Signal and modulation. Basic concepts.
Before trying to understand the radio receiver it is a good
idea to think about the fundamentals.
What is a signal, and how is the signal converted to
some other kind of signal by the modulation process ?
The terminology is sometimes confusing.
Modulator/demodulator is sometimes used arbitrarily for
voice SSB transmitters and receivers.
In case the audio output of an SSB receiver is used as
the input to another (perhaps digital) SSB receiver, the SSB
demodulator (product detector) is just another frequency
mixer in the signal path while the last mixer (perhaps digital)
becomes the "SSB demodulator".
Using the word modulation for the process of varying
some characteristic of a carrier wave in accordance with
a signal to be conveyed has long historical roots but it is
not well suited to give good understanding of the process
of conveying messages via radio transmissions.
Likewise demodulation for the process of deriving the
original modulation signal from a modulated carrier wave does
not define a very useful concept for our understanding.
With voice communication as an example, the signal
is the timevarying voltage at the microphone connector of the transmitter.
This signal is an audio signal,
and the voltage is a single-valued signed quantity that
varies with time.
The transmitter converts the audio signal delivered by the
microphone to a RF (radio frequency) signal which
is sent to the antenna, transmitted as free radio waves and
received by the receive antenna that catches the
signal for the receiver, as a weak copy of the transmitted
RF signal.
The receiver is responsible for removing undesired signals
(caused by other radio waves) and for converting the RF signal back to
an audio signal.
Note that the word "converting" is used.
The concepts of modulation and demodulation involve a carrier.
The carrier was a natural concept in old radio technology but
it is arbitrary and may be confusing in a more general treatment
of signals and various processes applied to them by analog or digital
hardware.
To understand
the arbitrariness of the carrier
look at different ways to produce and describe Morse code CW
transmissions.
The fundamental operations of a receiver
Amplification = "Make the signal bigger".
An ideal amplifier makes an output signal that differs from
the input signal only in that the voltage is multiplied by
some constant factor. It may also lower the impedance of the
signal.
Vout = k * Vin
Real amplifiers have all sorts of limitations.
Handling the limitations well is one of the most important
aspects of receiver design.
Filtering = "Attenuate interference"
The ideal filter does not affect the desired signal at all.
All signals with frequencies within the passband are unaffected
while frequencies outside the passband do not pass through the filter.
Real filters attenuate the desired signal somewhat and do not
have infinite attenuation in the stop band.
For analog receivers good crystal filters are available
and in digital receivers it is possible to implement
nearly ideal filters.
Adequate filtering is no longer the most difficult part in receiver design.
Frequency conversion = "Move the signal to another frequency"
The ideal frequency converter changes the frequencies of all signals
by an equal amount without changing them in any other way.
Frequency conversion is difficult in analog receivers while it
is trivial in digital circuits.
Frequency conversion as well as the sampling, the conversion
from analog to digital in a digital radio involves a local oscillator.
The local oscillator is never ideal; it has noise sidebands and spurs
that degrade receiver performance.
Frequency conversion including A/D conversion is the most critical
function of radio receivers.
Besides the difficulties caused by the impurities of the local
oscillator, mixers and A/D converters have the same problems as
amplifiers have - but they are usually more difficult.
The ideal amplification, the ideal filtering and the ideal frequency converting
are all linear processes.
Other operations A receiver may use additional operations
like gating out impulse noise.
It may also perform other non-linear operations like AM or FM detection
although AM is better received by use of linear processes only
(with one sideband for each ear)
In digital receivers a lot of new interference reduction methods
may be introduced.
Wideband interference from electrical discharges can be characterized
using large bandwidth which improves the S/N of the interference itself.
Once characterized properly the contribution of such signals in the
desired narrow passband can be canceled efficiently.
Unintended transmissions like modulation splatter from strong signals
at nearby frequencies can be canceled efficiently.
The receiver may build a model of the non-linearities of the offending
transmitter and use the extremely good S/N of its main signal
to calculate the splatter which is then used for cancellation.
The linear receiver
The ideal receiver for weak signals is the linear receiver.
It uses linear processes only and it may be implemented in analog or
digital hardware or some combination.
