I am having trouble pinning down why the relative permeability of a transformer core will not directly affect the output voltage. In fact the voltage is determined by the turns ratio and is independent of mu of core material.
Given this where is the flaw in the following reasoning:
Induced field strength H is proportional to current in primary coil, H=k I (to be exact , integral H*dl = If+dD/dt)
Magnetic flux density in core is B=mu H
Voltage in single turn of secondary is proportional to rate of change of B; V=A dB/dt = A mu dH/dt = A mu k dI/dt
From this (apparently specious) reasoning, output voltage depends on mu.