and is a constant depending on the midband gain. This is the characteristic of an ideal ”n-pole filter” with the gain falling by 6.02n dB as 8doubles. At temperature T°K, the initial noise power is kT W/Hz, where . For this is -112. 1 dBm/MHz. Assume an oscillator output power of 1 mW at the drive frequency, and a noise figure of 10 dB for the preamplifier. Noise originating in the klystron itself is then negligible in comparison, so that the klystron amplifies both drive and noise signals equally to give a noise power of 102.1 dB below output power at drive frequency. The relative gain then gives the noise power at other frequencies. The gain figures of Figure 4-30 are calculated for the PPM tube using a small-signal klystron program developed by Shared Applications, Inc. The cavity resonances are chosen to give the correct gap impedances to match the large-signal results for this tube. Appendix E explains the procedure. Figure 4-31 shows the noise power. It is less than -102 dB relative to output power in the frequency band containing the cavity resonances, and decreases by 24 dB per octave of frequency difference outside this band. A confined-flow tube can be made even better. A second-harmonic bunching cavity (see below) should further reduce the noise power by as much as 72 dB. At saturation the bunched beam contains harmonic currents of amplitude or greater at the output gap (whether or not the bunching section contains second-harmonic cavities). Harmonic output power depends on the coupled harmonic impedance of the output cavity, which is tuned to drive frequency and must have no spurious harmonic resonances. The impedance decreases with fre- quency shift at least as fast as , and output power as , where is the loaded of the output cavity, so that when and the second- harmonic output power is at most 43 dB below fundamental. Similarly, a second- harmonic bunching cavity, while improving bunching at drive frequency under saturated drive, reduces the gain of noise signals at nearby frequencies by about , where is now about 2000, so that noise power is reduced by -72 dB near drive frequency. Input noise at the second harmonic is, of course, filtered by the fundamental-frequency cavities.
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