The ideal receiver will be completely quiet, the output should be zero,
if a resistor that is kept at a temperature of -273 degrees Celsius
( 0 degrees Kelvin, "absolute zero") is connected to its input.
In case something else is connected (an antenna) the ideal receiver
will select a narrow part of the frequency spectrum, amplify it
and convert it to the audio frequency band.
That is all!
Linear processes may be applied in any order.
They may be split in several linear processes applied after each
other in any order.
Due to the limitations of the building blocks available one has to
use many linear processes to realize something that is nearly
an ideal linear receiver.
Below is a list of the most important building blocks of a receiver
for 144MHz which is probably the most difficult band with respect
to the fact that a very low noise figure is useful at the same time
as very strong interference may be present, consisting of both in-band
and out-of-band signals.
Note that the goal is to come as close as possible to an ideal receiver
so there are no compromises "just in case".
If compromises are required, they should be made with full awareness
of what the conflicting desires are, so that no valuable performance
features are thrown away in vain.
For EME (moonbounce, reflecting signals off the moon) it is
essential to have a receiver with a performance close to that of
an ideal receiver.
When morse coded messages are received at a level where many
repetitions are required, a small degradation of S/N
(signal-to-noise ratio) will have large effects.
Improving S/N as little as 0.2dB (5% in terms of power)
may be the difference between success and failure.
In "regular" communication an improvement of 1dB in
S/N can not be noticed at all.
Degrading the noise floor by a single dB makes it much easier
to improve immunity against cross-modulation and overload.
1. The input amplifier
The input amplifier should not add any significant noise to
the signal received from the antenna and it should not saturate
from strong signals that may be present.
Noise is best expressed as a noise temperature because noise
temperatures are additive.
Look here for some more info
on noise figures and noise temperatures
Obtaining near ideal noise performance of a receiver while
maintaining good immunity to cross-modulation and overloading
requires a good understanding of the problems involved.
Look at this link preamplifier design
which mainly discusses the input circuitry and the trade-off
between noise figure and selectivity and how that relates
to the LC ratio.
The discussion is relevant to higher bands where often too
low impedance levels are chosen for the input filters.
A 50 ohm transmission line high Q resonator may provide
unnecessarily good filtering while it degrades the noise
temperature too much.
A higher impedance for the input filter gives lower noise
and should be a good choice at 432 and 1296MHz where the
low sky temperature makes low system noise particularly important.
Once the compromise between noise performance and overload
characteristics has been decided one should be sure the preamplifier
is as close to ideal as possible for the particular device and technology.
The famous "Murphy's law" says something one should not forget.......
It is a good idea to place
an overload detector
at the output of all amplifiers that are followed by filters.
The need for a filter directly after the preamplifier is discussed below.
2. The second RF amplifier
The gain of the preamplifier is not sufficient to overcome
the noise floor of the first converting process
which is a frequency mixer in today's technology.
Some time in the future it will probably be an A/D converter.
Even though it is possible to make wideband amplifiers that allow
enough power output to make saturation impossible by the
RF power that can be delivered by the preamplifier it is generally
a good idea to insert some selectivity between the preamplifier
and the second RF stage.
Since this filter is not really needed there is no reason to
make it complicated or to allow much attenuation
within the passband.
The pre-amplifier is normally located very close to the antenna
while the rest of the receiver is placed indoors so there is an
attenuator in the form of a long cable between the preamplifier
and the second RF stage.
High preamplifier gain and low noise figure of the second
RF amplifier as well as modest losses are required for near ideal
performance.
Table 1 shows data for 144MHz.
The noise figure of the second RF amplifier includes all
the losses between the preamplifier and the second amplifier.
Attenuators inserted before an amplifier degrade the noise figure
equal to their attenuation.
