SLED-II With Variable Input Power.
Imagine one had an rf source whose whose output power could be varied arbitrarily during a pulse without loss of efficiency. Efficiency of rf energy compression could be maximized by tailoring SLED-II input amplitude A for each time bin so that, after the unavoidable initial bin reflection, power comes out only in the final compressed bin.
AoutN increases with increasing s until |AN| overtakes AN-1, after which we must normalize to |AN|, and AoutN falls off as 1/s.
, independent of N (>3).
, also independent of N!
NOTE: This optimizes Gain under these conditions, not efficiency. Letting s drop toward zero, with AN-1 going to 1 and all others to 0, raises efficiency toward T2 as the gain drops toward 1. Similarly, letting s go to one, with AN going to 1 and all others to 0, brings efficiency up to 1, although the conditions would also allow A1 going as high as 1, dropping the efficiency to 0.5. In either case, here to the gain drops to 1.
For lossless delay lines,
For T=1, this is constant input amplitude, and the efficiency is 0.873. However, we know the intrinsic efficiency for normal SLED-II at N=3 is 0.887, slightly higher. Here efficiency is not maximized by zeroing the second and fourth output bins. We can gain by leaking a little power into other bins while reducing the output power in bin 1.
For N=2, the requirements here lead to
Actually, for any N, efficiency is maximized to 1 with s=1, AN=1, all others zero. It also increases to a maximum of T2 at s=0, AN-1=1, all others zero. For both ot these cases, however, there is no gain. For higher values of N, where the first time bin output power is small, the technique here gives significant gain with approximately maximized efficiency.
Finally, for N=1, the requirements here lead to