Radio and Aliasing

[Bob Myers]

You imply here that the carrier has bandwidth; it doesn't. I assume you
meant to say "...modulating frequency exceeds the frequency of the
carrier,...."

Ooops - you're right. I misspoke when I used the word
"bandwidth". I was trying to figure out some way to
easily include the idea that the modulating signal doesn't
have to be just a sinusoid.

Bob M.

 

[Don Bowey]

Don Bowey wrote:
On 9/9/06 9:42 PM, in article
[email protected], "Radium"


Don Bowey wrote:
On 9/9/06 5:28 PM, in article
[email protected], "Radium"

The responses I've received have confused me.

What is the highest frequency that can be received on a 150 khz AM
radio receiver? Is it 150 khz, 300 khz, 75 khz, or 60 khz?


What is the bandwidth of the receiver? That is the limiting factor.

150 Khz



Some of the responses have told me that Nyquist theorem means that the
frequency of the station must be at least 2x [and due to physical
limitations, at least 2.5x] that of the highest frequency of the
modulation [audio] signal. Other responses have said different. Some
have said 150 khz can contain a modulation signal of 300 khz.

Which should I believe??

What are you attempting to do?

Find out the highest possible frequency of modulation that a 150 khz AM
station can transmit or receive.

In a previous post you said the bandwidth of the receiver is 150 kHz. Now
you say the carrier frequency of the signal is 150 kHz, So we can assume
the
bandwidth extends to 75 kHz above and below the carrier. Is this what you
assume for the receiver? If not then make your assumption set more
explicit.

Okay. Let me make a modification. Lets make the the the bandwidth of
the receiver 150 Ghz [notice that 'G'] but keep the carrier frequency
of 150 Khz. Now, what is the maximum frequency the the modulation can
be? I guess its 750 Mhz. Do I guess correctly?


What is the lowest physically-possible frequency of an AM station that
will allow me to hear a 20,000 khz tone on the receiver?

Are you assuming a standard double sideband signal, or a single sideband
signal?

Standard.

If the carrier frequency is 1 hz but the bandwidth of the reciever is
40 Khz, then could I [at least in theory] hear anything on the speaker
of the receiver?



Surely a 1 hz station wouldn't work for this [DUH!!!!]

You are establishing unrealistic conditions.

How is it unrealistic?

Here's one of your posts:

"Okay. Let me make a modification. Lets make the the the bandwidth of
the receiver 150 Ghz [notice that 'G'] but keep the carrier frequency
of 150 Khz. Now, what is the maximum frequency the the modulation can
be? I guess its 750 Mhz. Do I guess correctly?"


No you did not, and only a little homework on your part would show you why.

Here is an example: You have been advised that the carrier frequency must
be at least two times the highest (or only) modulation frequency. Let's
assume 2x is good enough, so obviously in a multiple guess test, an answer
of 75 kHz for a maximum modulation frequency is the right answer. The
process of modulating 75 kHz with a 150 kHz carrier will produce a sideband
signal at 75 kHz (lower sideband), and 225 kHz (upper sideband). The
carrier will also be present in the output as will other products. The
bandwidth required is nominally 150 kHz, in the range of 75 to 225 kHz.

Another example: You cannot modulate a high frequency on a 1 Hz carrier.
But now you know better, right? Anyone wishing to argue about this should
start a new thread in alt.sci.electronics.dumbideas


Google is your friend.

 

[Radium]

On 9/10/06 9:11 AM, in article
[email protected], "Radium"


Don Bowey wrote:
On 9/9/06 9:42 PM, in article
[email protected], "Radium"


Don Bowey wrote:
On 9/9/06 5:28 PM, in article
[email protected], "Radium"

The responses I've received have confused me.

What is the highest frequency that can be received on a 150 khz AM
radio receiver? Is it 150 khz, 300 khz, 75 khz, or 60 khz?


What is the bandwidth of the receiver? That is the limiting factor.

150 Khz



Some of the responses have told me that Nyquist theorem means that the
frequency of the station must be at least 2x [and due to physical
limitations, at least 2.5x] that of the highest frequency of the
modulation [audio] signal. Other responses have said different. Some
have said 150 khz can contain a modulation signal of 300 khz.

Which should I believe??

What are you attempting to do?

Find out the highest possible frequency of modulation that a 150 khz AM
station can transmit or receive.

In a previous post you said the bandwidth of the receiver is 150 kHz. Now
you say the carrier frequency of the signal is 150 kHz, So we can assume
the
bandwidth extends to 75 kHz above and below the carrier. Is this what you
assume for the receiver? If not then make your assumption set more
explicit.

