Vp1953,
In the IC world there is a luxury which is often taken for granted which is a low impedance can drive a high impedance with no consequences. On chip impedance matching is actually a detriment to efficiency why loose half your signal when you don't have to?
Distance between source and load will necessitate the need to match.
Remember that in any circuit there is a source and a load. if you optimize the load (your hypothetical LNA) while neglecting the source you will find that the total circuit or system will not be optimal.
For example: Imagine that this high impedance LNA is 1/4 wavelength from the source (at the frequency of interest) then the source will see a short and the load will see an open. In this case you will not get twice the signal of a matched system instead you may not see any signal and the source will have to pay the tax of driving a near short. So therefore a compromise must be made on both ends where a transmission impedance is selected as a standard.
Not being matched has several other issues, including being prone to interference, causing interference, undesired amplitude ripple, high sensitivity to parasitics,stability etc.
For LNA's the optimal power match is usually not the best noise match and in this case it may make sense to trade one off against the other.
significant
I asked myself the same question a while ago and if there is a distance between the source and load then matching is the lesser of all evils.
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