Receiver sensitivity and IF bandwidth??

Hi All,

I keep reading that the high-gain front-end stages of a microwave receiver almost completely sets the entire radio's NF and sensitivity, and that the following stages (the I.F.) have little effect except to amplify the signal and the noise equally to a higher amplitude for the radio's detector. This doesn't make complete sense to me, because the I.F. would have a HUGE effect on the receiver's signal-to-noise ratio, and therefore its sensitivity, if we simply narrowed the IF's bandwidth down from, let's say, 1MHz to 1kHz!! So, to me anyway, the I.F. would have a gigantic effect on the receiver's sensitivity, even if the front-end had infinite gain. Or am I missing something here?

(BTW: I fully realize we can't just narrow-down the receiver's bandwidth below the bandwidth of the modulated signal, but I'm just asking about all this on a theoretical basis to try and understand "sensitivity" a bit better).

Thanks,

-Bill

Reply to
billcalley
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Yes, you're missing something. White noise is specified by a power spectral density, like watts/Hz. In noise-generating items like resistances and amplifiers, the density is fairly constant over at least a few percent. The noise figure of an amplifier is a measure of the noise/unit bandwidth that amplifier adds; the noise temperature of an amplifier is another way of specifying the same thing.

Just as you say, if limit the bandwidth, you limit the noise If you make the mistake of aliasing (or mixing) a lot of out-of-band noise down into the band of the signal, that's obviously a bad thing. It's easy to make that mistake in the design of a single sideband detector or a digitizer that used an ADC with a very wide power bandwidth. But if you do a good job of filtering, it's generally not a problem.

Look at the amplifiers this way: let's say you have two identical stages of amplification. Each adds, in the band of interest (the signal bandwidth), 1 unit of power noise, refered to its input, and the gain is ten times in power. Let's say the signal itself is 10 units of power, and it comes accompanied by 1 unit of noise power. It's signal:noise power ratio is 10, which is also 10dB. So out of the first stage comes 100 units of signal power, 10 units of noise power from the noise associated with the signal, and 10 units of noise contributed by that amplifier. Now the signal:noise power ratio is

100:20, or 5, which is 7dB. Out of the second stage comes 1000 units of signal power, 100 units of noise power from the signal, 100 units of noise power from the first amplifier, and 10 units of noise power from the second amplifier. Now the signal:noise is 1000:210 = 4.76:1 = 6.78dB. So the first stage dropped the signal:noise by 3dB, and the second stage dropped it only 0.22dB more. And all this is considering ONLY the noise in the signal bandwidth; it's the only noise you SHOULD have to deal with at the output, assuming a good design.

Cheers, Tom

Reply to
Tom Bruhns

Noise figure compares the receiver noise with the noise from a purely dissipative element* at some temperature, usually 298K or 300K (i.e. "room temperature"). Both the receiver noise power and the source noise power are multiplied by the IF bandwidth, so it doesn't affect the noise figure.

The implicit assumption is that you've already fit the IF bandwidth to your signal of interest.

Note that microwave receivers are often pointed at sources (like the sky or the sun) whose apparent temperature is way different from 'room temperature', so they are often characterized by their "noise temperature" rather than noise figure. You'll find better statements by doing a web search, but in short the noise temperature is the temperature that a resistor would be at if it were contributing the amount of noise that the receiver front end is actually contributing**.

  • I'd like to say "resistor", but this is microwaves.

** This is not nearly so confusing when other people say it. Please don't ask me for clarification before I've had a good night's sleep!

--
Tim Wescott
Wescott Design Services
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Reply to
Tim Wescott

"billcalley"

** You are not wrong.

The ultimate ( ie weak signal) sensitivity of a receiver depends on its IF bandwidth - the narrower the better for weak signals.

A neat example of this is with the early NASA space probes sent to take pics of Mars and beyond. These typically stored all image data on board during their brief bypasses of the target planet, THEN sent them back to earth at leisure via a low power transmitter and a puny dish antenna - VERRRY SLOWLY.

