Any factor which affects the velocity of the electron beam produces phase changes in the RF output signal. As the RF drive level is increased into the non-linear region, the phase length of the tube increases as beam velocity is slowed by transfer of energy to the RF wave. This effect, called AM / PM conversion, is relatively insensitive to RF drive in the linear region. As the TWT is driven toward saturation, the rate of phase change increases. The peak value of AM / PM generally occurs at or several dB below saturation and is frequency dependent (typically increasing with increasing frequency for a given helix design). If the factor that changes beam velocity varies with time, the result is phase modulation of the RF output signal. The primary factor affecting the velocity of the beam is the cathode voltage. Other voltages or external affects (such as voltages induced by placement of a blower motor too close to the tube) have secondary affects. Typical phase pushing values for TWTs are:
- 100* / 1% change in Cathode Voltage
- 10* / 1% change in Grid "on" Voltage
- 0.0005* / 1% change in Collector Voltage
These numbers are approximate. The actual values of phase pushing for any specific TWT are determined by gun perveance, gain, efficiency, etc. Any periodic voltage modulation produces signal side bands, separated from the main signal by the modulation frequency. The depression below carrier of these spurious signals (* in dB) for sinusoidal ripple can roughly be approximated by the following expression:
A ±0.5 volt sinusoidal ripple on a 10 kV TWT with 10" input-to-output length produces -49.5 dBc sidebands at 10 Ghz. Peak-to-peak phase ripple (** in degrees) is directly related to small signal gain ripple (dG -- peak-to-peak in dB) by the following expression:
A small signal gain ripple of ±0.2 dB produces phase ripple of *1.35*. Time delay is the total time it takes for a signal to pass through the tube (typically 3 to 5 nsec) and is the derivative of phase delay. Thus, the same mechanisms that cause phase non-linearity are responsible for time delay distortion. The maximum rate of change of time delay (** in nsec / Mhz) due to gain and phase ripple is calculated by:
where dF is the frequency periodicity of the small signal gain ripple (in Hz). A 200 Mhz gain ripple with ±0.2 dB amplitude causes 3.7 psec / Mhz time delay distortion.