This is a slightly edited transcript of an email dialog between yours
truly and He, a "newbie" to Radio Astronomy.
He wrote: I was again looking at your book [Radio Astronomy Projects]
and started in on the TRF [Tuned Radio Frequency] receiver project, p.
3-16ff. I'm somewhat familiar with TRF receivers from the past "good
old days" and I guess I was expecting to see a picture of a box
somewhere with a dial, volume control, and tuning knob on it. Somehow
I think the concept you present in the book is a different slant on
this notion. Is there some reading material somewhere that can help me
explain the TRF receiver notion you are using in the book? Figure 3-17
doesn't agree with my preconceived idea of a TRF receiver.
I wrote: I notice that you also have John Kraus's book, so I presume
his definition of TPR [Total Power Receiver] is satisfactory.
Basically, the bandwidth of the system is established at the front
end, either by the bandwidth of the antenna feed or by the input
bandwidth of the receiver. If that entire bandwidth is maintained
right down to the detector (where the radio frequency power within
that bandwidth is convserted into direct current power), then that is
a TPR.
Hence, a TRF receiver is commonly taken to be a TPR [Total Power
Receiver] if it does not constrict the bandwidth anywhere between the
input and the detector. The TRF receiver is tuned to some center
frequency of a pass-band. But it need not be tunable because it can be
deliberately built for some specific center frequency of a pass-band
--hence, no 'tuning knob' on the TRF receiver in my book.
"Superhets" are also TPR's if they maintain the same bandwidth all the
way through the receiver up to the detector (e.g. diode rectifier),
even though the center frequency may vary from one section of the
receiver to another. For example, the center frequency could be 4 GHz
in the RF preamplifier and mixer stage(s), then 900 Mhz in the
following IF stage(s), and then 70 Mhz in the final IF stage(s) before
being "handed on" to the detector.
He wrote: Yes, Kraus's description of a TPR is more or less
satisfactory. It's sort of like walking into a dark room with the aid
of a weak flashlight (the weak flashlight corresponding to my prior
experience). Anyway, I'll deal with that later.
I think I follow your talk about bandwidth. It seems that if I take a
chunk of bandwidth, say, 20 Mhz, and preserve it to some point, then
the signal content is converted to power. The resulting power is what
is measured. OK, but how does one convert a raw signal to power? Is it
done with a circuit? That is, is the signal (I guess noise in the case
of RA [Radio Astronomy]) sampled, squared, summed, averaged and then
the square root taken?
OK, your talk about a non-tunable TRF is fine--that's why there is no
knob! But, how does one capture the end product? That is, what is now
considered to be the measurable item? Is it power, voltage, or
something else? Is there special circuitry to do this? That is, if I
had an old TRF receiver that was capable of tuning to some RA
frequency, it would probably not produce any output of interest
without adding some new circuitry. (I don't have a TRF device; this is
an example.)
I wrote: Any receiver is basically a chain of power amplifiers. The
amount of power amplification depends on the amount of power needed to
operate whatever indicating device one is using, such as a voltmeter,
A/D converter, or loud-speaker, etc. Recall that the instantaneous
power level at any point in the amplifier is the product of the
instantaneous voltage at that point and the instantaneous current that
the voltage is driving through or into that point (such as into a
resistor).
Prior to reaching the detector, the average signal voltage and the
average signal current--but not the power -- are zero all along the
line because they are sinusoidal waveforms and thus they spend half of
their time being positive and the other half being negative--hence,
zero average. Now comes the 'magic.' The sinusoidal waveforms are fed
into a rectifier--an electronic one-way valve--such as a crystal
diode. This device is arranged to chop off either the positive
excursions of the sine-wave or the negative. NOW the average voltage
and average current are no longer zero--we have a rapidly varying
voltage (or current) that is always either positive or always
negative. This rectified ("mutilated") waveform now has a non-zero
d.c. value (or slowly varying d.c.). A low-pass filter is used to
separate this "d.c." component from all of the other components
because they are varying too quickly to be of any use for the typical
indicating device. It is this filtered d.c. component that is fed into
a voltmeter, A/D converter, or whatever.
Please let me know if this story makes sense so far.
He wrote: Yes, it makes near perfect sense. However, let's try this
for clarification. Consider an AM [Amplitude Modulated] signal, and
realize that we are dealing with AM signals in RA. Suppose I have a
"crystal set" with an RF tuner in the front end. The output after the
diode is the AM signal riding on d.c. I don't actually know, but it
seems reasonable that there is a 'd.c.' portion that has a slowly
varying component, on which the audio signal is riding. I would think
a low pass filter lops off the audio signal leaving the slowly varying
'd.c.' component. One could proceed to measure this with a dc
voltmeter. Why they would want to do that I don't know.
