I know that IF frequency is the difference between the incoming signal
and the local oscilator frequency in a frequency synthesizer.
The I.F. is at either the _sum_ or the _difference_ frequency; it's up to
the designer.
The mixing (multiplication) of the frequencies that results in the sum and
difference, is not done in the synthesizer; it is done in the Mixer, a.k.a.
Converter stage.
My question is why in a frequency synthesizer we need the IF frequency>
In a receiver using an I.F., a synthesizer is commonly used to generate the
variable (tuning) frequencies, whereas the fixed frequency for the Mixer is
typically generated by a crystal oscillator.
If you elect to design a Direct Conversion receiver, you use only the
variable frequency tuning oscillator (or synthesizer) and demodulate
received signals directly to baseband audio - there is no I.F.
Don