RESTRICTIONS ON LINEAR PHASE, LOW-PASS NETWORKS WITH PRESCRIBED PARASITIC LOADS,

The problem considered here is that of a low-pass, linear phase filter operating between a resistive generator and a prescribed load containing parasitic reactances. The presence of the parasitic elements results in a minimum time delay-bandwidth restriction of a signal propagation between the generator and the load. Such a restriction is derived here by considering gain-bandwidth integrals for Gaussian transfer amplitude filters. For the very important case of unit d-c gain, these restrictions are expressed in terms of the Riemann Zeta function. For gains less than unity at d.c., the results are in terms of Appel integrals. The loads considered here have all their zeros of transmission at infinity. Author