N1OOQ Receiver Design

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http://www.geocities.com/capecanaveral/lab/3955/N1OOQ.html#N1OOQ%20RX%207

N1OOQ Receiver Design

These N1OOQ RX postings are intended to be a learning exercise for the
QRP-L folks, so if you have questions or comments, post them!
How's the level of detail? Too much or too little?

==============================================================================
Tom Randolph N1OOQ NE-QRP 419 QRP-L 87 ARRL randolph@asic.enet.dec.com
==============================================================================

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Chapters:

1. Basic Receiver Scheme, First IF Choice

2. Second IF Choice, Spurious Responses

3. Images and Spurs for All Bands

4. Block Diagram, Filter Tradeoffs

5. Mixer Tradeoffs, IMD, Intercepts

6. More Mixer Tradeoffs, Noise, Dynamic Range

   1. Reader Comments on Chapter 6

7. Diplexer Tradeoffs

8. Reader Comments

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N1OOQ RX #1: Basic receiver scheme, 1st IF choice

Let's start with the basic conversion scheme of this RX, and why I did it that way. The design inspirations were the big receiver projects in the ARRL book, "Solid State Design for the Radio Amateur". Get that book if you don't have it. It's a gold mine for the measly $10 or so. The 160m receiver with band converters in the Advanced Receiver Concepts chapter is the W1FB "His Eminence" receiver. The W7ZOI contest grade CW station is at the back of the book. Both first appeared in QST in the 70s.

I should note that this design isn't really up to the latest and greatest methods of RX design. Quieter and more linear designs exist or are in development by amateurs. Quieter means you hear more signals that are really there, because the radio doesn't lose them in it's own noise. More linear means that the radio itself generates less signals that aren't really there, because the circuits are designed to enhance only the real signals and to supress the spurious ones originating in the circuits themselves. Also, this is not going to be a portable radio! It'll probably draw something like 300-500 mA from the 12V supply. It will be a good performer, though (I hope, anyway! The design is entirely on paper at this date.)

I used the W1FB idea of a single-band RX with converters for my RX. This is one method of designing a dual-conversion RX. It's similar to what a transverter does on receive. The first conversion is from whatever band you're listening to, say 20m, to the band of the RX, 32 MHz in my RX. This is an easy way to get any signal in the MF/HF spectrum into your RX. Rather than having to tune all ham bands 1.8-29.7 MHz, the radio only needs to tune a single band, 32 MHz. The band converter for 20m doesn't need to do any tuning. It just converts the whole 20m band, 14.0-14.35 right up to 32.0-32.35, where the radio can tune it. This 32 MHz band is the 1st IF, the 1st intermediate frequency. Any band you want to listen to can be converted to this band, where the radio can easily deal with it.

The selection of what 1st IF freq to use is based on the nature of the circuit used to do the converting - a mixer. Mixers will take any two input frequencies and "mix" them to get two different output frequencies:

input1+input2, and input1-input2.

One of these output frequencies is our IF, and the other gets filtered out by the IF circuits, for instance:

18+14 = 32, 18-14 = 4.

The 18 MHz freq is known as the LO, the local oscillator. Our 20m band module will have an 18 MHz oscillator in it. As I said, the mixer will take ANY two frequencies and mix them to get the output frequencies, so we must ask: Can any other input frequency on our antenna mix with the local oscillator to give us an output at the IF? The answer can be had by adding and subtracting the LO from the IF freq:

32-18=14 MHz, our RF freq
32+18=50 Mhz

This 50 MHz freq is called the image. A signal at the image freq will be heard in our receiver if we don't filter it out. The filter before the mixer which performs this function is often called the pre-selector. The image rejection of the receiver is the measure of how attenuated this signal will be compared to the signal we want to receive. If we pick a low IF freq, the image will be nearby. Suppose we use 160m, 2 MHz, as the IF, as W1FB did in the "His Eminence" receiver:

Our LO for 20m is: 14-2=12 MHz

2+12=14 MHz, our RF freq
2-12=-10 MHz, our image freq

The -10 is valid. The signs don't matter much, becuase of the +/- nature of the output of the mixer: 12 +/- 10 indeed gives us outputs at 2 and 22 MHz. So the image is at 10 MHz - not all that far away from the desired signal at 14 MHz. It's difficult to construct filters that attenuate this image without killing the desired signal. In my RX, the image is at 50 MHz, while the desired signal is at 14 MHz. This is easily filtered without hurting the 14 MHz signal. I expect excelent image rejection on 20m.

