Crude calibration of an SDR

[JERRY TAYLOR]

My ignorance may be very clear in this post but here goes.  

According to ChatGPT:

Given a temperature of 290 K, a bandwidth of 2 MHz, and a 50-ohm impedance, you can calculate the thermal noise power and the corresponding voltage as follows:

1. Calculate Thermal Noise Power (P):

   Using the formula:

   P=kTB

   where:

   • k=1.38×10−23J/K (Boltzmann's constant),
   • T=290K,
   • B=2×106Hz.

   Plugging in the values:

   P=(1.38×10−23)×(290)×(2×106) P≈8.03×10−14W

2. Convert Power to Voltage (V):

   Using the formula:

   P=RV2​

   Rearranging gives:

   V=PR​

   where R=50ohms:

   V=(8.03×10−14)×(50)​ V≈4.015×10−12​≈6.34×10−6V or 6.34μV

Summary

• Thermal Noise Power: Approximately 8.03×10−14W (or about −151.9dBm)
• Voltage Equivalent: Approximately 6.34μV

These calculations give you the thermal noise voltage associated with a temperature of 290 K over a 2 MHz bandwidth in a 50-ohm system.

If Chat GPT is correct, then if I connect a 50 ohm dummy load to my SDR, which gives relative units, and using IF Average cumulations to get the output data to approximately 0.00000634 AND ASSUMING my SDR's output is LINEAR will this give me something roughly approximating absolute units?

Jerry

[Marcus D. Leech]

Yup, kTB is the formula for noise power in a given bandwidth, due to temperature.

So, a perfectly-matched 50-ohm resistor at 290K will produce some amount of input power to the receiver.  That is true.

However, the output of the receiver is proportional to:

G(Tsys+Tinput)

Where G is the overall gain of your system.  However, since "G" represents a largely-linear function, it kind of drops out.
  A change at the input of 5% will result in a change in the output of 5%, etc.

Now, something you can do is to swap in your antenna once you've made a measurement of the resistor, and point your
  antenna at a "quiet spot" in the sky--away from the galactic plane.  That will be about 4-6K or so.  That gives you two
  points, and you can use it in the "Y-factor" technique for estimating Tsys.

I won't discuss the "Y-factor technique" in detail here, because there are better treatises already out there.



Here, your Tinput is calculated from kTB as above.

But you don't know, precisely, what Tsys is.  So any calibration done with this single point is somewhat suspect.

Your Tsys, with a SawBird+ H1 will likely (depending on your dish properties, and where you're pointing) be somewhere in
  the 90 to 110K range, perhaps higher.

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[JERRY TAYLOR]

Thank you Marcus!

Jerry

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