At extreme range from earth , the data rates were sometimes down to only a few bits per second using bandwidths of only a few Hz. This, despite the use of giant radio astronomy telescopes as the receivers.

Fascinating.

...... Phil

Reply to
Phil Allison

I think that's the pivotal point, Tim; An assumption in any receiver design is that the IF bandwidth will be restricted to roughly the bandwidth of the received signal. It's pretty much WHY heterodyning exists - in order to be able to use a channel filter (IF filter) that doesn't need to be tuned when the receiver changes channel.

If the receiver bandwidth is a given, then the receiver's NF is indeed dominated by the NF of the first stage, provided that stage has a reasonably high gain.

--
Rick
Reply to
Rick H

The easy way to answer the question is to look at the equations for cascaded noise figure of multiple stages. Noise figure is measured at spot frequencies. The actual bandwidth doesn't affect the computation.

The equations use Noise Factor - a power ratio, rather than dB, and Gain as a power ratio, not in dB. Convert the Noise Figure of the stages to noise factor, and Gain in dB to power gain ratio by the equations below. Noise Factor is the increased noise power at the output, divided by the noise power at the input.

Nfactor = 10^(Nfigure_dB/10) Gain = 10^(PowerGain_dB/10)

Below, Fn = Noise Factor of stage N and Gn = gain of stage N

Ftotal = F1 + ((F2-1)/G1) + ((F3-1)/(G1*G2) + ((Fn - 1)/(G1*G2..*G(n-1)))

Ftotal_dB = 10 log (Ftotal)

The feature that you can observe is that every stage's contribution to the total noise factor is reduced by all the gain ahead of that stage. So a noisy stage late in the IF will not alter the final value very much - UNLESS the net gain to that point in the chain (G1*G2*G3...) is getting small. That's a big reason why LNA and LNB components have large gains. Their gain tends to isolate the effects of all cable losses getting to the receiver, the noise of subsequent stages, etc.

So pay attention to cascaded gain through the receiver, if you want to protect a noise figure. When losses start to reduce the net gain to less than say, 10 dB, its usually time for more gain. Of course, this all gets balanced against intermod distortion, which prevents you from just using huge gains everywhere.

Example: If F1 = F2 = F3 =4 (6 dB) and G1 = G2 = G3 = 10 (10 dB), the total noise factor is 4.33 (6.34 dB). But if G2 is a loss stage with G= 0.25 (-6 dB), the total NF rises to 5.37 (7.3dB). The cascaded gain is no longer 1000 (30 dB) but now its 25 (14 dB). And its stage 3's NF that degraded the result. At the end of stage 2, the cascaded NF is still about 4. The output noise power in this case is 3 dB higher due to the loss stage, so you'd measure 3 dB more noise at the output, regardless of final bandwidth.

The total output power (dBm) of the receiver in a 1 Hz bandwidth is [-174 dBm + Noise Figure_in_dB]. When you convert to total noise power in a bandwidth of interest, you add a factor for the IF bandwidth or measurement bandwidth. [-174 + NFdB +

10log(BW_in_Hz)]. If you have a minimum SNR requirement, then that gets added to this result to find the actual sensitivity of the receiver system, in the desired bandwidth. [ -174 + NFdB + 10log(BW_in_Hz)+Min_SNR_in_dB]. From this result, you can see that the bandwidth and NF are independent contributions to the final sensitivity. Since receiver bandwidth and required SNR are somewhat fixed based on what you are receiving, their contribution to sensitivity can't be adjusted very much. The only factor you have any real control over is NF.

Steve

Reply to
Steve

You missed out the receiver's gain: the -174dBm/Hz is subject to the receiver's gain and is degraded by the noise figure:

Total noise = kT * Noise_Factor * Gain (W/Hz) = -174 + Noise_Figure_in_dB + Gain_in_dB (dBm/Hz)

--
Rick
Reply to
Rick H

You're right. Thanks

Reply to
Steve

Rick H pointed out that my equations omitted gain as an additional term. Sorry for the error. You are correct to expect gain to be in there.

Steve

Reply to
Steve

Only terminology. They do exactly this - use a specified bandwidth in the IF depending on what signal you're after.