Our mixer has two input signals: the LO, and the RF, which is the signal we want to listen to. BOTH of these signals have images, but so far we've only dealt with the LO image. If we take the IF +/- the RF:

32-14=18 MHz, our LO
32+14=46 MHz, our RF image

This is another frequency we must filter out if we don't want to hear it in our RX. It's right up there with the 50 MHz LO image, so it shouldn't be a problem. Note that this image will only appear if there are incoming signals from the antenna at 14 and 46 MHz at the same time, making it less of a problem than the 50 Mhz image, which would appear every time a signal at 50 MHz arrived at the antenna.

There is yet one more thing to think about. What if a signal appears on the antenna at our IF freq, 32 MHz? This could leak through the mixer and right into the radio. If our 1st IF is at an HF freq, it's too near the signals we want to hear to easily filter. Moving the IF up into the VHF range eliminates the problem. IF rejection is another spec you see on radio maufacturer's data sheets, and in magazine test reports.

We now need to filter 32, 46, and 50 MHz when receiving 14 MHz. This is easy: construct a lowpass filter that cuts off at something like 16 MHz. It will have very high attenuation at those freqs. This is why a VHF 1st IF is a good idea. It's easy to get rid of a lot of crud that otherwise would require very tight, hard to build filters on every band module.

I picked this particular VHF frequency because the LO freqs for many of the ham bands will fall on common microprocessor crystal or oscillator freqs, or can be gotten by doubling a microprocessor crystal freq. Only a couple of custom crystals will be needed, for 160m and 80m. Also, 32 MHz isn't too terribly high up in the VHF range, so the actual layout of the 32 MHz circuits won't be too critical. I didn't want to have to deal with chip caps and the like in my 1st IF circuits.

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N1OOQ RX #2: 2nd IF choice, spurious responses

The basic receiver will be a superhet that tunes a small band at 32 MHz. We need to pick an IF freq, which will actually be the 2nd IF. The same criteria apply: we want the IF to be a good way away from the received band for decent image rejection and IF rejection. In this case, after the first conversion, it's all much less critical. The incoming signals have been filtered to a certain bandwidth by the band module pre-selector, converted to 32 MHz, and again filtered to a definite bandwidth, so we have only a relatively small chunk of spectrum around 32 MHz to deal with. Any signal that might cause an image or IF feedthrough response has been substantially attenuated.

32 MHz being up in the VHF, almost any lower HF freq will do for a 2nd IF for good image and IF rejection. Another problem, again originating in the nature of the mixer, is spurious signals. Mixers generate low-level harmonics of both input signals, and these cause low-level outputs on their sum and difference freqs. Any of these that happen to fall near our IF will be heard in the receiver as a spurious signal: one that doesn't really exist. Obviously, it would be in our best interest to pick a low HF range 2nd IF that causes a minimum of spurious outputs.

Unfortunately, there's no easy way to do this. Software exists to help with the process, but a lot of cut-and-try is required. The classic way is to form a table:

          | RF x1     x2     x3     x4     x5     x6     x7
          |    32     64     96     128    160    192    224
----------+--------------------------------------------------
LO x1 20  |   52,12  84,44  116,76  . . .
   x2 40  |   72,8   104,24
   x3 60  |   92,28
   x4 80  |   .
   x5 100 |   .
   x6 120 |   .
   x7 140 |                        268,12
   x8 160 |
   x9 180 |                                      372,12

The table can be extended out to any arbitrary size, but after about the 9th harmonic the spurs start to get too weak to worry about. For the 12 MHz 2nd IF we'll need a 20 MHz LO. The mixer products above show us that a couple of spurs will be present: 7xLO - 4xRF, and 6xRF - 9xLO. These are both fairly high harmonics, so will be weak if audible. How weak? Looking at the tables in a catalog of commercial double-balanced mixers gives us numbers in the -60 to -75 dB range for these particular spurs - around 10 s-units below the real RF signal, at 6 dB per s-unit. This is a decent IF freq. Most others I tried had substantially more spurs. A double-balanced mixer is a mixer specifically designed to cancel the harmonics that cause these problems, which is why the spurious products are so small.

We can figure out what incoming RF freq will cause the spur. The spur will only be audible when that RF freq is within the passband of the receiver.

7xLO - 4xRF = IF                        6xRF - 9xLO = IF
 140 - 4xRF = 12                        6xRF -  180 = 12
       4xRF = 140 - 12                         6xRF = 12 + 180
         RF = (140 - 12)/4                       RF = (12 + 180)/6
            = 32.0                                  = 32.0

These will only be audible when the receiver is tuned within a KHz or two of 32.0 MHz, the bottom edge of the band, and there's a signal there. This probably isn't a big problem. The bottom edge of every band will get converted in its particular band module to 32.0 MHz, so the spur will always be at the bottom edge of the particular band: 3.50 MHz, 7.00 MHz, 14.00 MHz, etc.