Okay. Let me make a modification. Lets make the the the bandwidth of
the receiver 150 Ghz [notice that 'G'] but keep the carrier frequency
of 150 Khz. Now, what is the maximum frequency the the modulation can
be? I guess its 750 Mhz. Do I guess correctly?


What is the lowest physically-possible frequency of an AM station that
will allow me to hear a 20,000 khz tone on the receiver?

Are you assuming a standard double sideband signal, or a single sideband
signal?

Standard.

If the carrier frequency is 1 hz but the bandwidth of the reciever is
40 Khz, then could I [at least in theory] hear anything on the speaker
of the receiver?



Surely a 1 hz station wouldn't work for this [DUH!!!!]

You are establishing unrealistic conditions.

How is it unrealistic?

Here's one of your posts:

"Okay. Let me make a modification. Lets make the the the bandwidth of
the receiver 150 Ghz [notice that 'G'] but keep the carrier frequency
of 150 Khz. Now, what is the maximum frequency the the modulation can
be? I guess its 750 Mhz. Do I guess correctly?"


No you did not, and only a little homework on your part would show you why.

Here is an example: You have been advised that the carrier frequency must
be at least two times the highest (or only) modulation frequency. Let's
assume 2x is good enough, so obviously in a multiple guess test, an answer
of 75 kHz for a maximum modulation frequency is the right answer. The
process of modulating 75 kHz with a 150 kHz carrier will produce a sideband
signal at 75 kHz (lower sideband), and 225 kHz (upper sideband). The
carrier will also be present in the output as will other products. The
bandwidth required is nominally 150 kHz, in the range of 75 to 225 kHz.

If the the carrier's frequency must be at least 2x the modulation
frequency, then how can a 150 KHz station carry a 225 Khz tone?

 

[John Larkin]

Another example: You cannot modulate a high frequency on a 1 Hz carrier.
But now you know better, right? Anyone wishing to argue about this should
start a new thread in alt.sci.electronics.dumbideas

If it's SSB, and not AM, you can modulate any amount of signal
bandwidth onto a 1 Hz carrier.

John

 

[Don Bowey]

On 9/10/06 6:17 PM, in article
[email protected], "Radium"

(snip)

You are establishing unrealistic conditions.

How is it unrealistic?

Here's one of your posts:

"Okay. Let me make a modification. Lets make the the the bandwidth of
the receiver 150 Ghz [notice that 'G'] but keep the carrier frequency
of 150 Khz. Now, what is the maximum frequency the the modulation can
be? I guess its 750 Mhz. Do I guess correctly?"


No you did not, and only a little homework on your part would show you why.

Here is an example: You have been advised that the carrier frequency must
be at least two times the highest (or only) modulation frequency. Let's
assume 2x is good enough, so obviously in a multiple guess test, an answer
of 75 kHz for a maximum modulation frequency is the right answer. The
process of modulating 75 kHz with a 150 kHz carrier will produce a sideband
signal at 75 kHz (lower sideband), and 225 kHz (upper sideband). The
carrier will also be present in the output as will other products. The
bandwidth required is nominally 150 kHz, in the range of 75 to 225 kHz.

If the the carrier's frequency must be at least 2x the modulation
frequency, then how can a 150 KHz station carry a 225 Khz tone?

Now you are wasting bandwidth and oxygen. Since you understand nothing you
are told and refuse to do any study on your own, I declare you a Troll.

 

[Don Bowey]

If it's SSB, and not AM, you can modulate any amount of signal
bandwidth onto a 1 Hz carrier.

John

This is the wrong thread for this topic, however.....

You really should read what you wrote. It is totally off the wall.

Don

 

[SDC]

Hi:

Lets say there is an AM station with a carrier frequency of 150 KHz.
What is the highest frequency of modulation that it can handle?

Legally, 5 kHz (well, OK, I can't say that for a 150 kHz
transmitter; I'm talking about the legal limits on radio
stations in the AM broadcast band, 535 - 1705 kHz).

Sorry. I meant to ask what is the highest audio frequency that can
[physically] be broadcasted through a 150 Khz carrier.

Errr.......... 150kHz maybe ? Maybe SSB can do better ?

Graham

Sorry. I meant to ask what is the highest audio frequency that can
[physically] be broadcasted through a 150 Khz carrier.

The highest "audio" frequency is about 20kHz, so my opinion is that
anything above 40kHz will do it really nicely and >=20kHz will 'just' do it.
(I'm more familiar with digital and the Nyquist theorem, but surely similar
rules apply.)

