The matching to the voltage noise to current noise ratio is about the point where the amplifier has the best noise figure. It is not about adding resistance to the input to match, but about where the amplifier would be at it's best. One would match something like a transformer if one uses it, as there no exra noise is added. The amp01 may still be OK with a 5 K source impedance. Because of the 2 inputs to current noise part would ideally need more than just 1 number for a full charactirization and both sides would contribute. There is a tendency for datasheets to be a bit optimistic with the current noise.
It is just that if one is well off, chances are to find a better other amplifier. If below 70% the noise resistance could use 2 amplifiers in parallel could reduce the noise.
The AD8421 would be a solution that has it's best noise figure at some 16 K, kind of close to 2 x amp01 in parallel. The noise figure is similar, just made for a difference source impedance.
With 33 K or source impedance the amp01 would give 5 nV from the voltage noise and a similar noise from the current noise. So some 7 nV/sqrt(Hz) total. With 5 K source impedance the current noise part would be smaller and the total noise more like 5.5 nV/sqrt(Hz). In addition there is also just the noise from the source resistance (e.g. some 10 nV/sqrt(Hz) for 6 K). So the overall noise can still to a large part from from the source impedance and not from the amplifier. So the possible advantage from a better amplifier is limited.
I spent many hours reading about current noise vs voltage noise. The dogma seems to be "thermal noise increases with a larger resistance value, whereas current noise decreases when resistance increases."
A web site mentioned this is just a myth. Maybe there are circuits where the above applies and there are other circuits where the following applies? How to know which circuit applies to the dogma and myth belows? Thanks.
https://www.analog.com/en/resources/technical-articles/11-myths-about-analog-noise-analysis.html"
8. The Amplifier with the Lowest Voltage Noise Is the Best Choice
When choosing an op amp, the voltage noise is often the only noise specification considered by the designer. It is important not to overlook the current noise as well. Except in special cases such as input bias current compensation, the current noise is typically the shot noise of the input bias current: in = √2 × q × IB. The current noise is converted to a voltage via the source resistance, so when there is a large resistance in front of the amplifier input, the current noise can be a larger noise contributor than the voltage noise. The typical case where current noise is a problem is when a low noise op amp is used with a large resistance in series with the input. For example, consider the ADA4898-1 low noise op amp with a 10 kΩ resistor in series with the input. The voltage noise of the ADA4898-1 is 0.9 nV/√Hz, the 10 kΩ resistor has 12.8 nV/√Hz, and the 2.4 pA/√Hz current noise times the 10 kΩ resistor is 24 nV/√Hz, the largest noise source in the system. In cases like this, where the current noise dominates, it is often possible to find a part with lower current noise and thereby reduce the noise of the system. This is especially true for precision amplifiers, but there are high speed FET input op amps that can help in high speed circuits as well. For example, instead of choosing the ADA4898-1 and not getting the benefit of the 0.9 nV/√Hz voltage noise, a JFET input amplifier such as the AD8033 or the ADA4817-1 could have been chosen.".
What kind of circuit where as the resistance increases, the current noise decreases?
What kind of circuit where as the resistance increases, the current noise also increases?