---------------------------------------------------------
Preamp | Second amp + loss | S/N loss |
gain | NF T T(ant)| At 215K At 272K |
(dB) | (dB) (K) (K) | (dB) (dB) |
--------------------------------------------------------|
15 | 1 75K 2.4K | 0.04 0.03 |
15 | 2 170K 5.4K | 0.11 0.09 |
15 | 3 290K 9.2K | 0.18 0.13 |
15 | 4 439K 14K | 0.27 0.22 |
15 | 5 627K 20K | 0.39 0.31 |
15 | 6 870K 28K | 0.53 0.41 |
20 | 1 75K 0.8K | 0.01 0.01 |
20 | 2 170K 1.7K | 0.03 0.03 |
20 | 3 290K 2.9K | 0.06 0.05 |
20 | 4 439K 4.4K | 0.09 0.07 |
20 | 5 627K 6.3K | 0.12 0.10 |
20 | 6 870K 8.7K | 0.17 0.14 |
20 | 10 2610K 26K | 0.50 0.40 |
25 | 1 75K 0.2K | 0.00 0.00 |
25 | 2 170K 0.5K | 0.01 0.01 |
25 | 3 290K 0.9K | 0.02 0.02 |
25 | 4 439K 1.4K | 0.03 0.02 |
25 | 5 627K 2.0K | 0.04 0.03 |
25 | 6 870K 2.8K | 0.06 0.05 |
25 | 10 2610K 8.2K | 0.16 0.13 |
30 | 10 2610 2.6K | 0.05 0.04 |
---------------------------------------------------------
Table 1.Degradation caused by the second RF amplifier.
The noise temperature caused by antenna and preamp are assumed
as follows:
Sky 167K 167K
Sidelobes 15K 40K
Antenna losses 5K 5K
Cable+relay 13K (0.2dB loss) 30K (0.4dB loss)
Preamp 15K (0.22dB NF) 30K (0.4dB NF)
Total 215K 272K
To obtain good dynamic range further down the signal
path it will be necessary to allow some contributions to
system noise from some more amplifier stages.
To keep the total excess noise low all the contributions
have to be very small, say 3K for each stage.
An inspection of table 1 shows that even on 144MHz where the
antenna temperature is not very low, the gain
of the preamplifier has to be at least 20 dB.
To allow 3dB cable/filter losses and a second RF amplifier NF of
2dB the preamplifier gain has to be 25dB.
A neutralized GAS-FET with power-matched output has a gain in
the order of 30dB and it allows 8dB combined filter and cable
attenuation if the second amplifier has a noise figure of 2dB.
Such a receiver front end does not have an optimum third order intercept
point for in-band signals, but performance is usually good enough for
practical purposes.
A
two tone test of an MGF1801 amplifier
shows a mediocre third order intercept
point of 0dBm at the input.
Signals up to about -30dBm can be allowed without serious
problems (two -30dBm signals give third order IMD spurs
corresponding to -83dBm at the input.
The noise floor is at -175dBm/Hz and to not destroy weak signal
operation the interfering stations have to have their noise
sidebands below -145dBc/Hz.
Amateur radio equipment is not quite that good as far as I know.
Should it turn out to be desirable, then it is not difficult to improve
in band IM3 of the preamplifier by noiseless feedback and a second
preamplifier using a device running at higher power, also with
feedback.
Table 2 shows the characteristics of a near ideal receiver based
on the output power matched MGF1801.
PREAMP
Antenna temperature = 200K
Preamp NF=0.2dB=15K
Preamp gain=27dB = 500 times in power
Noise temp at output of preamp=(200+15)*500=107500K
Input intercept point=0dBm
Saturated power output = 18 dBm
CABLE/FILTER
Losses=5dB (gain=0.315 times in power )
Output noise temp =0.315*107500 + ( 1 - . 315 ) * 290 = 34061K
SECOND RF AMPLIFIER
NF=2dB=170K
Noise temp at input=34061 + 170 = 34231K
Preamp intercept point at input = 0 + 27 - 5 = 22dBm
Saturated power input = 18 - 5 = 13dBm
Table 2. Typical use of an output power matched MGF1801 as
preamplifier if negligible system noise degradation is desired.
From the data in table 2 we can get the noise temperature at the input of the
second RF amplifier referred to the antenna input.
Trx = 34231 / ( 0.315 * 500 ) = 217.3
The contribution from the second stage is 2.3K.
The amount of gain required in the second RF amplifier will of course
depend strongly on what noise figure the next stage has.
The gain and output intercept point required for the
second RF amplifier is listed in table 3 for different assumptions
of the noise figure for the next step, usually a Schottky mixer.
