"TDOA" direction finder systems - Part 2 - Determining signal bearing from switching antennas in software.

Note:

This is a follow-up to a Part 1 blog post on this topic where we discuss in general how "rotating" (or switched) antennas may be used to determine the apparent bearing of a transmitter.  It is recommended that you read Part 1 FIRST and you can find it at:  "'TDOA' direction finder systems - Part 1 - how they work, and a few examples." - LINK.

In part 1 (linked above) we discussed a simple two-element "TDOA" (Time Difference Of Arrival) system for determining the bearing to a transmitter.  This method takes advantage of the fact that - under normal conditions - one can presume the incoming signal to be a wave "front", which is to say like ripples in water from a very distant source, they "sweep" over the receiver in lines that are at a right-angle to the direction from the transmitter.  Note that in this discussion, most of the emphasis will be placed on how it is done in the analog domain with switching antennas as this can help provide a clearer picture of what is going on.

Why this works

If we are using a two-antenna array, we can divine a difference between the arrival time of the two antennas as this drawing - stolen from part 1 of this article - illustrates:

Figure 1:
A diagram showing how the "TDOA" system works.
Click on the image for a larger version.

 

As illustrated in the top portion of the above illustration, the wave front "hits" the two elements at exactly the same time so, in theory, there is no difference between the signal from each of these elements.  In the bottom portion of the illustration, we can see that the wave front will hit the left-most element first and the RF will be out of phase at the second element (e.g. one element will "see" a the positive portion of the wave and the other will see the negative portion of the wave).

If we constrain ourselves with having just ONE receiver to use, you might ask yourself how one might use the signal from two antennas?  The answer is that one switches between the two antennas electronically - typically with diodes.  If the two signals are identical in their time of arrival - and the length of coaxial cable between the antenna and when one switches "perfectly" between the two antennas and there is no disturbance in the received signal, we know that the signal is likely to be broadside of our two-antenna array.

If the signal is NOT broadside to the the array, there will be a "glitch" in the waveform coming out of our receiver when we switch our antenna.  Because we are using an FM receiver - which detects modulation by observing the frequency change caused by audio modulation - we can also detect that "glitch".  To understand how this works, consider the following:

Recall the "Doppler Effect" (Wikipedia article - link) where the pitch of the horn of a car increases from its original when it is moving toward the observer - and it is lower in pitch when it moves away from the observer:  It is only at the instant that the car is closest to the observer that the pitch heard is the actual pitch of the horn.

Now, consider this same thing when we look at the lower diagram of Figure 1.  If we switch from the left-hand antenna to the right-hand antenna, we have effectively moved away from the transmitter and for an instant the frequency of the received signal was lower because - from the point of the receiver on the end of the coax cable - the antenna moved away from the transmitter.  Because changes in frequency going up and down cause the voltage coming out of the receiver to go up and down by the same amount, we will get a brief "glitch" from having changed the frequency for a brief instant when our antenna "moved".

If we then switch back from the right-hand antenna to the left-hand antenna, we have suddenly moved it closer to the transmitter and, again, we shift the frequency - but in the opposite direction, and the glitch we get in the receiver is opposite as well.

We can see the glitching of this signal in the following photo, also stolen from "Part 1" of this article:

Figure 2:
Example of the "glitches" seen on the audio of a receiver connected to a TDOA system that switches antennas.

The photo in Figure 2 is that of an oscilloscope trace of the audio output of the FM receiver connected to it and in it, we can see a positive-going "glitch" when we switch from one antenna to the other, and a negative-going glitch when we switch back again.

If we have a simple circuit that is switching the antennas back-and-forth - and it "knows" when this switch happens, we can determine several things:

• When the two antennas are broadside to the transmitter.  If we have the situation depicted in the top drawing of Figure 1, both antennas are equidistant and there will be NO glitches detected.
  

