Envelope Fluctuations in the Output of a Bandpass Limiter

The bandpass limiter is a key component in many communication systems. It is useful to model a bandpass limiter as a cascade combination of a hard limiter and a bandpass filter. If a bandpass signal is input to a bandpass limiter, the output of the hard limiter will be concentrated in an infinite number of spectral bands centered at odd multiples of the input center frequency (fundamental). If the bandpass limiter is assumed to be ideal, its output is then generally assumed to have a constant envelope regardless of the input. Since the hard limiter may give each spectral band an infinite width, the fundamental band can neither be perfectly transmitted by the filter nor can it be perfectly extracted from the other bands. Hence it is impossible to build a device with ideal behavior. Bounds on the envelope fluctuation in the output of a bandpass limiter are developed. If
\sigmaz^{2}
is the envelope variance of the bandpass limiter output,
\sigmas^{2}
is the envelope variance of the filtered fundamental band, and
D
is twice the average power at the output of the filter of the sum of all the harmonic bands, then
\sigmas^{2}\{max [(1 - D^{1/2}/\sigmas),0]\}^{2} \leq \sigmaz^{2} \leq \sigmas^{2} [1 + D^{1/2}/\sigmas]^{2}
. These bounds are apt to be reasonably close estimates of
\sigmaz^{2}
when
D^{1/2}/\sigmas
is much less than unity. If an upper bound
R
for
D^{1/2}/\sigmas
is available, a further bound can be derived from the bound given previously by substitution of
R
for
D^{1/2}/\sigmas
. Such a bound is derived for situations where the limiter output fundamental has finite rms bandwidth. Another such bound is derived for an example where the bandwidth is infinite. In this latter case, the bounds are compared with an exact computation.