Right now a lot of you are saying you never heard of a noise figure, so what am I talking about? People who have some familiarity with receivers for VHF, UHF and higher are probably more likely to have heard the term because it tends to be talked about more as you go higher in the spectrum. At lower frequencies, like HF radios and even things like VHF handie-talkies, people still tend to talk about sensitivity, using measurements of the signal power (or voltage) to achieve a certain Signal to Noise ratio or SNR, literally signal power divided by noise power; S/N. Sometimes instead of an SNR, you'll see SINAD, which is the desired signal to noise and adds distortion to the noise term.
Noise figure can be talked about for complete receivers or single circuits. It's a way of describing how much noise a component or circuit degrades the SNR of the signal going through it. How much noise it adds to the signal as it goes through it.
NF = (SNRout)/(SNRin)
Everything has a noise figure. For a passive circuit, the NF is
reciprocal of the gain. An attenuator (pad) with 3dB of attenuation or
3dB of loss means it had a gain of negative 3. That means the NF of a 3dB pad is
3dB. When you buy an amplifier, the specifications will generally include the
NF. To design for a noise figure and verify that what you've created
performs as you intended is "beyond the scope of this discussion."
In receiver design, it has become increasingly common to cascade constant impedance circuit elements or blocks. With the exception of some cable TV systems, which operate at 75 ohms, receivers tend to be designed as 50 ohm systems. To determine the overall gain of a system, and the signal levels at any stage is trivially easy. You add dB of gain and use negative numbers for the gain of a stage with loss (like a filter, cable or pad).
Gain Total = G1 + G2 + G3 + ... Gn
Noise figure is a bit more complex. The equation is well-known but can get a bit long in a hand calculator or spreadsheet. Named after the guy who first derived it, Harald Friis, the Friis equation is:
The 1, 2, 3, etc, are the stage numbers, so the cascade NF is always greater than the first stage's NF, F1. You can see the value of F at any stage is the sum of that first NF, and the stage's NF divided by the product of the gains to that point. Important note: these numbers are the linear gain and noise figure numbers, not expressed in decibels.
This is a vivid reminder to minimize losses before the first amplifier because you'll never get a better NF than that first stage. Since loss in all coaxial cables goes up with frequency, to reduce the losses before the first amplifier, a very common approach is to put the first stage of amplification, and downconversion at the antenna's feedpoint. The downconversion is to change to an easier frequency to handle with less loss in the cable.
How about some practical stuff? This is how you might compare the signal you measured to be required to get 10 dB SNR to what the math says you should get:
That would be like CW, just a carrier in a 500Hz BW and -133 dBm is a small signal. You might think you need a half microvolt, or a less. The number is much less: it's .05 microvolt or 50 nanovolts. If the receiver is in a quiet room connected directly to a signal generator, you should get that. This old post might be helpful. As should this chart that's in it.
Wow, I get enough trouble from using CB, let alone Ham.
ReplyDeleteBut then again I fiddle constantly trying to make the "perfect Beer" so...
How does NF apply to software defined radio? A detector algorithm, for instance, doesn't add any noise to a signal (unless you write it to do so!). Would this mean that s/w stages have noise figures of 1?
ReplyDeleteMost noise is thermal in analog circuitry. Or do we also count received RF noise from the external environment that is detected and amplified downstream? Gamma rays, lightning, My Mother The Car episodes, and such?
Anything before the sampling process has a noise figure; if nothing else, there are amplifiers and passive components before the ADC input that set the system NF.
DeleteI haven't kept up with the state of the art on ADCs since retirement, but the best ones I knew of were in the range of 16 bit converters, and because of the signals they were handling needed about 20 dB of gain to get the weakest signals to toggle the first converter bit (hand waving a bit here). If the architecture was direct sampling, which very few radios use, that was optimum, and limited to HF, so maybe limited to 100 MHz now. If there's undersampling involved, the higher spectrum windows drop off in their sensitivity and need more amplification.
The received noise from all the RF pollution you measure is not considered and (IMO) is the reason why people cling to sensitivity specs. instead of NF. In reality, radio installations get degraded by environmental noise all the time. I posted a plot in an earlier radio post that shows the effects of noise. Looking back on it, it's more thorough than this post.
I believe ADC's are up to 24-26 bits now, but I haven't looked at them for a long time. Tough design job.
DeleteADCs to 24 and 26 have been around for a long time, it's the speed that limited them. What determined the ones I consider best is that they specified the Spurious Free Dynamic Range, and the best at the time was 105 dB SFDR - in the first band (DC to clock/2). That part came out years before it went in a radio I designed. SFDR is arguably more important than NF in HF receivers.
DeleteSomeone who designed ICs (different company/time/place) said sometimes a part performed better than their software predicted it could. They just put it on the market and were happy.
I've always been on the s/w side rather than the h/w, but I had to know enough about the system to write functional algorithms. The first ADC I ever dealt with was made by Tektronix. It consisted of a cathode ray tube with a deflected beam that lit up a strip of deposited conductors on the inside of the face of the tube (!) so that it could have a nice high sampling rate. What a Frankensteinian monster that was, but it was faster than silicon could do at the time (circa 1983).
DeleteI remember talking to my parents over a MARS station phone call when I was in Korea in 1969 - their voices sounded like they got hold of some bad helium. Is that caused by noise figure?
ReplyDeleteNo, that's from the radio being slightly mis-tuned. Single sideband or SSB - virtually all HF voice communications like MARS - is very susceptible to that. They usually say it sounds like Donald Duck, but he sounds better.
DeleteTNX 4 the review
ReplyDelete