• When antenna "A" is closer to the transmitter.  If we arbitrarily assign one of the antennas as "A" and the other as "B", we can see - by way of our "thought experiment" above - that if antenna "A" is closer to the transmitter than "B", our frequency will go DOWN for an instant when we switch from "A" to "B" - and vice-versa when it switches back.  Let us say that this produces the pattern of "glitches" that we seen in Figure 2.
  

• When antenna "B" is closer to the transmitter.  If we take the above situation and rotate our two-antenna array around 180 degrees, antenna "B" will be closer to the transmitter than "A" and when our switch from "A" to "B" happens, our frequency will go UP for an instant when it does so - and vice-versa.  In that case, our oscilloscope will show the glitches depicted in Figure 2 upside-down.

In other words, by looking at the polarity of the glitches from our receiver, we can tell if the transmitter is to our left or to our right.  We can also infer a little bit about how far to the left or right our transmitter is by looking at the amplitude of the glitches:  If the signal is off the side of the antenna as depicted in the lower part of Figure 1, the glitches will be at the strongest - and the amplitude of the glitches will diminish as we get closer to having the two elements parallel as depicted in the top part of Figure  1.

There is an obvious limitation to this:  Unless we sweep the antenna back and forth, all we can do is tell if the antenna is to our left or right.

Walking about with an antenna like this it is easy to sweep back and forth and with some practice, one can infer whether the the transmitter is to the left or right and in front or behind - but if you have a fixed antenna array (one that is not moving) or if you are in a vehicle where their orientation is fixed with respect to the direction of travel, this becomes inconvenient as you cannot tell if it is in front or behind.

Adding more antennas

Suppose that we want to know both "left and right" and "front and back" at the same time - and in that case, you would be correct if you presumed that you were to be able to do this by adding one more antenna and - and then did some switching between them.  Consider the case in Figure 3, below:

Figure 3:
A 3-antenna vertical array, with elements A, B and C.  A right-angle is formed between antennas "A" and "B" and "A" and "C".   Also see Figure #4.
Click on the image for a larger version.

 

In Figure 3 and 4 we have three vertical antennas - separated by less than 1/4 wavelength at the frequency of interest ¹ and we also have two transmitters located 90 degrees apart from each other.  Note that these antennas are laid out in a "three-sided square" - that is, if you were to draw lines between "A" and "B" and "A" and "C" they would form a precise right angle.

We know already from our example in Figure 1 that if we are receiving Transmitter #1 that we will get our "glitch" if we switch between antenna "A" and "B" - but since antennas "A" and "C" are the same distance from Transmitter #1, we will get NO glitch.

Similarly, if we are listening to Transmitter #2, if we switch between antenna "A" and "C", we will get a glitch as "C" is closer to the transmitter than "A" - but since antennas "A" and "B" are the same distance, we would get not glitch.

From this example we can see that if we have three antennas, we can switch them alternately to resolve our "Left/Right" and "Front/Back" ambiguity at all times.  For example, let us consider what happens in the presence of Transmitter #2:

• Switch from antenna "A" to antenna "B":  The antennas are equidistant from Transmitter #2, so there is no glitch.
  

• Switch from antenna "A" to antenna "C":  We get a glitch in our received audio when we do this because antenna "C" is closer to Transmitter #2 than antenna "A".  Furthermore, we can tell by the polarity of the glitch that antenna "C" is closer to the transmitter.

Let us now presume that our array in Figure 3 and 4 was atop a vehicle and the front of the vehicle was pointed toward the left - toward Transmitter #1:  With just the above information we would know that this transmitter was located precisely to our right - and that if we wanted to drive toward it, we would need to make a right turn.

Figure 4:
A 3-antenna vertical array, with elements A, B and
C as viewed from the top.
Click on the image for a larger version.

Bearings in between the antennas

What if there a third transmitter (Transmitter #3 in Figure 4) located halfway between Transmitter #1 and Transmitter #2 and we were still in our car pointed at Transmitter #1?  You would be correct in presuming that:

• Switching between Antenna "A" and "B" would indicate that the unknown transmitter would be to the front of the car.
  