.... Steve

 

[John Larkin]

Obviously, it is not only the peaks which "sample" the signal,
but you CAN use sampling theory in an analysis of AM if
you treat it from that perspective. It's hardly "my" theory.

Bob M.

OK, take the carrier sinewave and express it as a sequence of impulses
at sufficient density to trace the sine shape pretty well. Number
those, say, 64 impulses and apply the sampling math to each. Now sum
the amplitude and phase of the resulting signal samples, all 64 of
them, and correct for the artifacts.

Or stay continuous use a trig identity or two.

John

 

[John Larkin]

This is the wrong thread for this topic, however.....

You really should read what you wrote. It is totally off the wall.

Whose wall? It's correct. All you do to make a USB signal is shift the
spectrum up by some "carrier" frequency, and 1 Hz is as good as any
other value. All a SSB receiver does is shift it back down.

John

 

[Don Bowey]

Ooops - you're right. I misspoke when I used the word
"bandwidth". I was trying to figure out some way to
easily include the idea that the modulating signal doesn't
have to be just a sinusoid.

Bob M.

Along the same lines, but not quite on topic, there may be an advantage in
using a square wave carrier in a low-level (ring, etc) modulator, rather
than a sine wave. A single "AM modulation" sample amplitude is time
variant; it includes a span of time of almost a half cycle of the carrier
frequency. It seems to me that a square wave carrier would provide a longer
sample than would a sine wave. Filtering the output of carrier harmonics,
etc, would be simple. I think there should be a measurable difference in
distortion.

What do you think?

Don

 

[Don Bowey]

Whose wall? It's correct. All you do to make a USB signal is shift the
spectrum up by some "carrier" frequency, and 1 Hz is as good as any
other value. All a SSB receiver does is shift it back down.

John

It's nonsense.

Tell me how you modulate a 300 to 3000 Hz voice signal using a 1 Hz carrier.
Where is the 2:1 carrier to highest modulation frequency in this concept of
yours?

Don

 

[John Larkin]

It's nonsense.

Tell me how you modulate a 300 to 3000 Hz voice signal using a 1 Hz carrier.
Where is the 2:1 carrier to highest modulation frequency in this concept of
yours?

Don

The 2:1 limit is for AM, where you obviously get into trouble if the
lower sideband has frequency components that get below zero frequency
and fold back. SSB/Upper sideband doesn't have that problem, because
all the modulation products are *above* the carrier frequency. As I
said, USB is merely an up-shift of the signal spectrum, by any amount.

The two common SSB generation techniques are the phasing method (which
works fine for your example) and the balanced mixer followed by a
sideband filter, which doesn't work with these numbers. But a
double-conversion mixer+filter method will work: modulate the signal
with a carrier, say 100 KHz; filter out the lower sideband, so that
the spectrum is now 100300 to 103000 Hz;; mix that with 99,999 Hz to
shift the spectrum back down, now 301 to 3001 Hz. Voila, a 300-3000 Hz
signal SSB modulated onto a 1 Hz carrier.

You can purchase an audio-band frequency shifter. Set the shift to +1
Hz and the result will be exactly the same as audio modulated SSB onto
a 1 Hz carrier. If it lets you, set the shift to 28.2 MHz and you'll
be generating legal USB signals for the 10-meter ham band. It's all
the same.

John

 

[Don Bowey]

The 2:1 limit is for AM, where you obviously get into trouble if the
lower sideband has frequency components that get below zero frequency
and fold back. SSB/Upper sideband doesn't have that problem, because
all the modulation products are *above* the carrier frequency. As I
said, USB is merely an up-shift of the signal spectrum, by any amount.

The two common SSB generation techniques are the phasing method (which
works fine for your example) and the balanced mixer followed by a
sideband filter, which doesn't work with these numbers. But a
double-conversion mixer+filter method will work: modulate the signal
with a carrier, say 100 KHz; filter out the lower sideband, so that
the spectrum is now 100300 to 103000 Hz;; mix that with 99,999 Hz to
shift the spectrum back down, now 301 to 3001 Hz. Voila, a 300-3000 Hz
signal SSB modulated onto a 1 Hz carrier.

No, all you did was shift the spectrum down. I certainly accept SSB as a
form of AM, but you did not modulate a 300 - 3000 Hz signal, with a 1 Hz
carrier.

You can purchase an audio-band frequency shifter. Set the shift to +1
Hz and the result will be exactly the same as audio modulated SSB onto
a 1 Hz carrier. If it lets you, set the shift to 28.2 MHz and you'll
be generating legal USB signals for the 10-meter ham band. It's all
the same.

