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Receiver sensitivity and IF bandwidth??

B

billcalley

Jan 1, 1970
0
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
 
T

Tom Bruhns

Jan 1, 1970
0
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

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
 
T

Tim Wescott

Jan 1, 1970
0
billcalley said:
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
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
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html
 
P

Phil Allison

Jan 1, 1970
0
"billcalley"
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).


** 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
 
B

billcalley

Jan 1, 1970
0
All an amplifier can do is amplify what's at its input. Whatever the
signal is in reference to the noise, that ratio will remain at the output,
even though the actual voltage level will be higher at the output of
the amplifier compared with the input.

To use a broad example, 1v of noise and 0.1v of signal at an amplifier's
input will mean 10v of noise and 1v of signal at the the output if
the gain is ten. You haven't altered the ratio, just made everything
louder.

It's like turning up the volume on a hearing aid to hear the person
next to you, but which also amplifies the other sounds in the room that
were already stronger than the person; you haven't actually fixed the problem
because the problem was that the person was weaker than the surrounding
sounds.

So if you have a first stage that adds noise to the mix, noise that
will help to mask the desired signal, then you've made things worse.
Forever down the signal chain, there is nothing you can do to fix
the problem, because once that noise is added, any later amplification
amplifies it along with the desired signal. If that stage in
the broad example generated 1v of noise, that equals the level of
the desired signal, and thus has made the situation worse.

So you want to get that signal up fast without adding any noise, or
at least as little as possible. So for low level microphones, you'll
often see a transformer to boost the signal, because it will introduce
less noise than an active stage.

A low noise first rf stage will indeed set the stage. It will
amplify the incoming signal (and the background noise equally) but will
add little of its own noise to mask the signal. If it's not low noise,
then any incoming signal has to be above a certain level to stay
above that noise.

There is background noise picked up by the antenna along with the
desired signal. That level varies with frequency, becoming more
significant the higher up you go. You can't do anything about
that, it's part of basic communication (well you can, but that's
another story). But you can work at making sure as little noise as
possible is added to the mix.

Later stages don't matter, because the signal is stronger
and the noise generated by later stages will not have the same impact.
So that previous broad example, 10v of noise and 1volt of signal out
of the first stage, the second stage will amplify that by ten again,
so its output is 100v of noise (I said that was a broad example) and
10volts of signal, but if the stage adds 1 volt of noise
that 1v is now 1/10th the level of the desired signal, when before
it was stronger than the desired signal.

Michael



Thanks Tom, Tim, Phil, and Michael for some great answers!

I guess I need time to digest all this. But what I still don't
get -- just taking Michael's terrific response as a good example -- is
while I know that the receiver's front-end sets the ratio between the
input signal and the receiver's noise, and that this S/N ratio cannot
then be improved by the receiver's I.F. *amplification* stages, why
can't the receiver's I.F. *filter* stages simply passband filter out
most of that wideband input noise to improve the receiver's SNR, which
should then improve the sensitivity of the receiver? That's the part
that still has me stumped...

Thanks All,

-Bill
 
R

Rick H

Jan 1, 1970
0
In sci.electronics.design Tim Wescott said:
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.

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.
 
S

Steve

Jan 1, 1970
0
billcalley said:
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

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
 
T

Tim Wescott

Jan 1, 1970
0
Thanks Tom, Tim, Phil, and Michael for some great answers!

I guess I need time to digest all this. But what I still don't
get -- just taking Michael's terrific response as a good example -- is
while I know that the receiver's front-end sets the ratio between the
input signal and the receiver's noise, and that this S/N ratio cannot
then be improved by the receiver's I.F. *amplification* stages, why
can't the receiver's I.F. *filter* stages simply passband filter out
most of that wideband input noise to improve the receiver's SNR, which
should then improve the sensitivity of the receiver? That's the part
that still has me stumped...

