The Decibel Measurement System

Because of the use of the decibel measurement system in the following paragraphs, you will be introduced to it at this point. Technicians who deal with communications and radar equipment most often speak of the gain of an amplifier or a system in terms of units called DECIBELS (dB). Throughout your Navy career you will use decibels as an indicator of equipment performance; therefore, you need to have a basic understanding of the decibel system of measurement. Because the actual calculation of decibel measurements is seldom required in practical applications, the explanation given in this module is somewhat simplified. Most modern test equipment is designed to measure and indicate decibels directly which eliminates the need for complicated mathematical calculations. Nevertheless, a basic explanation of the decibel measurement system is necessary for you to understand the significance of dB readings and equipment gain ratings which are expressed in decibels.

The basic unit of measurement in the system is not the decibel, but the bel, named in honor of the American inventor, Alexander Graham Bell. The bel is a unit that expresses the logarithmic ratio between the input and output of any given component, circuit, or system and may be expressed in terms of voltage, current, or power. Most often it is used to show the ratio between input and output power. The formula is as follows:

The gain of an amplifier can be expressed in bels by dividing the output (P1) by the input (P2) and taking the base 10 logarithm of the resulting quotient. Thus, if an amplifier doubles the power, the quotient will be 2. If you consult a logarithm table, you will find that the base 10 logarithm of 2 is 0.3; so the power gain of the amplifier is 0.3 bel. Experience has taught that because the bel is a rather large unit, it is difficult to apply. A more practical unit that can be applied more easily is the decibel (1/10 bel). Any figure expressed in bels can easily be converted to decibels by multiplying the figure by 10 or simply by moving the decimal one place to the right. The previously found ratio of 0.3 is therefore equal to 3 decibels.

The reason for using the decibel system when expressing signal strength may be seen in the power ratios in table 2-1. For example, to say that a reference signal has increased 50 dB is much easier than to say the output has increased 100,000 times. The amount of increase or decrease from a chosen reference level is the basis of the decibel measurement system, not the reference level itself. Whether the input power is increased from 1 watt to 100 watts or from 1,000 watts to 100,000 watts, the amount of increase is still 20 decibels.

Table 2-1. - Decibel Power Ratios

Examine table 2-1 again, and take particular note of the power ratios for source levels of 3 dB and 6 dB. As the table illustrates, an increase of 3 dB represents a doubling of power. The reverse is also true. If a signal decreases by 3 dB, half the power is lost. For example, a 1,000 watt signal decreased by 3 dB will equal 500 watts while a 1,000 watt signal increased by 3 dB equals 2,000 watts.

The attenuator is a widely used piece of test equipment that can be used to demonstrate the importance of the decibel as a unit of measurement. Attenuators are used to reduce a signal to a smaller level for use or measurement. Most attenuators are rated by the number of decibels the signal is reduced. The technician's job is to know the relationship between the dB rating and the power reduction it represents. This is so important, in fact, that every student of electronics should memorize the relationships in table 2-1 through the 60 dB range. The technician will have to apply this knowledge to prevent damage to valuable equipment. A helpful hint is to note that the first digit of the source level (on the chart) is the same number as the corresponding power of 10 exponent; i.e., 40 dB = 1 X 10⁴ or 10,000. A 20 dB attenuator, for example, will reduce an input signal by a factor of 100. In other words, a 100-milliwatt signal will be reduced to 1 milliwatt. A 30 dB attenuator will reduce the same 100-milliwatt signal by a factor of 1,000 and produce an output of 0.1 milliwatt. When an attenuator of the required size is not available, attenuators of several smaller sizes may be added directly together to reach the desired amount of attenuation. A 10 dB attenuator and a 20 dB attenuator add directly to equal 30 dB of attenuation. The same relationship exists with amplifier stages as well. If an amplifier has two stages rated at 10 dB each, the total amplifier gain will be 20 dB.

When you speak of the dB level of a signal, you are really speaking of a logarithmic comparison between the input and output signals. The input signal is normally used as the reference level. However, the application sometimes requires the use of a standard reference signal. The most widely used reference level is a 1-milliwatt signal. The standard decibel abbreviation of dB is changed to dBm to indicate the use of the 1-milliwatt standard reference. Thus, a signal level of +3 dBm is 3 dB above 1 milliwatt, and a signal level of -3 dBm is 3 dB below 1 milliwatt. Whether using dB or dBm, a plus (+) sign (or no sign at all) indicates the output signal is larger than the reference; a minus (-) sign indicates the output signal is less than the reference.

The Navy student of electronics will encounter the dBm system of measurement most often as a figure indicating the receiver sensitivity of radar or communications equipment. Typically, a radar receiver will be rated at approximately -107 dBm, which means the receiver will detect a signal 107 dB below 1 milliwatt.

