Minimum phase shift network

As two phases in quadrature will allow Carr-Purcell Meiboom-Gill, T, and or other spin-locking experiments, we recommend this as a minimum. However, providing different rf phases for the transmitter pulses is not difficult and this capability should not increase the cost of the spectrometer very much so you might as well go for four orthogonal phases. As discussed elsewhere, the phase shifts can be performed in the IF stage rather than at the carrier frequency so that one phase shifting network can suffice for all carrier frequencies. 

KKTs are tools brought to network theory by the work of Kramers (1926) and Kronig (1929) on X-ray optics. Just as the reciprocity theorem, they are purely mathematical rules of general validity in any passive, linear, reciprocal network of a minimum phase shift type. By minimum-phase networks, we mean ladder networks that do not have poles in the right half plane of the Wessel diagram. A ladder network is of minimum phase type a bridge where signal can come from more than one ladder is not necessarily of the minimum-phase type. The transforms are only possible when the functions are finite-valued at all frequencies. With impedance Z = R- -jX the transforms are ... 

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