John

Don

 

[Bob Myers]

OK, take the carrier sinewave and express it as a sequence of impulses
at sufficient density to trace the sine shape pretty well. Number
those, say, 64 impulses and apply the sampling math to each. Now sum
the amplitude and phase of the resulting signal samples, all 64 of
them, and correct for the artifacts.

John, we're not in disagreement at all here, really. All I've been
trying to say all along is that you CAN make an analogy to
sampling, if that happens to be a more comfortable place
for a given person to be coming from to consider what's going
on. No, AM radio is NOT sampling, and the analogy (like any)
breaks down if you look to closely at it. But analogies like this
are often useful for getting the basics across to people. OK?

Bob M.

 

[Bob Myers]

Along the same lines, but not quite on topic, there may be an advantage in
using a square wave carrier in a low-level (ring, etc) modulator, rather
than a sine wave. A single "AM modulation" sample amplitude is time
variant; it includes a span of time of almost a half cycle of the carrier
frequency. It seems to me that a square wave carrier would provide a
longer
sample than would a sine wave. Filtering the output of carrier harmonics,
etc, would be simple. I think there should be a measurable difference in
distortion.

Well, a classic AM modulator is based on a Class C output
stage, which I guess is sort-of what you're thinking of here.
In short, it doesn't matter if the modulator is fed with an
actual "sinusoidal" carrier, as long as you can control the
amplitude of the output via the modulating signal, and you
can be assured of throwing out any undesirable components
that might result. A Google search for "modulation transformer"
will no doubt turn up more information on this approach, but
that basic idea is that you have a high-powered audio amp
which is plate-modulating a Class C RF amp via a transformer.
The advantage, of course, is that you have a much more
efficient RF stage than would be the case if you had to
modulate the carrier and THEN amplifier the result linearly.
This is a very common approach in AM (but not for
SSBSC, for obvious reasons).

Bob M.

 

[Bob Myers]

If it's SSB, and not AM, you can modulate any amount of signal
bandwidth onto a 1 Hz carrier.

Rather pointless, though, since the result is equivalent
to the modulating (baseband) signal shifted up by
1 Hz....

 

[John Larkin]

John, we're not in disagreement at all here, really. All I've been
trying to say all along is that you CAN make an analogy to
sampling, if that happens to be a more comfortable place
for a given person to be coming from to consider what's going
on. No, AM radio is NOT sampling, and the analogy (like any)
breaks down if you look to closely at it. But analogies like this
are often useful for getting the basics across to people. OK?

Bob M.

OK, but not if they mis-state quantitative reality by 2:1.

John

 

[John Larkin]

Rather pointless, though, since the result is equivalent
to the modulating (baseband) signal shifted up by
1 Hz....

And that's all SSB is! The old analog long-distance telephone carrier
stuff wasn't as extreme, but they stacked SSB voiceband signals every
4 KHz, with the first one at baseband. So the second signal was
300-3400 Hz modulated onto a 4 KHz carrier. They did all this with
tubes, and saved a huge amount of copper and telephone poles. One FDM
version (Western Electric type "O") placed the first carrier at 6 KHz,
but put two voice signals on each carrier, one USB and the other LSB;
that put 6 KHz of signal onto a 6 KHz carrier, but it was two
different signals!

John

 

[Don Bowey]

And that's all SSB is! The old analog long-distance telephone carrier
stuff wasn't as extreme, but they stacked SSB voiceband signals every
4 KHz, with the first one at baseband. So the second signal was
300-3400 Hz modulated onto a 4 KHz carrier. They did all this with
tubes, and saved a huge amount of copper and telephone poles. One FDM
version (Western Electric type "O") placed the first carrier at 6 KHz,
but put two voice signals on each carrier, one USB and the other LSB;
that put 6 KHz of signal onto a 6 KHz carrier, but it was two
different signals!

John

Scrapped O Carrier filters were great for homebrew sideband equipment.

There was one telco carrier system arrangement that was "extreme;" that was
the use of the EB bank with K and L Carrier. The Emergency Bank put two 1.8
kHz channels in the 4 kHz spectrum of the K or L Carrier's channel spacing.
As I recall, the A channel of the two had normal orientation (USB), and the
B channel had LSB orientation. The (suppressed) carriers were 4 kHz apart.
The B channel of the L chan 1 shared the carrier of the A channel of L chan
2. The whole stack gave us 24 crappy channels in the space of 12 good
channels.

Don

 

[Don Bowey]

Well, a classic AM modulator is based on a Class C output
stage, which I guess is sort-of what you're thinking of here.

No, I specified a low-level modulator such as a diode ring, which can be
easily filtered. I don't think I would try it with plate modulation