Thanks All,

-Bill

What's got you stumped is a confusion between noise figure and
signal-to-noise ratio. Noise figure compares wideband noise to wideband
noise, and is a measure of how well you did with your receiver front-end
and mixer stages. Signal to noise ratio compares the (probably narrow
band in some sense) signal to noise, and is a measure of how well you did
with your entire receiver design, including the IF filter.

Two different measures, two different numbers. Apples & Oranges, etc.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
 
T

Tom Bruhns

Jan 1, 1970
0
Thanks Tom, Tim, Phil, and Michael for some great answers!

I guess I need time to digest all this. But what I still don't
get -- just taking Michael's terrific response as a good example -- is
while I know that the receiver's front-end sets the ratio between the
input signal and the receiver's noise, and that this S/N ratio cannot
then be improved by the receiver's I.F. *amplification* stages, why
can't the receiver's I.F. *filter* stages simply passband filter out
most of that wideband input noise to improve the receiver's SNR, which
should then improve the sensitivity of the receiver? That's the part
that still has me stumped...

Thanks All,

-Bill

Bill, re-read my posting. The analysis is for noise only in the
bandwidth of the signal. There is no way you can get rid of that
noise without also getting rid of signal as well. If you integrate
the entire noise power at the front end, the signal to noise ratio
would appear to be much worse than it really is. The analysis never
counts noise outside the band of interest.

Or, put another way, the analysis always considers noise on a per-unit-
bandwidth basis.

If you have an extremely narrow signal, you may be able to improve the
apparent signal-to-noise ratio by narrowing your filter, but you'll
never be able to narrow the filter enough to get rid of the noise
that's in the bandwidth of the signal, whatever that is. The one hope
left there is to synchronously detect the signal. This is possible in
equipment that generates a test signal and looks at a response on
exactly that frequency; then you can average, synchronized to the
signal itself, and the uncorrelated noise will continue to drop, 3dB
for every doubling of the integration time.

Cheers,
Tom
 
M

Mark

Jan 1, 1970
0
Thanks Tom, Tim, Phil, and Michael for some great answers!

I guess I need time to digest all this. But what I still don't
get -- just taking Michael's terrific response as a good example -- is
while I know that the receiver's front-end sets the ratio between the
input signal and the receiver's noise, and that this S/N ratio cannot
then be improved by the receiver's I.F. *amplification* stages, why
can't the receiver's I.F. *filter* stages simply passband filter out
most of that wideband input noise to improve the receiver's SNR, which
should then improve the sensitivity of the receiver? That's the part
that still has me stumped...

Thanks All,

-Bill- Hide quoted text -

- Show quoted text -

another way to think of it is that the desried input signal has a
power DENSITY, i.e. power per Hz BW. and the front end ciruicts have
a noise DENSITY, i.e. noise power per Hz that is determined by the
noise figure. Then when the noise and signl go therough the IF
filter, the IF filter sets the BW. If the signal is very narrow, the
filter can be very narrow and will let in only the minimum possible
amount of noise. Both the noise figure and IF bandwidth are important
in determining sensitivity. But the IF BW cannot be less then the
desired signal BW. And the Noise figure can't be less than 0 dB.

I think one of the key concepts you may be missing is that even the
antenna picks up noise with the signal so there is a limit to the
acheivable sensitivity even if you had a "perfect" receiver. A
perfect receiver would have a 0 dB noise figure. That does not mean
there is NO noise, it means there is no EXTRA noise beyond that which
the antenna picks up.
The lowest noise floor for space communicarions is the 3degK floor.
For Earth comm its room temperature. The "perfect" receiver also has a
BW no wider than it needs to be to pass the desired signal but it must
be wide enough to pass the signal and therefore also passes that
amount of noise.

