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The phase shift is produced by the reactive load on the coil (RC network). This is the usual way FM was demodulated before PLL ICs became available. The quad coil did not work as well as the PLL at low SNRs.
You can use any coil of suitable inductance and required Q. The Inductance (along with other reactive elements, like capacitances in the transistor, though marginal at 455 KHz) decides the phase shift and Q decides the slope.
Like earlier stated by flautulent, this is one way to demodulate FM.
Suggest search for "FM demodulation" quadrature on Google.
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