Amplifiers with a noise figure of 2 dB and saturated power outputs up to
two watts are not difficult to design.
Saturated Min output
NF Temp | Gain power out IP3
(dB) (K) | (dB) (dBm) (dBm)
6 865 | 4.4 17.4 26.4
9 2013 | 8.1 21.1 30.1
12 4307 | 11.4 24.4 33.4
15 8880 | 14.5 27.5 36.5
18 18009 | 17.6 30.6 39.6
21 36221 | 20.6 33.6 42.6
Table 3.Gain, output power and third order
intercept point required in RF amplifier 2 for different
noise figures of the third stage to make third stage
contribute with 2K at the antenna input.
This table is based on the data of table 2.
3. The RF bandpass filter
The first conversion, be it an A/D-converter or a Schottky
mixer has spurious responses.
A filter with adequate suppression for signals on the
spurious frequencies has to be inserted in the signal path
before the first conversion step.
If necessary the RF bandpass filter can be made very narrow
with high attenuation in the passband.
Any attenuation caused by the bandpass filter adds to the
noise figure of the third stage which leads to the need for a
bigger transistor in the second RF stage as shown in table 2.
When using radio A/D converters with today's technology the
sampling speed is typically 50 to 100MHz.
All frequencies between 0 and 200MHz will fall between 0 and
half the sampling frequency in the digital data.
The RF bandpass filter must allow only one set of alias frequencies
to reach the A/D-converter.
When using a local oscillator and a frequency mixer for the
first conversion, the RF filter has to suppress not only the
mirror frequency but also the frequencies that would mix with
the LO overtones and give an output at the IF frequency.
A narrow RF filter will also suppress false responses caused
by spurs that may be present in the LO signal.
There are more reasons for a narrow RF filter,
see below.
4. The first conversion.
A/D converter or schottky diode mixer.
Some day an A/D-converter will be the first mixer in receivers up to
hundreds MHz.
Today's (year 2001) technology allows 14bit at 65MHz sampling frequency
using for example AD6644 from Analog Devices.
Such a chip offers typically 74dB S/N at a bandwidth of 32.5 MHz corresponding
to 150dBc/Hz at saturation (74dB is at 1dB from saturation).
The peak-to-peak amplitude such a device needs for full range is 2.2V
corresponding to about 11dBm in a 50 ohm load.
The noise floor is then at -138dBm/Hz which corresponds to a noise
figure of 37dB all referenced to a 50 ohm load.
(The input impedance of AD6644 is 1000 ohms so the power actually
consumed by the chip is -2dBm for full scale and the noise
figure is about 30dB when referenced to 1000 ohms).
The AD6644 receives noise from nearly 10 times more bandwidth and
it is not possible to lower the noise figure by more than about 6dB
without using a selective amplifier or without degrading the dynamic range.
Allowing 3dB loss for the RF filter, table 3 shows that the AD6644
will need 39.6dB gain in the second RF stage if the AD6644 is
terminated in a 50 ohm resistor.
Saturation will occur at 14dBm, 38.6 dB below the level where
the MGF1801 saturates.
Two signals at 7dBm will give third order intermodulation products
at -83dBm which means that the third order intercept point is
at 52dBm.
This corresponds to -9.6dBm at the antenna input,
which is only 9.6dB worse compared to the MGF1801 preamplifier.
High level Schottky mixers (level 23 from Mini-Circuits)) have third
order intercept points around 30dBm and 1dB compression at around 15dBm.
Selecting 10dB gain for the second RF amplifier using some transistor
that can deliver 200mW (23dBm) through the RF filter and impedance
matching network required by the mixer will make a level 23 mixer
saturate just before the preamplifier with a third order
intercept point around -2dBm at the input.
Since mixers attenuate by about 8dB and the noise figure at the mixer
input has to be maximum 10.4dB, the amplifier after the mixer
must have very low noise to not degrade the system noise figure.
Compensating poor noise figure in the IF amplifier by more gain in the
second RF amplifier will degrade system intercept point.
It follows from the discussion above that the MGF1801 power matched
and neutralized amplifier is good enough when it comes to power handling
capabilities.
