> does the 2k in series affect noise performance?
Yes.
2K pure resistance has about 0.8 microvolts of noise over the audio band. This is generally lower than the active device noise, unless you have been VERY careful in your amplifier noise analysis. It is over 120dB below "hi-fi line level", and it is hard to find a source that is as quiet as a 2K resistor.
Common phono pickups have self-resistance of a few K, so another 2K adds a little noise (when the needle is not in a groove!). However such pickups mostly can't pull a 2K load, being intended to work with 47K.
Dynamic microphones have low output and self-resistance near 200 ohms. I assure you that a cheap PA head with 2K resistors in the input diff-amp will have enough excess hiss to notice. Not when the band is playing, but it was a poor choice for a children's poetry reading in a live room. I have another board with 470 ohm inverting inputs, and nobody complained about its noise, but mikes do sound different with ~500Ω load than with the >2K loads most mikes are designed for and most boards provide.
> how do you calculate the input impedance of such a stage (JFET input)?
If gain and feedback is "high", then the input impedance is 2K.
If gain is low, much lower than 100K/2K= ~25, so feedback is nearly zero, the input is 2K+(100K||47K)= ~32K.
If gain is around 100, the 100K will act like ~50K to ground, so input is ~27K. If gain is like 500, the 100K looks like 10K, so we have ~6K. Open loop gain needs to be near 2,500 to get that 100K to look like 2K, and get total input impedance down toward 4K. You need gain of 25,000 to get to within 10% of the pure 2K.
> resistor to the ground (47k) does not affect input impedance and gain.
It does, a little. I admit and agree that it makes about no practical difference for these values. It also adds noise: depending on the external source impedance, maybe less than 1dB and certainly less than the noise most sources (full of 2K and 50K resistors) already have. I do wonder why JFETs need 47K gate-leak resistor.
> What if the input impedance of the LTP is 50k
If it is JFET: then something is mighty wrong.
Even for high-current BJTs, the naked input resistance is increased by feedback. For any well-defined high-NFB design, it will be "infinite enough". If low-NFB, you need to do some elaborate calculations, throw it at SPICE, or whomp-up a breadboard (the best way to get the real answer).
