Starting conditions for backward-wave oscillators with large loss and large space charge

Starting conditions of backward-wave oscillators are obtained both analytically and numerically for large loss and large space charge. Analytical results are obtained for zero loss and space charge up to infinity and for zero space charge and loss up to infinity. Computer results are carried out for circuit loss up to 225 dB and space charge up to QC = 25. An analytical equation is developed for computing starting conditions for large loss approaching infinite values and for large space charge approaching infinite values. Since the starting C is proportional to the loss per wavelength, large values of loss in a backward-wave oscillator can prevent oscillation from occurring unless the current can be made sufficiently large; i.e., the starting C is independent of length.