SM 5 BSZ - A general discussion on radio receivers.
(Oct 05 2002)

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.

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

Losses=5dB (gain=0.315 times in power )
Output noise temp =0.315*107500 + ( 1 - . 315 ) * 290 = 34061K

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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