OK, now let's switch the discussion to a noise signal, which I believe
is what RA receivers really get. We tune our little crystal set to
some RA frequency. The same thing happens as with the AM signal,
correct? I realize that you said varying d.c. signal, so I presume it
is of interest to measure this 'd.c.' signal over time. I suppose we
could measure both the voltage and current, multiply them together and
derive power. Is this where we are?
Maybe this will clear things up for me. Admittedly my knowledge of how
AM and general receivers work, I get the impression from looking at
the receiver chapter (7) of Kraus' RA book again that what may be
different about receivers used in RA is that the detector operates
using a square-law detector. Perhaps this is so for AM detection?
I wrote: This is getting to be fun--as it should be! Anyway,
square-law is just a special case of rectification in the diode--the
lower part of the I-V curve for a diode has a shape close to a
square-law curve (i.e. parabolic), so it is convenient to operate the
crystal down in that region if one wants an output voltage (or
current) that is more or less linearly related to the signal power.
Getting back to the nitty-gritty, recall that the electromagnetic
noise coming from a stellar thermal source is a sequence of short
bursts of RF, of random amplitudes, random intervals between bursts,
and random SINUSOIDAL frequency components (Fourier components).
After a suitable amount of power amplification, one could simply feed
this RF power into a thermistor, thereby warming it up and measuring
its resistance change, etc. Recall that the thermistor can't
distinguish between positive and negative-going voltage or current.
Some power-meters work on this principle.
But, for somewhat faster response to changes in average signal power,
it is still more convenient to use a diode.
How is this so far?
He wrote: Well, we may be homing in on a solution.
But I need to bring up the AM analogy again. Once the detector and
low-pass filter in the post-detection part of the receiver have
removed the modulated signal from the composites waveform (consisting
of RF carrier plus audio modulation) the audio modulation is then
passed to an (audio) amplfier and then to a speaker. I hear music. In
AM, I'm not sure whether they use the square-law portion of the
detector or not. Maybe it doesn't make much difference. Suppose I want
to hear power. I wouldn't use an AM radio, at least, I don't think I
would. So I must need to do something differently to my AM receiver to
hear power. I don't know what that is. Maybe I feed the output into a
resistor and measure the power across it by computing I*V and then
send that to a recorder instead of a speaker.
Yes, the nitty-gritty part all makes sense to me. However, going back
to the AM analogy, I can't hear it, so I must want to record it
somehow. If I record every twist and turn of the sinusoidal like
noise, I think I'd run out of computer disk space or chart paper in
one big hurry. I would think I'd want to measure the power over some
period, say, 1 second, by simply (maybe not so) multiplying I and V
and integrating the result, then report that to the recording device.
Regarding thermistors, I'll have to look up how they work.
You asked "How is this so far?" Well, I'm hanging in there. I guess
I'll know how far when 1 see your response to the above.
I wrote:
1. I think that the idea of "hearing power" along with the idea that
"every twist and turn of the sinusoidal-like noise must be recorded"
are probably the two remaining significant hurdles in this discussion.
2. First, regarding "hearing power," let's try this on for size: If
the detector produces 1 volt RMS [Root Mean Square] of AM modulation
(or slowly varying d.c.) across a 1k resistor, then the average power
level being dissipated in the resistor at that instant is 1 mW. If the
resistor is replaced by earphones having an impedance of 1k, then 1 mW
is being converted into acoustic power (let's disregard possible
phase-angle and transducer efficiency effects for the moment). This 1
mW perhaps is enough--for a good pair of earphones--to hear the
modulation. Strictly speaking, I don't think we ever say that we are
listening to "voltage" or to "current". We simply say that the power
level is sufficient for the particular output device that we are
using. For example, a particular output device may require 10 volts at
0.1 mA but another one requires 0.1 volts at 10 mA--either way, we
have 1 mW. In the first case, I think we would say that the device is
mainly "voltage" driven, and in the second case it is mainly "current'
driven. Similarly, vacuum tubes were "voltage" driven whereas
transistors are "current" driven. But, where there's a voltage there
is also a current, and vice versa; and, where there is voltage along
with current, there is power.
3. Second, the waveform at the output of the low-pass filter following
the detector no longer has high-frequency (e.g. 4 GHz) components. If
the time-constant of this filter (or its upper cutoff frequency) is
long enough (let's say 10 seconds), and if we consider the reading on
a voltage-indicating meter connected to the output of this low-pass
filter, we will see a slowly varying (changes occurring in less than
10 seconds would not show up) voltage corresponding to the slowly
varying modulation envelope of the original composite signal. BUT, we
could just as easily connect a current-indicating meter and observe
the corresponding slowly varying current tracing out the modulation
envelope. Or, we could just as easily have a meter that is calibrated
in terms of power (rather than volts or amps).