There's one more thing to think about for this 2nd IF: we will be building crystal filters at this freq, and we'll need a BFO at this freq. The crystal filters will determine the bandwidth of the receiver: 500 Hz for CW, 2500 Hz for SSB. If we want to use commonly available microprocessor crystals, we want the IF to be on one of those freqs. We have a wide selection between 1 and 24 MHz. I tried a few different freqs before settling on 12 MHz.

We could get rid of one of the spurs by picking a slightly different IF. 12.288 MHz crystals are available. The other spur would move up into the band we want to listen to, though. Also, we lose our nice 20 MHz LO. As is, we can count the LO freq and ignore the first two digits to get our exact RF freq. With a 12.288 MHz IF and a 19.712 MHz LO, we cant. There are now programmable digital freq readouts for sale that can handle this, though.

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N1OOQ RX #3: images and spurs for all bands

In no. 1, we determined that the image and IF rejection on 20m would be good. ALL of the bands will have their own image and IF rejection numbers. In no. 2, we looked at spurious output from the 2nd mixer. ALL of our mixers will have similar spurs. To be thorough, we should check all of this.

IMAGES that will mix to 32.000 MHz
band   bottom edge   LO   LO image   RF image
----------------------------------------------
160       1800      30200   62200    33800
 80       3500      28500   60500    35500
 40       7000      25000   57000    39000
 30      10000      22000   54000    42000
 20      14000      18000   50000    46000
 17      18000      14000   46000    50000

A filter that cuts off everything above about 19 MHz would be more than adequate to kill all of these images and the 1st IF of 32.0 MHz. We should be able to get excellent image rejection and IF rejection on all six bands.

1ST MIXER PRODUCTS at or near 32.000 MHz
band   LO x   RF x   @ RF of   ~ dB down
------------------------------------------
160     -      -

 80     0      9       3555     >85
        2      7       3555     >85
        
 40     1      8       7125     >85
        3      6       7125     >85

 30     -      -

 20     8      8      14000     >85

 17     8      8      18000     >85
------------------------------------------
 15     1      2      21500      45
        3      0        -        10   (birdie at 33.0 MHz)
        
 12     9      4      24200      60
 
 10     6      2      28000      55
        8      0        -        35   (birdie at 32.0 MHz)

I cheated a bit and used a PC program to find these spurs, but a table, such as in article no. 2, for each band would work. Our six bands have only a few very weak spurs. This is good, as the 1st IF is wideband and untuned. That means these spurs will be audible across the entire band if RF hits the antenna at the freq listed. There's nothing stopping energy anywhere in the particular band from getting into the 1st mixer, and the LO will always be at the same freq, ready to mix it to 32.0 MHz. If there's a megawatt shortwave broadcaster on 7125 at night, I could be in trouble on 40m!

I included the three high bands to show one reason why I decided to drop them. Some big harmonics of the LO for 15m and 10m would be very close to the 1st IF. These birdies would suck up a lot of the available power in the IF amp. This would leave little available power to amplify the signal we actually want to listen to, making our receiver deaf! In the 10m case, the birdie is right on the IF freq. We'd be able to hear it, good and loud!

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N1OOQ RX #4: block diagram, filter tradeoffs

Ok, at this point we've gone far enough along with the verbal description that it's time to attempt a partial block diagram:

   preselector  mixer  diplexer   amp   preselector  mixer  diplexer   amp 

                                   |\                                   |\ 
      +-----+           +---+32 MHz| \     +-----+           +---+12 MHz| \
 a    |  _  |     -     |   |----->|  \    |  _  |     -     |   |----->|  \
 n--->| / \ |--->|X|--->|   |      |  /--->| / \ |--->|X|--->|   |      |  /
 t    |     |     -     |   |--+   | /     |     |     -     |   |--+   | /
      +-----+     ^     +---+  |   |/      +-----+     ^     +---+  |   |/ 
   13.8-14.7 MHz  |            \          30-34 MHz    |            \      
                  |            /                       |            /      
                  |            \ 50                    |            \ 50   
              18.0 MHz         |                 20.0-20.5 MHz      |      
                 LO           gnd                     VFO          gnd     
|                     |
 ----------+---------- 
           |
     20m band module

We've examined the selection and problems of IF frequencies, now let's start going over the tradeoffs of these various circuits in detail.