A 10dB improvement is not difficult by noiseless feed back, but to
utilize the improvement one has to design very special low-noise,
high-level mixer/IF combinations.
The radio A/D-converter has superb linearity.
IP3 is only about 8dB lower compared to a well designed level 23
Schottky mixer.
A Schottky diode mixer can be driven into the non linear region
by a single very strong interfering signal without any serious
degradation for a desired weak signal while the A/D-converter
produces useless data when saturated.
Saturation comes about 36dB earlier in an AD6644 so if there
is only one interfering signal, the Schottky diode mixer
would stand about a 30dB higher interference level.
It is quite clear that already today's A/D-technology is extremely
attractive.
Who will interface it to the PC?
In case the Schottky mixer is not properly terminated
the dynamic range is easily 20dB lower.
Read here about
using Schottky diode mixers
5. The first local oscillator
If the first conversion is realized with an A/D-converter, the first LO
is the sampling clock which has a fixed frequency.
The first LO will be at a fixed frequency also when
a Schottky mixer is used in conjunction with a wideband IF.
Typically an LO frequency of 116MHz is used to convert
144MHz to 28MHz.
Fixed frequency oscillators using X-tals can be made with
very low phase noise.
It may seem very simple to use a 12.88888MHz X-tal and two
frequency triplers to produce 116MHz.
Good filtering is required however because 13 x 12.88888 =
167.55 which may cause a spurious response at 139.55 which
may not be suppressed much by the RF filters.
Good filters with two LC circuits to make the output
of all frequency multiplier stages pure will prevent this problem.
When the first IF is routed to a narrow filter at typically
9MHz or 10.7MHz the first LO has to have variable frequency.
It is very difficult to make good variable frequency oscillators.
Therefore the first LO is usually the limiting factor for receiver
dynamic range in well designed receivers when the first
IF has narrow bandwidth.
There are many articles in amateur literature on the
design of low noise frequency synthesizers for LO use.
Selecting a good frequency for the first local oscillator
is not easy.
There are many problems.
For example using 116 MHz to convert 144 MHz to 28 MHz has the
following problem:
A signal at 145.3 MHz will produce its main signal
at the IF port at 29.3 MHz.
If the signal is very strong, the third overtone of the
IF signal at 87.9 MHz will be present inside the mixer where it will
be mixed with 116 MHz to produce a false signal at 28.1 MHz
that will cause interfere for signals at 144.1 MHz.
Another way to explain the same spurious response is to say that
the third overtone of the RF signal at 435.9 MHz mixes with the fourth
overtone of the LO at 464 MHz to produce a false IF signal at 28.1 MHz.
There will always be combinations of overtones of the IF signal
and the LO or its overtones that fall within the IF passband
causing spurs at some frequencies.
In order to minimize the problems caused by such spurs it is a good idea to
avoid LO/IF combinations that give spurs like this of low order
and it is also a good idea to not make the RF passband wider than
necessary.
6.Wideband IF filters and amplifiers
The problem to amplify and filter the signal present at the
output of the first mixer is identical to the problem
of designing the RF amplifier and RF filter section.
The noise figure does not have to be as low - the only
reason to have a very low noise figure is to get good dynamic
range.
If the IF amplifier has a noise figure of 0.6dB = 43K the
stage limiting the dynamic range will be allowed to contribute
with 127K for the IF noise figure to become 2dB.
If the IF amplifier has a noise figure of 1.6dB =130K
the gain of the IF amplifier has to be increased by 5dB to
keep the IF noise figure at 2dB.
That would be a bad idea. It is better to increase RF gain and
accept a worse IF noise figure.
The purpose of the wideband IF filter is to suppress
the mirror frequency and the spurious responses of the next
frequency conversion.
The first wideband IF filter may also be used to shape
the pulse response of the receiver to allow an efficient
noise blanker.
A wide bandwidth with more or less gaussian frequency response
makes interference pulses very short and allows an efficient
noise blanker.
7. Conversion to the baseband.
The conversion to the baseband is normally incomplete in analog
receivers.
The baseband signal is a complex signal that has two components,
in-phase (I) and quadrature (Q).