Mark
 
B

billcalley

Jan 1, 1970
0
another way to think of it is that the desried input signal has a
power DENSITY, i.e. power per Hz BW. and the front end ciruicts have
a noise DENSITY, i.e. noise power per Hz that is determined by the
noise figure. Then when the noise and signl go therough the IF
filter, the IF filter sets the BW. If the signal is very narrow, the
filter can be very narrow and will let in only the minimum possible
amount of noise. Both the noise figure and IF bandwidth are important
in determining sensitivity. But the IF BW cannot be less then the
desired signal BW. And the Noise figure can't be less than 0 dB.

I think one of the key concepts you may be missing is that even the
antenna picks up noise with the signal so there is a limit to the
acheivable sensitivity even if you had a "perfect" receiver. A
perfect receiver would have a 0 dB noise figure. That does not mean
there is NO noise, it means there is no EXTRA noise beyond that which
the antenna picks up.
The lowest noise floor for space communicarions is the 3degK floor.
For Earth comm its room temperature. The "perfect" receiver also has a
BW no wider than it needs to be to pass the desired signal but it must
be wide enough to pass the signal and therefore also passes that
amount of noise.

Mark- Hide quoted text -

- Show quoted text -


Thanks a lot guys. I think I understand all this now (at least I hope
I do!):

1. If we can decrease the receiver's NF *or* bandwidth (which will
decrease the added noise levels), then we will improve our SNR, and
therefore our sensitivity.

2. The NF dominates microwave receiver designs because that is
normally all we will have any control over when we are given the SNR/
BW/modulation that will be used in the system.

3. Since it is measured at a single spot frequency of 1Hz, NF itself
is completely independent of bandwidth.

4. After the receiver's high gain frontend receives the transmitted RF
signal-with-noise, and then adds its own frontend circuit noise, the
I.F. stages will only be able to, at best, maintain this same signal-
to-noise ratio as set by the frontend. No improvement in SNR will be
possible, since the I.F.'s bandwidth will be "set in stone" for the
specific modulation in use, and cannot be less wide than the
modulation itself. (Therefore, when the receiver's bandwidth is
fixed, then the system NF is directly related to the receiver's
sensitivity).

5. I guess I will logically have to assume that the calculation for
receiver sensitivity, -174+NF+10log(BW)+SNRmin, must take for granted
that the receiver's I.F. gain will be high enough to increase the
received signal power enough to properly drive the detector (even at
the lowest RF input signal levels), since gain is not part of this
sensitivity equation... why it is not, I have no idea!

Thanks for all of the unbelievably helpful responses!

-Bill
 
A

Andrew Holme

Jan 1, 1970
0
while I know that the receiver's front-end sets the ratio between the
input signal and the receiver's noise, and that this S/N ratio cannot
then be improved by the receiver's I.F. *amplification* stages, why
can't the receiver's I.F. *filter* stages simply passband filter out
most of that wideband input noise to improve the receiver's SNR, which
should then improve the sensitivity of the receiver? That's the part
that still has me stumped...

Yes, noise at the loudspeaker reduces as you narrow the IF; but you can't go
narrower than the bandwidth of the signal. Even CW requires some bandwidth.
You still need to minimise noise generated by the receiver itself - to which
the first stage makes the biggest contribution.
 
R

Rick H

Jan 1, 1970
0
In sci.electronics.design Steve said:
The total output power (dBm) of the receiver in a 1 Hz bandwidth is [-174
dBm + Noise Figure_in_dB].

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)
 
B

Bob Masta

Jan 1, 1970
0
If you have an extremely narrow signal, you may be able to improve the
apparent signal-to-noise ratio by narrowing your filter, but you'll
never be able to narrow the filter enough to get rid of the noise
that's in the bandwidth of the signal, whatever that is. The one hope
left there is to synchronously detect the signal. This is possible in
equipment that generates a test signal and looks at a response on
exactly that frequency; then you can average, synchronized to the
signal itself, and the uncorrelated noise will continue to drop, 3dB
for every doubling of the integration time.
Readers who want to learn more about this general technique can check
out my series of articles on "Synchronous Waveform Averaging" at
www.daqarta.com/author.htm
(Titles appear about halfway down that page, after the "Gut-Level
Fourier Transforms" series.)

