# Understanding Noise Figure of LNA (HP 461A amplifier)

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 )

## 1 Answer

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.

• Thanks. Indeed it looks like your calculations (leading to 4nV/1Hz, which anyway were MAX specs and you downapproximated 150Mhz to 100Mhz for easy of calculations) are matched by reality: This is the reading of my HP 8591E spectrum analyzer in linear mode (Volts, not dbm): dropbox.com/s/jdjuyivll6yvpku/lin.png And it gives 2nV/1Hz. At the same time, however, there must be some mistake in how I made my calculations for Noise Figure. The noise density at -160dBm/Hz should mean 174-160=14db of Noise Figure (??). My calculations lead to 0.33db Thanks! Commented Jul 13, 2020 at 18:25
• Added: I found the mistake in the calculations, specifically the error is in the calculations of the Noise temperature. I used the equation "1e-19 = t*300*k", but really I should have used "1e-19 = t * k", which gives a temperature of 7200K, a noise Factor of 25 and a Noise figure of 14db, which is what my Spectrum Analyzer measures. THANKS! Commented Jul 13, 2020 at 18:40