microwave tubes and describe the limitations of conventional tubes. Describe the basic principles of velocity modulation. Outline the development of microwave tubes. Describe the basic theory of operation of klystrons including multicavity and reflex klystrons. Explain the basic theory of operation of traveling-wave tubes and backward-wave oscillators. ">
Upon completion of this chapter the student will be able to:
The waveguides discussed in chapter 1 serve to transport microwave energy from one place to another. Energy is transported after it has been generated or amplified in a previous stage of the circuit. In this chapter you will be introduced to the special components used in those circuits.
Microwave energy is used in both radar and communications applications. The fact that the frequencies are very high and the wavelengths very short presents special problems in circuit design. Components that were previously satisfactory for signal generation and amplification use are no longer useful in the microwave region. The theory of operation for these components is discussed in this chapter. Because the theory of operation is sometimes difficult to understand, you need to pay particular attention to detail as you study this chapter. It is written in the simplest manner possible while retaining the necessary technical complexity.
The efficiency of conventional tubes is largely independent of frequency up to a certain limit. When frequency increases beyond that limit, several factors combine to rapidly decrease tube efficiency. Tubes that are efficient in the microwave range usually operate on the theory of VELOCITY MODULATION, a concept that avoids the problems encountered in conventional tubes. Velocity modulation is more easily understood if the factors that limit the frequency range of a conventional tube are thoroughly understood. Therefore, the frequency limitations of conventional tubes will be discussed before the concepts and applications of velocity modulation are explained. You may want to review NEETS, Module 6, Introduction to Electronic Emission, Tubes, and Power Supplies, Chapters 1 and 2, for a refresher on vacuum tubes before proceeding.
Frequency Limitations of Conventional Tubes
Three characteristics of ordinary vacuum tubes become increasingly important as frequency rises. These characteristics are interelectrode capacitance, lead inductance, and electron transit time.
The INTERELECTRODE CAPACITANCES in a vacuum tube, at low or medium radio frequencies, produce capacitive reactances that are so large that no serious effects upon tube operation are noticeable. However, as the frequency increases, the reactances become small enough to materially affect the performance of a circuit. For example, in figure 2-1, view (A), a 1-picofarad capacitor has a reactance of 159,000 ohms at 1 megahertz. If this capacitor was the interelectrode capacitance between the grid and plate of a tube, and the rf voltage between these electrodes was 500 volts, then 3.15 milliamperes of current would flow through the interelectrode capacitance. Current flow in this small amount would not seriously affect circuit performance. On the other hand, at a frequency of 100 megahertz the reactance would decrease to approximately 1,590 ohms and, with the same voltage applied, current would increase to 315 milliamperes (view (B)). Current in this amount would definitely affect circuit performance.
Figure 2-1A. - Interelectrode capacitance in a vacuum tube. 1 MEGAHERTZ
Figure 2-1B. - Interelectrode capacitance in a vacuum tube. 100
Figure 2-1C. - Interelectrode capacitance in a vacuum tube. INTERELECTRODE CAPACITANCE IN A TUNED-PLATE TUNED-GRID OSCILLATOR
A good point to remember is that the higher the frequency, or the larger the interelectrode capacitance, the higher will be the current through this capacitance. The circuit in figure 2-1, view (C), shows the interelectrode capacitance between the grid and the cathode (Cgk) in parallel with the signal source. As the frequency of the input signal increases, the effective grid-to-cathode impedance of the tube decreases because of a decrease in the reactance of the interelectrode capacitance. If the signal frequency is 100 megahertz or greater, the reactance of the grid-to-cathode capacitance is so small that much of the signal is short-circuited within the tube. Since the interelectrode capacitances are effectively in parallel with the tuned circuits, as shown in views (A), (B), and (C), they will also affect the frequency at which the tuned circuits resonate.
Another frequency-limiting factor is the LEAD INDUCTANCE of the tube elements. Since the lead inductances within a tube are effectively in parallel with the interelectrode capacitance, the net effect is to raise the frequency limit. However, the inductance of the cathode lead is common to both the grid and plate circuits. This provides a path for degenerative feedback which reduces overall circuit efficiency.
A third limitation caused by tube construction is TRANSIT TIME. Transit time is the time required for electrons to travel from the cathode to the plate. While some small amount of transit time is required for electrons to travel from the cathode to the plate, the time is insignificant at low frequencies. In fact, the transit time is so insignificant at low frequencies that it is generally not considered to be a hindering factor. However, at high frequencies, transit time becomes an appreciable portion of a signal cycle and begins to hinder efficiency. For example, a transit time of 1 nanosecond, which is not unusual, is only 0.001 cycle at a frequency of 1 megahertz. The same transit time becomes equal to the time required for an entire cycle at 1,000 megahertz. Transit time depends on electrode spacing and existing voltage potentials. Transit times in excess of 0.1 cycle cause a significant decrease in tube efficiency. This decrease in efficiency is caused, in part, by a phase shift between plate current and grid voltage.
If the tube is to operate efficiently, the plate current must be in phase with the grid-signal voltage and 180 degrees out of phase with the plate voltage. When transit time approaches 1/4 cycle, this phase relationship between the elements does not hold true. A positive swing of a high-frequency grid signal causes electrons to leave the cathode and flow to the plate. Initially this current is in phase with the grid voltage. However, since transit time is an appreciable part of a cycle, the current arriving at the plate now lags the grid-signal voltage. As a result, the power output of the tube decreases and the plate power dissipation increases. Another loss of power occurs because of ELECTROSTATIC INDUCTION.
The electrons forming the plate current also electrostatically induce potentials in the grid as they move past it. This electrostatic induction in the grid causes currents of positive charges to move back and forth in the grid structure. This back and forth action is similar to the action of hole current in semiconductor devices. When transit-time effect is not a factor (as in low frequencies), the current induced in one side of the grid by the approaching electrons is equal to the current induced on the other side by the receding electrons. The net effect is zero since the currents are in opposite directions and cancel each other. However, when transit time is an appreciable part of a cycle, the number of electrons approaching the grid is not always equal to the number going away. As a result, the induced currents do not cancel. This uncancelled current produces a power loss in the grid that is considered resistive in nature. In other words, the tube acts as if a resistor were connected between the grid and the cathode. The resistance of this imaginary resistor decreases rapidly as the frequency increases. The resistance may become so low that the grid is essentially short-circuited to the cathode, preventing proper operation of the tube.
Several methods are available to reduce the limitations of conventional tubes, but none work well when frequency increases beyond 1,000 megahertz. Interelectrode capacitance can be reduced by moving the electrodes further apart or by reducing the size of the tube and its electrodes. Moving the electrodes apart increases the problems associated with transit time, and reducing the size of the tube lowers the power-handling capability. You can see that efforts to reduce certain limitations in conventional tubes are compromises that are often in direct opposition to each other. The net effect is an upper limit of approximately 1,000 megahertz, beyond which conventional tubes are not practical.
Q.1 What happens to the impedance of interelectrode capacitance as frequency increases?
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