Best regards,


Bob Masta

DAQARTA v3.50
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Scope, Spectrum, Spectrogram, Signal Generator
Science with your sound card!
 
S

Steve

Jan 1, 1970
0
Rick H said:
In sci.electronics.design Steve said:
The total output power (dBm) of the receiver in a 1 Hz bandwidth is [-174
dBm + Noise Figure_in_dB].

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)

You're right. Thanks
 
S

Steve

Jan 1, 1970
0
billcalley said:
Thanks a lot guys. I think I understand all this now (at least I hope
I do!):

1. If we can decrease the receiver's NF *or* bandwidth (which will
decrease the added noise levels), then we will improve our SNR, and
therefore our sensitivity.

2. The NF dominates microwave receiver designs because that is
normally all we will have any control over when we are given the SNR/
BW/modulation that will be used in the system.

3. Since it is measured at a single spot frequency of 1Hz, NF itself
is completely independent of bandwidth.

4. After the receiver's high gain frontend receives the transmitted RF
signal-with-noise, and then adds its own frontend circuit noise, the
I.F. stages will only be able to, at best, maintain this same signal-
to-noise ratio as set by the frontend. No improvement in SNR will be
possible, since the I.F.'s bandwidth will be "set in stone" for the
specific modulation in use, and cannot be less wide than the
modulation itself. (Therefore, when the receiver's bandwidth is
fixed, then the system NF is directly related to the receiver's
sensitivity).

5. I guess I will logically have to assume that the calculation for
receiver sensitivity, -174+NF+10log(BW)+SNRmin, must take for granted
that the receiver's I.F. gain will be high enough to increase the
received signal power enough to properly drive the detector (even at
the lowest RF input signal levels), since gain is not part of this
sensitivity equation... why it is not, I have no idea!

Thanks for all of the unbelievably helpful responses!

-Bill

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
 
R

Rich Grise

Jan 1, 1970
0
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?

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.
(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).

Hope This Helps!
Rich
 
J

JosephKK

Jan 1, 1970
0
billcalley [email protected] posted to sci.electronics.design:
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

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).
 
J

JosephKK

Jan 1, 1970
0
Tom Bruhns [email protected] posted to sci.electronics.design:
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

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

JosephKK

Jan 1, 1970
0
billcalley [email protected] posted to sci.electronics.design:
Thanks a lot guys. I think I understand all this now (at least I
hope I do!):

1. If we can decrease the receiver's NF *or* bandwidth (which will
decrease the added noise levels), then we will improve our SNR, and
therefore our sensitivity.

2. The NF dominates microwave receiver designs because that is
normally all we will have any control over when we are given the
SNR/ BW/modulation that will be used in the system.

3. Since it is measured at a single spot frequency of 1Hz, NF
itself is completely independent of bandwidth.

Er, not quite. It is a tradeoff bewteen bandwidth versus noise versus
datarate. Please see Shannon's law
4. After the receiver's high gain frontend receives the transmitted
RF signal-with-noise, and then adds its own frontend circuit noise,
the I.F. stages will only be able to, at best, maintain this same
signal-
to-noise ratio as set by the frontend. No improvement in SNR will
be possible, since the I.F.'s bandwidth will be "set in stone" for
the specific modulation in use, and cannot be less wide than the
modulation itself. (Therefore, when the receiver's bandwidth is
fixed, then the system NF is directly related to the receiver's
sensitivity).

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.
5. I guess I will logically have to assume that the calculation for
receiver sensitivity, -174+NF+10log(BW)+SNRmin, must take for
granted that the receiver's I.F. gain will be high enough to
increase the received signal power enough to properly drive the
detector (even at the lowest RF input signal levels), since gain is
not part of this sensitivity equation... why it is not, I have no
idea!

Thanks for all of the unbelievably helpful responses!

-Bill

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.
 
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