one type is replaced by another of the same type it is common to find that b varies from 50% to 300% of its nominal value for the same type of transistor. There are two basic internal characteristics that have a serious effect upon a transistor s d.c. operating point over temperature. They are changes in the base emitter voltage (DVBE) and changes in current gain (Db). As temperature increases, the required base-emitter voltage (VBE) of a silicon transistor for the same collector current decreases at the rate of about 2.3 mv/ C. This means that if VBE was 0.7 V for a given collector current before a temperature rise, then the same VBE of 0.7 V after a temperature rise will now produce an increase in base current and more collector current; that in turn causes a further increment in transistor temperature, more base and collector current, and so on, until the transistor eventually overheats and burns itself out in a process known as thermal runaway. To prevent this cyclic action we must reduce the effective VBE with temperature. There are several ways of biasing bi-polar transistors in order to increase bias stability. Complete step-by-step design instructions are included with each circuit configuration. For ease of understanding, a.c. components such as tuned circuits, inductors and capacitors have deliberately been left out of the circuits because they play little part in setting the operating bias point. However, a.c. components will be consideredat a later stage when we come to design r.f. amplifiers. Collector current characteristics If you were to plot collector current (IC) of an NPN transistor against collector emitter (VCE) for various values of the base current (IB), you will get the graph shown in Figure. In practice, the graph is either released by transistor manufacturers or you can obtain it by using an automatic transistor curve plotter. The points to note about these characteristics are: the knee of these curves occurs when VCE is at about V; collector current (IC) increases with base current (IB) above the knee voltage.

29 Current gain Because of the slightly non-linear relation between collector current and base current, there are two ways of specifying the current gain of a transistor in the common emitter circuit. The d.c. current gain (hfe) is simply obtained by dividing the collector current by the base current. This value is important in switching circuits. For most amplification purposes, we are only concerned with small variations in collector current, and a more appropriate way of specifying current gain is to divide the change in collector current by the change in base current and obtain the small signal current gain hfe or b. Operating point The point at which a transistor operates is very important. For example at point P2 of Figure 6.4 (see inset), if we choose the operating point to be at VCE = 5 V and IC = 13 ma, it is immediately clear that you will not get VCE excursions è 5 V because the transistor will not function when VCE = 0. The same argument is true with current because you will not get current excursions less than zero. Therefore the operating point must be carefully chosen for your intended purpose. This act of choosing the operating point is called biasing. The importance of biasing cannot be over-emphasised because, as you will see later, d.c. biasing also alters the a.c. parameters of a transistor. If the a.c. parameters of your transistor cannot be held constant (within limits) then your r.f. design will not be stable. Transistor stability Before designing a circuit, it is important to check whether the active device which we will use is (i) unconditionally stable or (ii) conditionally stable. This is necessary because different conditions require the appropriate design method. It is possible to calculate potential instabilities in transistors even before an amplifier is built. This calculation serves as a useful aid in finding a suitable transistor for a particular application.

30 To calculate a transistor s stability with s-parameters, we first calculate an intermediate quantity Ds where Ds = s11s22 s12s21 We do this because in the expressions that follow, you will find that the quantity Ds is used many times and we can save ourselves considerable work by doing this. The Rollett stability factor (K) is calculated as: 1 + Ds 2 s11 2 s22 2 K = (2)( s21 ) ( s12 ) If K is greater than 1, the transistor is unconditionally stable for any combination of source and load impedance. If K is less than 1, the transistor is potentially unstable and will most likely oscillate with certain combinations of source and load impedances. With K less than 1, we must be extremely careful in choosing source and load impedances for the transistor. It does not mean that the transistor cannot be used for a particular application; it merely indicates that the transistor will have to be used with more care. If K is less than 1, there are several approaches that we can take to complete the design: select another bias point for the transistor; choose a different transistor; design the amplifier heeding carefully detailed procedures that we will introduce shortly. Maximum available gain The maximum gain we can ever get from a transistor under conjugately matched conditions is called the maximum available gain (MAG). Maximum available gain is calculated in two steps.

31 (1) Calculate an intermediate quantity called B1, where B1 = 1 + s11 2 s22 2 Ds 2 MAG = 10 log + 10 log K ± 1 MAG = maximum available gain in db K = stability factor

32 Transistor Characterization Lecturer-36 In order to design an amplifier circuit using a transistor, the frequency dependence of the gain as well as the input and output impedances must be determined. The network analyzer and a measurement fixture will be used to make these measurements. The results can be imported into the CAD software for simulating the performance of circuits using the transistor. 1.) Before starting the measurement, the network analyzer must be calibrated. Since the transistor does not have standard microwave connectors on its terminals, a test fixture will be used to hold the transistor and bring the test signals in and out of the transistor. In order to calibrate the network analyzer without standard connectors, a set of calibration standards compatible with the test fixture must be used. These calibration standards are electrically similar to those used in previous labs; only the physical configuration is designed to match the performance of the test fixture as closely as possible. Due to the fragility of these calibration standards, the instructor will demonstrate this calibration. Another important point is that since the transistor has significant gain, it is necessary to engage the attenuators that are internal to the network analyzer to avoid overloading the analyzer. The frequency range will be set from 10 MHz to 6 GHz, using 801 data points. As with the previous lab, the IC-CAP software package will be used to control the instruments for measuring the characteristics of the transistor. The semiconductor parameter analyzer will be used to supply the DC voltages and currents for the measurements. The outputs (SMU s) of the 4155C should be connected to the bias connections on the back of the network analyzer; SMU1 should connect to Port 1, and SMU2 to Port 2. Once these connections have been verified, start IC-CAP (source ee40458.csh or ee40458.sh, then run iccap ). Since the measurement equipment configuration is different than previously (the HP 4155C for biasing the transistor has been added), go to the hardware window and confirm that the interface