I am almost lost when I think more about that, now I am quite confused about this question:
In the picture above, why do we not consider the mismatch effect between LNA and Mixer?
If the connection between LNA and Mixer is long enough to be considered as a transmission line (as show in the picture below), then we need to use matching networks. But what happens when the length of the transmission line (L) reduce to Zero? IF we remove the matching networks, I think there should be reflection loss due to the mismatch ports, am I right? Why we don't care about it?
1. Inside ICs, the connection length between LNA and Mixer is very short (in RF range), transmission line effect is not considered. Though the mismatched ports cause reflection power and thus power loss, at this time we are more concerned about the signal voltage that couples to the mixer. For a CMOS mixer, the input MOSFET convert the input voltage signal into current signal, we do not care much about the input current (very small infact, P=V*I, so input power can be small). Most active mixer such as Gilbert cell have a certain conversion gain, which relax the power delivery requirement from LNA to mixer.
2. When LNA and Mixer is connected through a transmission line, mismatched load introduces standing wave along the transmission line, the singnal voltage (amplitude=Vmix) received at the mixer input port is not always equal to the one at the LNA output port (Vlna). Depending on the length, ZL, Z0 and bla bla bla, Vmix will vary from 0 to 2*Vlna (corret me if I am wrong). That's the reason why we need to match them. If you are designing PA, the reflection power from the antenna due to mismatch causes power loss and can even damage the PA.