How's that?
He wrote: Yes, I agree about power. I used this "hear" somewhat
metaphorically to emphasize that there seems to be a difference
between how an AM receiver works and a TPR receiver works. I realize
that probably no one is going to do RA with an AM receiver. However,
if one can modify the IF stage (I believe this is where the change
would most likely take place) to work in -- say -- a 1.42 GHz range,
then I suspect there would still be something that would not be like
TPR. That is, one would probably need to change the detector circuitry
or the post-detection circuitry. Maybe stick an integrator m the
post-detection circuitry.
Regarding the first sentence of your paragraph #2 above, I would think
it represents noise, the kind RA'ers like.
Yes, I believe that I agree with the rest of paragraph #2. It seems to
correspond to my statement above about treating the post-detection
circuitry differently. We have (mathematically) integrated the signal.
I believe we have somehow smoothed the (good) noise that has made it
(survived?) into the post-detection circuitry, thereby gives us some
(power) measurement of that noise.
By the way, I started poking around at the concept of minimum
detectable power in Kraus yesterday, pp. 7-8 to 7-11. 1 believe he
talks to the point you were making above about the post-detector
circuitry in his example on page 7-11. See ** below.
How's that? Well, "Tune will tell" (1 say that with my tongue firmly
planted m my cheek, in reference to RC constant).
Let me make a divergence on how I envision the RA signal. I believe
1.42 GHz is the frequency of ionized (?) hydrogen. If I had a single
such atom, I would see some pure signal at 1.42 GHz. However, since we
are 'seeing' clouds of hydrogen and individual atoms are excited m
slightly different ways, we see stuff coming at us over a range of
frequencies centered at 1.42 GHz. This is noise (in the sense of some
incoherent signal). To make sense out of this we are really interested
in the power of the whole mess, and not any individual signal. I'll
let you comment on that view.
** From above: I started asking myself what is the minimum detectable
signal (power) that I will be able to detect with my 10 foot dish that
is sitting out in the yard waiting for a sunny day to be assembled. I
went back to your book and looked at your back of the envelope
calculations to see the answer. I followed your calculations, but
realized I don't have a receiver to do any of those calc's with.
That's when I turned to Kraus. I was thwarted by both your practical
approach and his theoretical approach, since I really have no receiver
data to make such calc's. This isn't bad. It just made me realize, I
hope correctly, that any plan I might have to make a 'theoretical'
guess at what objects I might observe with a 10 foot dish (any, for
that matter) were not going to be easy to come by. Another way of
saying this is that unlike optical astronomy it does not seem like I
can say if I build a 12 inch mirror my limiting magnitude will be x.
I wrote:
1. Back a while ago, you said "However, going back to the AM analogy,
I can't hear it, so I must want to record it somehow." I should have
picked up on this because, in fact, that noise from a radio telescope
receiver CAN be heard, and with the greatest of ease--simply feed the
output of the post-detection filter to an adequate audio amplifier and
you will hear nice "white" noise. Actually, the post-detection filter
would not really be needed because the audio amplifier would not
respond to any frequency components that were outside its pass-band.
2. When you say "there seems to be a difference between how an AM
receiver works and how a TPR receiver works," I respond by saying that
there is NO difference as far as the output of the detector is
concerned. If a TPR is using a rectifier as a detector, then it is
thereby an AM receiver. In fact, a receiver with a label "I am a TPR"
with a bandwidth of 10 or 15 kHz or so, is tuned to your favorite AM
station, it would produce exactly the same output at its detector as
does the AM receiver at its detector.
3. When you say "I realize that probably no one is going to do RA with
an AM receiver," I think we are homing in on the target because in
fact, RA receivers ARE AM receivers--they perhaps are not all TPR's,
and perhaps are not all operating as "square-law" receivers, but they
are all surely AM!
There are a number of other points to which I would like to respond,
but let us leave those for another day. For the moment, how acceptable
are the three paragraphs above?
He wrote:
"1. Back a while ago, you said "However, going back to the AM
analogy, I can't hear it, so I must want to record it somehow." I
should have> picked up on this because, in fact, that noise CAN be
heard with the> greatest of ease--simply feed the output of the
post-detection filter to an adequate audio amplifier and you will hear
nice "white" noise.. Actually, the post-detection filter would not
really be needed because the audio amplifier would not respond to any
frequency components that were outside its pass-band."
Good.