The preselectors are simply bandpass filters. Before this, I've been saying that a simple lowpass filter would be plenty to keep crap out of the receiver. That's true as far as image and IF rejection. There's more,though. We have introduced the IF amps above in the block diagram. Amplifiers in an ideal world would be totally linear. In other words, the output would be an exact amplified replica of the input. In the real world, all amplifiers add some distortion to the signal. This distortion is similar to that in the mixer products table of article no. 2. Every signal into the amplifier mixes slightly with every other signal, producing output that we don't want. This is IMD, intermodulation distortion, or intermod. Also, all amplifiers have a definite amount of power that they can source to the next stage. If one strong signal, well out of the band we're interested in listening to, were to use up all of that power, there would be none available for the signal we want to hear. Our receiver would seem "deaf" for no apparent reason. This is known as overloading or desense. Yet another problem is caused by the mixer: Any random noise, at any freq, reaching it will get mixed with the signals we want to hear, making them noisier. This is called noise modulation.

Obviously, it would behoove us to only allow a minimum range of signals into the mixer and amp. A filter that passes the whole band we're interested in, and not much more, is ideal. In practice, very small passbands are difficult to get without introducing a lot of insertion loss. The filter is made just wide enough to reduce the loss to an acceptable level. Also, very narrow passbands tend to result in extremes of component values. A slightly wider than ideal filter is sometimes necessary in order to be able to build it with real components.

There are several easily-constructed bandpass filter types to choose from: Butterworth, Chebyshev, Elliptical, etc. Any of theses are readily built with practical inductors and capacitors at HF. The differences are in the mathematical description, the slope of the cutoff, and the change in phase vs freq. We only need to concern ourselves with the cutoff of our preselectors. For the most part, it's not too critical how sharply the filters cut off the unwanted freqs. The signals that will cause the biggest problems are many MHz away - the images and the IF. They will be heavily attenuated no matter which filter type we select. When the slope of the cutoff isn't critical, Butterworth is probably the best choice. Its passband is flat, and it's easily tuned by peaking a signal. All of the preselectors are Butterworth except the 160m filter. At 1.8 MHz, the cutoff is indeed critical: the AM broadcast band is only 200 KHz away. A Chebyshev filter provides the sharper cutoff we need, while still being fairly easy to tune. The passband is not flat like Butterworth, but has some slight ripple. Elliptical filters allow even sharper cutoff than Chebyshev, but there are several tuned traps that aren't easily adjusted without a spectrum analyzer.

The 32 MHz bandpass filter before the 2nd mixer is considerably less critical than the band module filters. It's there mainly to stop any oddball mixer products of the 1st mixer from reaching the 2nd mixer. Also, we want to cut down the bandwidth of the noise generated in the 1st IF circuits before it reaches the 2nd mixer. In modern synthesized rigs, this would be a fairly broadband crystal filter. With our wideband 1st IF, 32.0-32.5 MHz or so, we can't use crystals, so we just chop it down as narrow as possible without too much insertion loss, using a Butterworth filter. This is the highest-freq LC filter in the receiver, so some of the components will have impractically small values if the bandwidth is too small. A bandwidth of around 4 MHz is about the best compromise between images, noise, and component values.

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N1OOQ RX #5: mixer tradeoffs, IMD, intercepts

We'll now look at the tradeoffs of mixers. There is a lot to cover, so this will come in two postings. The concepts learned here will also be useful when we get to the IF amps.

There are many kinds of circuits that we can use as mixers. A simple diode goes a long way as far as just mixing two signals and getting an output. The problem with simple mixers is that a lot of stuff that we don't want also comes out the other end. In particular, the two input signals and all their harmonics make a real mess of the output. Circuits can be designed using balance to cancel out certain of the inputs. A single-balanced mixer cancels one of the inputs but lets the other pass through to the output. This is useful in some situations where one incoming signal is very small compared to the other.

The best types of mixers are double-balanced. These use a circuit that cancels both input signals and their harmonics at the output, leaving you with a fairly clean output. The residual junk can be easily filtered to insignificant levels. Double-balanced mixers also offer isolation between input ports. This is important to avoid the signal from one input getting into the other input and modulating the source, resulting in even more junk.

All mixer circuits are limited in the amount of power they can handle without distorting. All of them add some noise to the signal. The major tradeoff between the various types of double-balanced mixers is between distortion and noise. Generally, those mixers with conversion gain contribute less noise and more distortion, and those with conversion loss give more noise and less distortion. Gain means that the signal gets amplified as well as mixed; the output is bigger than the input. This of course requires active devices. The amplification of the active devices means less drive power is needed from the oscillator. Loss means that the signal gets attenuated as well as mixed; the output is smaller than the input. Diode mixers generally have conversion loss. More power is need from the oscillator to drive this type of mixer, 5 to 20 mW being typical.

