Receive-chain noise and integration time calculator

Why the order of the stages matters

Every stage in a receive chain adds noise, but the noise it adds is divided by all the gain in front of it. That's the Friis formula, and it's the reason the first stage decides almost everything:

A piece of coax is a stage with gain below one. A cable with loss L (as a linear ratio) sitting at physical temperature T_phys adds (L − 1) × T_phys of noise and divides the signal by L. Put it in front of the LNA and you pay that noise in full and then pay again, because every later stage is now divided by less gain. Put it after an LNA with 30 dB of gain and its contribution drops a thousandfold.

Worked example

With the defaults: 0.3 m of LMR-400-equivalent and 0.1 dB of adapters before an LNA with 0.6 dB noise figure and 30 dB gain, then 30 m of LMR-400 equivalent, then an SDR with a 6 dB noise figure. The receiver comes out at about 58 K. The LNA itself is 44 K of that, the short cable and adapters ahead of it another 10 K, and the 30 m run and the SDR together about 3 K, even though that run is close to 5 dB of loss. That's what a well-ordered chain looks like: the LNA's own noise is the floor.

Move the LNA to the receiver end of the same 30 m of coax and the receiver temperature goes to about 760 K, thirteen times the good chain. Do it with RG-8X, nearly 10 dB of loss over that run, and it's about 3,000 K. Leave the LNA out entirely and it's over 3,300 K. This is the whole of LAB-006's argument about feedline, in one number.

How long to integrate

System temperature is the receiver plus what the antenna itself delivers: cold sky, the Galactic continuum, and the warm ground its sidelobes see. The radiometer equation says how quickly averaging beats that noise down:

B is the width of one spectral channel. A 10 kHz channel is 2.1 km/s of velocity, a reasonable resolution for Galactic hydrogen. Wider channels integrate faster and blur the profile; narrower ones resolve more and take longer.

The line strength is the hard input to guess. Peak hydrogen brightness temperatures along the Galactic plane are tens of kelvin, up to around 100 K. A small antenna with a wide beam averages that over a patch of sky that includes fainter gas, and its efficiency scales it down again, so what reaches your receiver is a fraction of the peak. 10 K is a deliberately conservative starting guess for a dish pointed at the inner plane; use less for a horn pointed off the plane.

Treat the result as a floor. The radiometer equation assumes the noise is perfectly random. Real spectra are limited by gain drift, a ripply baseline and RFI, which is why people take reference spectra off the line or frequency-switch, and why a spectrum that "should" take a few seconds usually gets minutes.