" 2. When you say "there seems to be a difference between how an AM
receiver works and how a TPR receiver works," I respond by saying that
there is NO difference as far as the output of the detector is
concerned. If a TPR is using a rectifier as a detector, then it is
thereby an AM receiver. In fact, a TPR with a bandwidth of 10 or 15
kHz or so, tuned to your favourtie AM station, would produce exactly
the same output at its detector as does the AM receiver at its>
detector."
Good. Continuing...
" 3. When you say "I realize that probably no one is going to do RA
with an AM receiver," I think we are homing in on the target because
in fact, RA receivers ARE AM receivers--they perhaps are not all be
TPR's, and perhaps are not all operating as "square-law" receivers,
but they are all surely AM!"
Wonderful. This is good, and I think at the heart of my questions.
(Maybe I've stretched the AM metaphor or analogy past it's usefulness.
Let me go back to the last line now.)
What would I have to do to make this "AM receiver (superhet)", quite
possibly purchased from Radio Shack, into a TPR? Let's also assume
that I really want to use this receiver on the moon where there is no
attentuation that will preventme from listening to signals from, say,
Jupiter. As a part of this fiction, let's also assume there are
signals from Jupiter (noise) in the 560-1600 Khz range. I hope not
signals that contain intelligence. :-) Anyway, how do I change this
receiver to the TPR concept? I'm looking for a broad answer and not a
detailed answer. For example, I suspect you might say that the
detector must work in the square-law range, the audio amplifiers in
the post-detection phase should be replaced, and, *of course*, the
speakers should be replaced by a recorder. :-)
"There are a number of other points to which I would like to respond,
but let us leave those for another day. For the moment, how acceptable
are the three paragraphs above?"
Regardless of your answer to my question in the last paragraph, I
think we should put the TPR topic on hold. I think we are pretty much
in agreement about the basics of receivers. On to other topics ...
I wrote: Before responding to the question, I would like to emphasize
that there is NOTHING--as far as I know, anyway--SPECIAL about a TPR.
It just happens to be a receiver that maintains a given bandwidth all
the way from its input right up to the detector. In typical superhets
(whether AM or FM) the bandwidth in the front end is usually larger
than the bandwidth in the IF strip, so they are not TPR's.
Hence, to answer the question, there is NOTHING that can be done to
that Radio Shack AM receiver to make it into a TPR unless one is
willing to redo it so that the bandwidth in the IF (which could be 10
kHz or so) is equal to the bandwidth of the front end (perhaps 100 kHz
or so).
Whether a TPR operates in the square-law region or not is usually no
big problem because it is quite easy to calibrate the receiver so that
the calibrated output of the detector corresponds to input power
rather than to input voltage. As a matter of fact, the so-called
"square-law" region is not really accurate enough for some
applications and the receiver is calibrated in any case. Moreover,
since the square-law region is associated with very low d.c. voltages
(fractions of a mV), it is often enough simpler to use enough RF gain
ahead of the detector so that the detector output becomes larger; say,
fractions of a volt. The output meter scale will not be linear in
power units, but so what? We simply calibrate the thing.
He wrote
"Before responding to the question, I would like to emphasize that
there is NOTHING--as far as I know, anyway--SPECIAL about a TPR. It
just happens to be a receiver that maintains a given bandwidth all the
way from the input of the receiver right up to the detector. In
typical superhets (whether AM or FM) the bandwidth in the front end is
usually larger than the bandwidth in the IF strip, so they are not
TPR's."
Wonderful. Now we've gotten somewhere.
" Hence, to answer the question, there is NOTHING that can be done to>
that Radio Shack AM receiver to make it into a TPR unless one is
willing to redo it so that the bandwidth in the IF (which could be 10
kHz or so) is equal to the bandwidth of the front end (perhaps 100 kHz
or so). Whether a TPR operates in the square-law region or not is
usually no big problem because it is quite easy to calibrate the
receiver so that the calibrated output of the detector corresponds to
input power rather than to input voltage."
Good. Now we're cookin'.
" As a matter of fact, the so-called "square-law" region is not
really> accurate enough for some applications and the receiver is
calibrated in any case. Moreover, since the square-law region is
associated with very low d.c. voltages (fractions of a mV), it is
often enough simpler to use enough RF gain ahead of the detector so
that the detector output is larger; say, fractions of a volt. The
output meter scale will not be linear in power units, but so what? We
simply calibrate the thing."
Teriffic. I think you've given me a good insight into all this. I'll
want to review more throughly receiver construction/design, but I
think we've just moved back into the ballpark.
We can probably go off to new subjects. I think you said you had some
comments on a few tangential subjects I brought up a few messages ago.
I suspect that they may concern minimum detectable power and possible
RA signal sources (probably my broad reference to 1.42GHz).
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Updated Feb. 17, 2000, by Ian McCarthy.