The receiver's mixers are all double-balanced diode rings. This type of mixer is similar to a bridge rectifier, has about 7 dB conversion loss, and is pretty clean under large signal conditions. These mixers are particular about the impedance on the three ports. In order to realize their peak performance, they must see close to 50 ohms across a wide bandwidth on all three ports. The diplexer handles this at the output port. It passes the IF signal on to the 50 ohm input of the amplifier, while terminating all other frequencies into a 50 ohm resistor. It's essentially just a bandpass filter to the IF output, and a bandstop filter to the 50 ohm resistor, the band in question being the IF +/- a MHz or two. At the oscillator input port, a 3 dB resistive attenuator will provide 50 ohm termination. We can easily afford to throw away 3 dB's of oscillator power to get a nice, clean 50 ohms. At the signal input port, we can't attenuate without killing the sensitivity of our receiver. We'll have to rely on the 50 ohm antenna or the 50 ohm output of the previous IF amp to provide termination through the bandpass filters. We will be using about 20 mW to drive the mixers in this receiver. With the 3 dB attenuators, this means we'll need 40 mW out of the oscillators.

IMD is the biggest distortion worry in mixers. Close together signals generate small IMD products in the mixer that appear nearby, close enough to appear within the band we're listening to and get detected just like a real signal. This is due again to harmonics of the two signals, generated by the mixer itself, mixing and producing output. If the two signals are separated by, say, 10 KHz, the IMD products will appear at 10 KHz above the higher signal, and 10 KHz below the lower signal:

               signal       signal
                 |            |
                 |            |
                 |            |
                 |            |
   IMD           |            |           IMD
    |            |            |            |
    |            |            |            |
     <- 10 KHz -> <- 10 KHz -> <- 10 KHz ->

Two close, strong stations will generate IMD products like these. If we happen to be operating at one of the IMD freqs, we'll hear the IMD as QRM every time both strong stations have the key down at the same time.

The IMD output of a mixer can be judged by its 3rd-order intercept point. You may have heard this term before. The concept is easy to understand and is applicable to any active stage in a radio. At normal low power levels, the IMD products in mixer circuits are well below the level of the signal itself. As the signal power is increased, the level of the IMD products rises much faster than the level of the signal itself. At some theoretical point, the circuit is putting out as much junk as signal. This is the intercept point. In practice, most circuits' gain levels off well before it reaches that level, but the concept is useful for comparison and prediction.

        |                 o .
        |                o.
    IPo |- - - - - - - -o   <----- intercept point
        |             .o|
        |           . o 
        |         .  o  |       . = signal out
        |       .   o           o = IMD out
   Pout |     .    o    |
        |   .     o             IPo is the output intercept
        | .      o      |       IPi is the input intercept
        +-------------------    for any circuit, IPi = IPo - gain
            Pin        IPi

Intercept is usually rated in dBm, decibels relative to a millwatt. Our diode-ring mixers have output intercepts of about +14 dBm. The input intercepts are IPi = +14 - (-7) = +21 dBm. What does this mean? With an input signal of +21 dBm, which is 126 mW, the theoretical IMD output will be as high as the theoretical signal output. For every dB we reduce the input, this 3rd-order IMD will drop by 3 dB. We can now predict how much junk will come out with a certain level of signal in:

input level     signal dB down     IMD dB down     IMD dB down
                from IPi           from IPi        from signal
----------------------------------------------------------------------------

Pin             IPi-Pin            (IPi-Pin)x3     (IPi-Pin)x3 - (IPi-Pin)
  0 dBm         21 dB              21x3 =  63 dB    63-21 =  42 dB
-10 dBm         31 dB              31x3 =  93 dB    93-31 =  62 dB
-20 dBm         41 dB              41x3 = 123 dB   123-41 =  82 dB
-30 dBm         51 dB              51x3 = 153 dB   153-51 = 102 dB

Obviously, the IMD products drop to an imperceptable level much more quickly than the signal power drops. Plugging higher IPi values into the equations would give us lower IMD levels. This tells us that mixers with a higher intercept rating cause less distortion than those with a lower rating. We should use a mixer with as high an intercept as we can get for lowest IMD. If we're willing to pay the price in oscillator power, diode-ring mixers are among the better in this respect. This receiver was designed to be a home station rig, with performance up to commercial rig standards, so I went all out. Many QRP rigs are designed for minimum current draw from batteries, so low power is a must. Active mixers such as the NE602 are a blessing in such cases, even though IMD is a bit higher. There are experimental active mixers in development with intercepts as high as +50 dBm, with relatively low oscillator power. Future receivers may have 20-30 dB more IMD resistance than anything currently available!