The two signals I and Q contain the same frequencies and their
phase relation contains information about the signal
in the baseband, i.e. whether its spectrum is above or below the
frequency of the last LO (the BFO).
In analog receivers one uses a narrow filter (the last IF filter)
to ensure that no signal is present on the image side of the last LO so
one is sure any signal present in the baseband must be due to signals
on the wanted side of the LO.
Consequently there is no need to produce both I and Q because their
phase relation will give no new information at all.
An analog receiver for AM (amplitude modulation) may convert
the IF signal to a complete baseband signal with both I and Q.
If the frequency of the LO is very close to the carrier of the
AM signal, the Q signal can be used to control the last LO's frequency
through a low pass filter.
This way the LO becomes phase locked to the carrier and the modulation
is in the I signal only.
The noise in the Q channel will not contribute and some improvement
in the received signal's S/N ratio is possible this way.
Digital signal processing is easier (more efficient) in the baseband
with complex signals.
There are several different ways to go from RF to the digital baseband
I/Q-pair.
Sampling at RF frequencies
In case the RF signal is fed to a AD6644 sampling at 65MHz, a 144MHz
signal will reflect at 14MHz in the digital data stream.
A general purpose DSP or a modern PC computer is not fast enough
to process data at 65MHz.
There is a chip AD6620 (Analog Devices) that does frequency mixing
to the baseband by multiplying the input samples with a sine/cosine
function at the frequency specified by the user.
The AD6620 is normally used to sample the RF signal directly so the input
data stream is real data.
To listen to 144MHz for weak signals one would make the internal
digital oscillator of the chip operate at 14.15MHz typically,
(which would correspond to 144.15MHz).
The 14.0MHz signal corresponding to 144.0 is then converted to
two signals at 150kHz with a phase shift of 90 degrees between them.
14.3 MHz corresponding to 144.3 MHz will also be converted to two
signals at 150kHz but with the opposite phase shift.
Due to the precise phase and amplitude relations possible in digital
circuits these two signals can be completely separated in
later processing stages.
The AD6620 is normally used to sample the RF signal directly so the input
data stream is real data.
This means that besides the difference frequency 150kHz, the sum
frequencies around 28.15MHz will be generated in the digital data stream.
The AD6620 contains decimating filters that gradually bring the sampling
speed down.
The internal resolution of the AD6620 is 23 bits.
When the sampling rate is reduced, more bits are needed in
order to not degrade the dynamic range. The AD 6620 with
14 bits at 65MHz sampling speed corresponds to:
No of bits to retain AD6644 dynamic range
at different sampling speeds.
Speed No of bits S/N
65MHz 14 74dB
16MHz 15 80dB
4MHz 16 86dB
1MHz 17 92dB
250kHz 18 98dB
63kHz 19 104dB
16kHz 20 110dB
The noise floor of the AD 6644 is at -149 dBc/Hz.
I have no practical experience with AD6644 and AD6620.
With a rather more complicated soundboard solution
High performance hardware for Linrad
it is possible to get a noise floor that is similar when using a
modified Delta44 soundboard.
The soundboard based solution is at least 15dB better than the AD6644
and AD6620 combination for signals immediately outside the passband
seen by the A/D-converter.
Sampling at audio frequencies
When using an audio board to convert from analog to digital form
there are two ways to go.
One is to filter out a well defined passband by means of an IF
filter with steep skirts that will allow a very good suppression
of the image frequency on the other side of the LO frequency.
In this case a single mixer and one A/D converter channel is required
for each RF channel.
With a standard audio board, sampling at 44.1 kHz one can receive
two independent signals this way at bandwidths up to about 20kHz.
For a practical implementation look at
pc dsp for MSDOS
When the A/D converter is sampling real data (the filter method)
the conversion to complex data is done in the computer.
The other way is to produce the baseband complex pair I and Q in
analog hardware (direct conversion radio) in which case two
audio channels are needed for each RF signal.
Creating the baseband signal in analog hardware saves some computer time
and gives more bandwidth, twice as much due to the use of two
audio channels.
It is advantageous to not have to design sophisticated IF filters.
Here are two versions of direct conversion radios:
Very low cost radio
Optimized direct conversion receiver for 144 MHz
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