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The thermal noise of a resistance depends only on that resistance. However, there is always some parasitic capacitance. That capacitance against the resistance causes a low pass filter. So in a ...
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#1: Initial revision
The thermal noise of a resistance depends only on that resistance. However, there is always some parasitic capacitance. That capacitance against the resistance causes a low pass filter. So in a sense, yes, the frequency content of thermal noise does vary with resistance in the real world due to the inevitable parasitic capacitance.