We can use the intercept concept to eval‎uate the IMD handling of the entire receiver as well as the mixer alone. 3rd-order intercepts are often listed in receiver specs and magazine test reports. A simple analysis is easy to do. If we reasonably assume everything after the mixer is pretty linear, we need only consider the circuitry from the antenna to the mixer to get a fair estimate of the receiver IPi. The only thing in the path is the preselector filter. The LC circuit of the filter contributes no IMD, only insertion loss. Insertion loss is added directly to the IPi; 1 dB of loss means a signal 1 dB stronger is need to generate the same IMD products. The filter does indeed have about 1 dB of insertion loss, so we can expect the IPi of the receiver to be around +22 dBm. The values in the table above are good estimates of what will happen in the first mixer.

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N1OOQ RX #6: more mixer tradeoffs, noise, dynamic range

Mixers not only distort the incoming signals, but add some noise to them as well. Distortion is a regular change in the shape of the sinusoidal waveform, an adding of harmonic components, but noise is random. It amounts to continuous random changes of the amplitude and phase of the waveform. All circuits add noise. The only way to avoid it is to cool the circuits to absolute zero, as most of the noise has its origin in the thermal energy of the components.

Noise is rather different than distortion, as the amount of noise added by a particular circuit isn't necessarily linked to the gain of the circuit. It's helpful to think of the added noise as a fixed chunk of noise power. A weak but clean incoming signal will be similar in strength to the added noise power; the signal-to-noise ratio will be low at the output. A strong, clean signal will be much more powerful than the added noise power; the signal-to-noise will be high.

A circuit will, however, amplify or attenuate any noise already on the input signal according to the gain. If the incoming signal is very noisy, the small chunk of extra noise added by the circuit will be covered up by that input noise. If the incoming signal is very quiet, the extra noise added by the circuit will be very noticable when the signal is small. Once a signal is amplified up out of the noise floor, we needn't be fussy about adding a small extra chunk of noise to it, as the signal will totally overwhelm that little bit of noise. Only the stages before the first gain stage need be painstaking about noise.

Again, all circuits add noise, even passive ones. Many circuits, for instance, our antenna, can be modeled as a resistor. The noise power in a resistor is:

                                                        -23
Pn = kTB,     where k is Boltzmann's constant, 1.38 x 10    W/K.
                    T is the temperature in Kelvin, about 290K at room temp.
                    B is the bandwidth we're interested in.

Note that the noise depends only on the temperature. Hotter circuits add more noise. As a baseline, any resistor at room temperature has a noise power of -174 dBm in a 1 Hz bandwidth. Converting to typical receiver bandwidths:

CW bandwidth noise  = -174 + 10 log 500             where 10 log x is the
                    = -174 + 27   = -147 dBm        conversion from ratio x
                                                    to dB. This can also be
SSB bandwidth noise = -174 + 10 log 2500            looked up in a table of
                    = -174 + 34   = -140 dBm        dB vs power ratio.

So the noise power on a room temperature antenna, at a bandwidth of 500 and 2500 Hz, is -147 dBm and -140 dBm, respectively. This amount of noise is always present on the antenna, and sets a limit on receiver performance. Signals weaker than about -140 dBm (about 0.03 uV peak in a 50 ohm antenna) will be lost in the noise of the antenna. A real receiver actually adds some noise to this, so the noise floor is somewhat higher, maybe -130 dBm for an HF receiver. This is known as the minimum discernable signal, or MDS. The difference between the natural noise and the MDS is the noise figure, or NF, of the receiver.

NF is a convenient way of specifying how much noise is added by a particular circuit. It is just the ratio signal-to-noise-in/signal-to-noise-out, called the noise factor, converted to decibels. A signal-to-noise ratio is signal power/noise power, so the overall definition of noise figure is

             /  Psig_in / Pnoise_in  \
NF = 10 log (  ---------------------  )
             \ Psig_out / Pnoise_out /

Note that this equation has no meaning if we don't specify what the input noise is. Since all circuits add noise, there is always input noise, -174 dBm or more in a 1 Hz bandwidth, as above. The NF is generally specified in just that way, with the input noise being that from a 290K resistor. An ideal circuit would have a NF of zero, adding no noise, only gain or loss, to the noise input.

As an example, let's say our circuit has only a room-temperature resistor at the input, zero gain, and a 5 dB NF, a ratio of about 3.2:1. The noise power at the output is Pnoise_in x 3.2, and the signal power is just Psig_in. If the circuit had gain, the noise power at the output would be Pnoise_in x 3.2 x gain, and the signal power would be Psig_in x gain. Either way, signal-to-noise-in/signal-to-noise-out is about 3.2, so NF is about 5 dB. Since all circuits add some noise, the NF is always greater than 0.