The importance of understanding the decibel system of measurement can easily be seen in the case of receiver-sensitivity measurements. At first glance a loss of 3 dBm from a number as large as -107 dBm seems insignificant; however, it becomes extremely important when the number indicates receiver sensitivity in the decibel system. When the sensitivity falls to -104 dBm, the receiver will only detect a signal that is twice as large as a signal at -107 dBm.

The Traveling-Wave Tube

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 1 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 physical construction of a typical twt is shown in figure 2-13. 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 directional couplers that have no physical connection to the helix. If the rf energy is transported on coaxial cables, the coaxial couplers are wound in a helical manner similar to that shown in figure 2-13. If the rf energy is transported in waveguides, waveguide directional couplers are used. The attenuator prevents any reflected waves from traveling back down the helix.

Figure 2-13. - Physical construction of a twt.

A simplified version of twt operation is shown in figure 2-14. In the figure, an electron beam is passing along a nonresonant transmission line represented by a straight wire. The input to the transmission line is an rf wave which travels on the line from input to output. The line will transport a wide range of rf frequencies if it is terminated in the characteristic impedance of the line. The electromagnetic waves traveling down the line produce electric fields that interact with the electrons of the beam.

Figure 2-14. - Simplified twt.

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, as shown in figure 2-14.

However, because the waves travel along the wire at the speed of light, the simple twt shown in figure 2-14 will not work. At present no way is known to accelerate an electron beam to the speed of light. Since the electron beam cannot travel faster than the wave on the wire, bunching will not take place and the tube will not work. The twt is therefore designed with a delay structure to slow the traveling wave down to or below the speed of the electrons in the beam. A common twt delay structure is a wire, wound in the form of a long coil or helix, as shown in figure 2-15, view (A). The shape of the helix slows the effective velocity of the wave along the common axis of the helix and the tube to about one-tenth the speed of light. The wave still travels down the helix wire at the speed of light, but the coiled shape causes the wave to travel a much greater total distance than the electron beam. The speed at which the wave travels down the tube can be varied by changing the number of turns or the diameter of the turns in the helix wire. The helical delay structure works well because it has the added advantage of causing a large proportion of electric fields that are parallel to the electron beam. The parallel fields provide maximum interaction between the fields and the electron beam.

Figure 2-15. - Functional diagram of a twt.

In a typical twt, the electron beam is directed down the center of the helix while, at the same time, an rf signal is coupled onto the helix. The electrons of the beam are velocity-modulated by the electric fields produced by the rf signal.

Amplification begins as the electron bunches form and release energy to the signal on the helix. The slightly amplified signal causes a denser electron bunch which, in turn, amplifies the signal even more. The amplification process is continuous as the rf wave and the electron beam travel down the length of the tube.

Any portion of the twt output signal that reflects back to the input will cause oscillations within the tube which results in a decrease in amplification. Attenuators are placed along the length of the helix to prevent reflections from reaching the input. The attenuator causes a loss in amplitude, as can be seen in figure 2-15, view (B), but it can be placed so as to minimize losses while still isolating the input from the output.

The relatively low efficiency of the twt partially offsets the advantages of high gain and wide bandwidth. The internal attenuator reduces the gain of the tube, and the power required to energize the focusing magnet is an operational loss that cannot be recovered. The twt also produces heat which must be dissipated by either air-conditioning or liquid-cooling systems. All of these factors reduce the overall efficiency of the twt, but the advantages of high gain and wide bandwidth are usually enough to overcome the disadvantages.

The Backward-Wave Oscillator

The BACKWARD-WAVE OSCILLATOR (bwo) is a microwave-frequency, velocity-modulated tube that operates on the same principle as the twt. However, a traveling wave that moves from the electron gun end of the tube toward the collector is not used in the bwo. Instead, the bwo extracts energy from the electron. beam by using a backward wave that travels from the collector toward the electron gun (cathode). Otherwise, the electron bunching action and energy extraction from the electron beam is very similar to the actions in a twt.

The typical bwo is constructed from a folded transmission line or waveguide that winds back and forth across the path of the electron beam, as shown in figure 2-16. The folded waveguide in the illustration serves the same purpose as the helix in a twt. The fixed spacing of the folded waveguide limits the bandwidth of the bwo. Since the frequency of a given waveguide is constant, the frequency of the bwo is controlled by the transit time of the electron beam. The transit time is controlled by the collector potential. Thus, the output frequency can be changed by varying the collector voltage, which is a definite advantage. As in the twt, the electron beam in the bwo is focused by a magnet placed around the body of the tube.

Figure 2-16. - Typical bwo.

Q.26 What is the primary use of the twt?
Q.27 The magnet surrounding the body of a twt serves what purpose?
Q.28 How are the input and output directional couplers in a twt connected to the helix?
Q.29 What relationship must exist between the electron beam and the traveling wave for bunching to occur in the electron beam of a twt?
Q.30 What structure in the twt delays the forward progress of the traveling wave?