Limiter circuit is not needed in the following detector:

Concept:

• Frequency Demodulators are often sensitive to amplitude variations. Therefore a limiter amplifier stage must be used before the detector, to remove amplitude variations in the signal which would be detected as noise.
• The limiter acts as a Class-A amplifier at lower amplitudes; at higher amplitudes, it becomes a saturated amplifier that clips off the peaks and limits the amplitude.
• The FM ratio detector was the more common because it offered a better level of amplitude modulation rejection of amplitude modulation.
• This enabled the circuit to provide a greater level of noise immunity as most noise is amplitude noise.
• Additional limiter circuit is not required since the output voltage is not affected by amplitude variations in the incoming signals. 

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It also enables the FM detector to operate more effectively even with lower levels of limiting in the preceding IF stages of the receiver.