The noise added by a particular mixer depends on the design of the mixer. Active mixers have noise figures in the 1 to 10 dB range, depending on the circuit type and the active devices used. Diodes add little noise, but they do have insertion loss. Such attenuating circuits are adequately modeled as a resistor for noise purposes, and as such add a constant amount of noise, as above. The noise in this resistor model is the same as that used when specifying NF, -174 dBm, but the signal is attenuated. The signal-to-noise ratio at the input of the combined circuit is therefore degraded by the amount of attenuation, and the circuit adds its attenuation directly to the NF of the following circuits. Hence, our diode-ring mixer adds 6-7 dB to the NF of the IF amplifier.

We can get an estimate of the receiver's overall NF by similarly analyzing the circuitry between the mixer and the antenna. Again, there will be only a bandpass filter with insertion loss (and additional NF) of around 1 dB. The NF of our receiver will be the NF of the IF amp + 7 dB + 1 dB. Assuming a 5 dB NF for the amp, the receiver NF will be about 13 dB. The receiver's MDS can now be estimated:

-147 dBm + 13 dB = -134 dBm    500 Hz bandwidth
-140 dBm + 13 dB = -127 dBm   2500 Hz bandwidth

We have, in these last two articles, established two limits on the receiver's performance. At the strong signal end, IMD in the front-end components sets the limit on how big a signal we can copy without distortion. At the weak signal end, noise in the front end limits how small a signal we can copy without drowning in the noise. This clean-signal spread is called the dynamic range of the receiver. We can put a number on it:

DR = (signal level where IMD products rise above front-end noise) - MDS

In article #5, we saw that IMD products at an input signal of -30 dBm, one microwatt, were about 153 dB below the IPi of +21 dBm, or -132 dBm. This is similar to the MDS we calculated above, so this is approximately the point at which the products will become audible. With some algebraic manipulation of the equations in that article, we can get a formula for the exact signal level:

       MDS + 2 IPi
sig = -------------
           3

So the signal levels that will cause audible IMD are:

(-134 + 2 x 21) / 3 = -31 dBm    500 Hz bandwidth
(-127 + 2 x 21) / 3 = -28 dBm   2500 Hz bandwidth

and the DR is:

(-31) - (-134) = 103 dB    500 Hz bandwidth
(-28) - (-127) =  99 dB   2500 Hz bandwidth

This being an HF receiver, some sensitivity (i.e. low NF) was sacrificed to maximize DR. Atmospheric noise will generally drown the noise of the receiver's front end at these freqs. We could add a preamp to boost sensitivity if we don't mind losing some of the mixer's nice, high IPi. A +10 dB preamp would reduce the +21 dBm IPi to +11 dBm. Assuming a preamp NF of 5 dB, MDS would be -140 dBm + 5 dB = -135 dBm, an 8 dB increase in sensitivity. The signal level that will cause IMD is now (-135 + 2 x 11) / 3 = -38 dBm, and the DR is (-38) - (-135) = 97 dB, a loss of only 2 dB in DR. This is a reasonable tradeoff, and a switchable preamp would likely be a useful addition to the receiver. IMD in the preamp itself would then become a limiting factor in the RX performance, and should be carefully handled.

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Subject: Re: N1OOQ RX #6: more mixer tradeoffs, noise, dynamic range

Just a brief comment regarding HF noise.

Adding a preamplifier at the front end of a receiver that is atmospheric noise limited does nothing to improve performance, save an increase in end-to-end gain which might be desired to yield an increase in output "loudness".

With respect to noise, SNR is set by the signal strength to atmospheric noise level at the antenna terminals, and only noise cancelation and processing bandwidth reduction will improve output SNR. Only when atmospheric noise decreases to a level below the effective input noise figure of the receiver does the introduction of a low noise preamplifier yield an improved SNR.

Atmospheric noise is strongly dependent on frequency, time of day, solar activity, and a vast array of natural and man-made noise sources. HF receivers come equipped with built in RF pre-amplifiers (as well as front end attenuators) to aid the operator toward maximizing the instantaneous dynamic range of his/her receiving system for any given set of operating conditions.

Grayline operation can most benefit form careful utilization of such resources. An attenuator might be appropriate on 160 meters where many strong signals abound, as well as a high level of atmospheric noise as the atmosphere is in transition. 10 meters at the other extreme may suffer little degradation in performance due to atmospheric noise, and a low noise front-end preamplifier might enable detection of signals that might otherwise be dominated by front end receiver noise. Needless to say, attenuators are the order of the day during major contests:-)

72 de N3GO, Gary Raleigh, NC

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N1OOQ RX #7: diplexer tradeoffs

Between the mixers and the IF amps are the diplexers. These circuits are designed to pass a small range of freqs on to the amps, while terminating all other freqs into a 50 ohm resistor. This prevents reflection of any mixer products back into the mixer's output port, where it could degrade the mixer's intercept point. Also, this protects the IF amps from having to deal with too large a range of input freqs. The input impedance of the amps can be controlled to look like 50 ohms across a wide bandwidth, just what we want on the mixer output, but every signal other than the IF is just potential distortion-causing junk to the amp. For instance, the first couple of harmonics of the LO are strong enough to cause concern. We don't want to use up the IF amp in amplifying these junk freqs.

