Understanding Noise Figure of LNA (HP 461A amplifier)

Question

I have recently got a HP 461A linear amplifier (from the 60's) which works from 1Khz to 150Mhz.

I have checked that:

1. it's input gives a SWR <1.1 across all spectrum (i.e., the input impedance is very close to the nominal 50ohm).
2. The 40db Gain is very flat across the spectrum, with +/- 1db deviation at most.

Now I am trying to calculate it's noise values (Factor, Figure, Noise Density, etc), and I want to understand all calculations mostly for educational purposes.

I have a HP 8591E spectrum analyzer so I did the following:

1. Connected a 50ohm terminator at the input of the amplifier
2. Connected the output of the amplifier to my SA.
3. Configured the SA to take into consideration the 40db external amp.
4. Used the "Noise Marker" functionality to measure the noise density power in dBm/Hz.

The result is a reading of about -160dBm/Hz (at the moment, summer, room temperature is 300K) See: https://www.dropbox.com/s/udp72vmsg0yqlfh/dbm1.png

I am still a bit surprised by my measurements. They seem too good to be true for this >50years old unit. Doing some calculations,

1. -160dBm/Hz is equivalent to 1e-19 Watts/Hz(https://www.wolframalpha.com/input/?i=-160+%3D+10*log_10%28p%2F0.001%29)
2. From this I can (using the formula from https://en.wikipedia.org/wiki/Noise_temperature) calculate the Noise Temperature T=24.1 (https://www.wolframalpha.com/input/?i=1e-19+%3D+t*300*k%2C+k%3D1.381*10%5E%28%E2%88%9223%29)
3. From this (again using the equation in https://www.wolframalpha.com/input/?i=-160+%3D+10*log_10%28p%2F0.001%29) I obtain a Noise Factor of 1.08 (https://www.wolframalpha.com/input/?i=%28300%2B24.1%29%2F300).
4. Taking 10*log_10 of the Noise Factor, I obtain a Noise Figure of 0.33.

All these numbers seem quite impressive. Are they really possible? Granted this HP 461A amplifier did cost >300 USD in 1964 (more than 2k of todays USD, accordingly with https://www.usinflationcalculator.com/)... but is it possible that it is really so good, even compared to today's amplifiers?

Regarding noise, it's original Manual/Datasheet only says "less than 40uV of equivalent wideband (150Mhz) input noise".

Perhaps, rather than focusing on the specific measurements of my amplifier, I'd just like to know if my calculations are correct/sensible. So:

GENERAL QUESTION: If I read in a datasheet that a LNA has noise figure of 0.33, how much should I expect (from purely mathematical calculations) when I plug a 50ohm resistor at the amplifier's input, and measure the noise power density (in dBm/Hz) of its output with a modern spectrum analyzer?

NOTE: I have also asked this question on the EEVBlog forum (see: https://www.eevblog.com/forum/rf-microwave/help-understanding-noise-figure-of-amplifier/msg3134954/#msg3134954 )

Answer 1

Noise Figure requires a given Input Noise Density, often 50 ohms.

You may be more interested in the Noise Voltage, so you can use 300 ohm antennas, or 600 ohm audio, or magnetic beacon sensors that are just inductors.

So let us compute theNoise Density (nanoVolts/square_root_Hertz). And the equivalent Rnoise. I use Rnoise as an easy design concept, to combine with other discrete resistors in a circuit and predict the total noise.

The datasheet gives 40 microVolts INPUT, over 150MHz bandwidth. That is, this is input_referred_noise (RTI).

Now scale that by sqrt(150,000,000). For easy math, use sqrt(100,000,000) which is 10,000.

So the internal broadband noise (per root_Hertz) is

• 40 microVolts / 10,000 = 4 nanoVolts

Knowing 62 ohms produces 1 nanoVolt, and this math predicts 4nV, the

equivalent internal Rnoise of that first transistor is

• 62 ohms / (4nv/1nv)^2 = 62 * (4 * 4) = 1,000 ohm Rnoise.

Lots of transistors can achieve that noise floor.

I recall Hewlett Packard had long had access to ultra_small resolution photo-lithography machines, maybe even electron-beam machines.

I would not be surprised if HP produced special electronic systems for the US government. For national defense there really is no price limit on monitoring other nations' radio/radar emissions. Even back in the 1960s.

These systems simply are built, to avoid any surprises, at whatever cost.