But, while the front end gives you "sensitivity", the limited bandwidth of the IF gives you "selectivity," which is a way of looking at it in colloquial terms.

Hope This Helps! Rich

Reply to
Rich Grise

billcalley snipped-for-privacy@yahoo.com posted to sci.electronics.design:

While i was still learning, i had to run the stage by stage calculations many many times. As a result i have learned that it is completely true in most cases. When gain is low to allow high dynamic range the next stage sometimes impacts sensitivity or noise figure. Now after having cranked the calculations soo many times, i just do a cursory check for getting near the boundary conditions i have found (about 3 dB gain, nearly the same NF).

Reply to
JosephKK

Tom Bruhns snipped-for-privacy@msn.com posted to sci.electronics.design:

Thanks Tom. It has been 40 years since i regularly cranked the arithmetic, but that is just how they work.

Reply to
JosephKK

billcalley snipped-for-privacy@yahoo.com posted to sci.electronics.design:

Er, not quite. It is a tradeoff bewteen bandwidth versus noise versus datarate. Please see Shannon's law

Except that there are dynamically programmable transmitter receiver pairs that adapt bandwidth and datarate to manage current noise environment. Space exploration vehicles like the voyager do this. Newer software defined radios also do things like this.

Please note that the current IF bandwidth sets the measurement bandwidth for the S/N measurement. This property is called selectivity. As discussed for 3. and 4. above this impacts S/N for the total receiver.

Reply to
JosephKK

----------------------------------

ME:

JOE: "Er, not quite. It is a tradeoff bewteen bandwidth versus noise versus datarate. Please see Shannon's law."

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Thanks for the further info Joe. But now my head REALLY hurts! I had no idea that a receiver's NF could change with a change in bandwidth and/or data rate. I think I'm going to have to hit the books yet again!!

Best regards,

-Bill

Reply to
billcalley

Your quite right, reducing the bandwidth does have a huge effect. Recievers are usually made to recieve information of some sort which is contained in the sidebands and therefore the bandwith has to be fixed to that width. Once youve fixed it, the recievers SN ratio is now dependent on the front end performance.

Reply to
cbarn24050

Bill: Hold the headache. Noise Figure doesn't change with bandwidth, nor is it related to channel capacity and Shannon's law. On the other hand, total output noise power does change with bandwidth, just as SNR and sensitivity both change with bandwidth. But you already understood that. Noise Figure is a figure-of-merit for a receiver, and it is independent of the actual bandwidth of the receive path (precisely so that you can make a single useful measurement for a receiver with switched IF bandwidths). I refer you back to the (corrected) sensitivity equation where their independence is clearly seen.

Steve

Reply to
Steve

I think Steve already presented the Friis Noise Figure Equation for you. That should explain the above part of the problem for you.

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Yes, given white noise, the total noise power will increase as the bandwidth is increased. But receiver composite (cascaded) bandwidth is designed almost as a matter of tautology: "It should be wide enough to pass the desired signal, and no wider." (Obviously there is a bit of play in that, depending on the expected environmental conditions.) IOW, it would make no sense to have a 1 MHz composite receiver bandwidth if the signal bandwidth was 3 kHz.

As Lathi writes on p.531 of Signals, Systems, and Communications, "[C]orrelation in the time domain is filtering action in the frequency domain." That is, a filter whose bandwidth is matched to the signal bandwidth is correlated to the signal (or vice versa).

LOL. You'll have a big-ass signal to deal with if the gain is infinite. TINSTAAFL!

Yes, See Friis.

Also, under low noise conditions, some modulation system's SNR gets better as the signal bandwidth is increased. For example, FM and PM with do 6 dB better as signal bandwidth is doubled. Most Comm Theory texts will include that (mathematical) development.

Reply to
Simon S Aysdie

Steve snipped-for-privacy@comcast.net posted to sci.electronics.design:

I do not remember that one. Please post for us, with the proper explanation. There is a clear implication of such dependency in Shannon's law though.

Reply to
JosephKK

this is only true above "threshold"

Mark

Reply to
Mark

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