In some cases, the vast majority of the junk we want to filter is above the IF, and a simple lowpass/highpass arrangement will work. This is usually the case if the IF is very low, for instance 455 KHz, or if we're mixing to audio in a product detector.

In this receiver, with its VHF and HF IF's, bandpass/bandstop circuits are needed. They consist of simply a parallel tuned circuit to ground, through a 50 ohm resistor, and a series tuned circuit to the input of the amp. The parallel circuit blocks only the IF, terminating all other freqs in the resistor. The series circuit passes only the IF, blocking all other freqs. The 50 ohm input of the amplifier at the IF, combined with the 50 ohm resistor at other freqs, gives a reasonably smooth 50 ohm termination at all freqs. If the tuned circuits aren't well matched in freq, there will be some bumps in this smooth termination, so some tweeking of the diplexers is a must. The bandwidths (the Q of the tuned circuits) are kept somewhat wide, a couple of MHz, to make this tuning easier. This also keeps insertion loss to a minimum, preserving our NF.

The diplexers are made up of LC tuned circuits. We have to make sure there are no L's or C's in the preceeding or following circuits that will interact with these and cause resonances that we don't want, as we need to do with any LC filter. Strange resonances will cause impedance bumps and reflections, messing up all our careful termination.

The diplexers in this receiver are unidirectional, that is, the diplexing action will not occur in the reverse direction. The IF would be passed backwards to the input, but every other freq would be reflected rather than dissipated in a resistor. This might be cause for concern in some receiver systems, where impedance after the diplexer isn't consistent across a wide freq range, and signals get reflected back toward the mixer.

You may have heard the similar term, "duplexer", before. A diplexer isolates two very different frequency bands, like our IF and all other freqs. This isn't terribly difficult to do with LC filters. A duplexer isolates two very close frequecies, for instance, the input and output freq of a VHF repeater. This is rather difficult, and is done with tuned cavities.

    These N1OOQ RX postings are intended to be a learning exercise for the
    QRP-L folks, so if you have questions or comments, post them! How's the
    level of detail? Too much or too little?

==============================================================================
Tom Randolph N1OOQ NE-QRP 419 QRP-L 87 ARRL randolph@asic.enet.dec.com
==============================================================================

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Reader Comments

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Subject: N1OOQ RX Posts and IF gain

Tom asked -

"These N1OOQ RX postings are intended to be a learning exercise for the
    QRP-L folks, so if you have questions or comments, post them! How's the
    level of detail? Too much or too little?"

Tom - I like your posts. I don't always read all of them, but if you are discussing a topic of interest to me I usually read it. I always skim them. Good stuff. When you are finished with them all I propose you put them in a single file and make it available to FTP.

I have a question about your IF filters and gain distribution. I assume from your posts that you are using two IF filter bandwidths, one for CW and one for SSB. How are you normalizing the gain through the filters, or maybe I should ask are you normalizing the gain through the filters? There are at least two ways to do this, one is to adjust the gain so that the signal strength is the same through the filters. This will have the effect of lowering the noise when using the CW filter. The second method is to adjust the gain so that the integrated noise is the same through the filters, this will have the effect of increasing the signal strength when using the CW filter. This technique of normalizing the gain so that the noise is the same seems to be the most transparent to the user, that is unless there is a signal present there is no indication to the user that the bandwidth has changed. Sherwood touches on this subject in his December 1977 Ham Radio article. Most commercial rigs do not normalize at all which results in both the noise and signal changing when bandwidths are changed. This normalization would require an additional IF amplifier for the CW filter.

Duffey KK6MC/5

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Subject: re: N1OOQ RX Posts and IF gain

Duffey KK6MC/5 asks:

> I have a question about your IF filters and gain distribution. I assume
> from your posts that you are using two IF filter bandwidths, one for CW and
> one for SSB. How are you normalizing the gain through the filters, or maybe
> I should ask are you normalizing the gain through the filters? There are at

Yup, two different filters. I was just going to ignore the difference in gain and/or noise. I've never had a two-filter radio... how annoying is it?

The difference in noise would be about sqrt ( 2500/500 ), which is 2.24 or 3.5 dB. The difference in gain will depend on the insertion loss of the filters, which aren't built yet!

Tom

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