• Switching between Antenna "A" and "C" would indicate that the unknown transmitter would be to the right of the car.
• We get "glitches" when switching between either pairs of antennas (A/B and A/C) - but these "glitches" are at lower amplitude than if the transmitter were in the direction of Transmitter #1 or Transmitter #2.
  

Could it be that if we measured the relative amplitude and polarity of the glitches we get from switching the two pairs of antennas (A/B and A/C) that we could infer something about the bearing of the signal?

The answer is YES.

By using simple trigonometry we can figure out - by comparing the amplitudes of the glitches and noting their relative polarity - the bearing of the transmitter with respect to the antenna array - and the specific thing we need is the inverse function "ArcTangent".

If you set your "Wayback" machine to High School, you will remember that you could plot a point on a piece of X/Y graph paper  and relative to the origin, use the ratio of the X/Y values to determine the angle of a line drawn between that point and the origin.  As it turns out, there is a function in many computer languages that is useful in this case - namely the "atan2()" function in which we put our "x" and "y" values.

Figure 5:
Depiction of the "atan2" function and how to get the angle, θ.
This diagram is modified from the Wikipedia "atan2"
article - link.
Click on the image for a larger version.

Let us consider the drawing in Figure 5.  If you remember much of your high-school math, you'll remember that if straight-up is zero degrees and the right-pointing arrow is 90 degrees that the "mid-point" between the two would naturally be 45 degrees.

What you might also remember is that if you were drop a line between the dot marked as (x,y) in Figure 5 and the "x" axis - and draw another line between it and the "y" axis - those lines would be the same length.

By extension, you can see that if you know the "x" and "y" coordinates of the dot depicted in Figure 5 - and "x" and/or "y" can be either positive or negative - you can represent any angle.

Referring back to Figure 2, recall that you will get a "glitch" when you switch antennas that are at different distances from the transmitter - and further recall that in Figures 3 and 4 that you can use the switching between antennas "A" and "B" to determine if the transmitter is in front or behind the car - and "A" and "C" to determine if it is to the left or right of the car.

If we presume that the "y" axis (up/down) is front/back of the car and the "x" axis is right/left, we can see that if we have an equal amount of "glitching" from the A/B switch ("y" axis) and the A/C switch ("x" axis) - and both of these glitches go positive - we would then know that the transmitter was 45 degrees to the right of straight ahead.

Similarly, if we were to note that our "A/B" ("y" axis) glitch was very slightly negative - indicating that the signal was behind and and that our "A/C" glitch was strongly negative indicating that it was far to our left:  This condition is depicted with the vector terminating in point "A" in Figure 5 to show that the transmitter was, in fact, to the left and just behind us - perhaps at an angle of about 260 degrees.

Using 4 antennas

The use of three antennas isn't common - particularly with an "L" (right-angle) arrangement - but one could do that.  What is more common is to arrange four antennas in a square and "rotate" them using diode switches with one antenna being active at a given instant - and having more antennas and more switching between antennas to create our glitches gives us more data to work with which can only help reduce the uncertainty of the bearing.  Consider the diagram of Figure 6.

Figure 6:
A four antenna arrangement.
Click on the image for a larger version.

In this arrangement we have four antennas arranged in a perfect square - and this time we are going to switch them in the following pattern:

    A->B->C->D->A

Now let us suppose that we are receiving Transmitter "A" - so we would get the following "glitch" patterns on our receiver:

• A->B:  Positive glitch (A is closer to TX #1 than B so the the source is seen to move farther away)
  
• B->C:  No glitch (B and C are the same distance from TX #1)
  
• C->D:  Negative glitch (D is closer to TX #1 than C so the source is seen to move closer)
  
• D->A:  No glitch (A and B are the same distance from TX #1)
  

As expected, going from "A" to "B" results in a glitch that we'll call "positive" as antenna "B" is farther away from the transmitter than "A" - but when we "rotate" to the other side and switch from "C" to "D" - because we are going to an antenna that is closer, the glitch will have the opposite polarity as the one we got when we switched from "A" to "B" - but both glitches will have the same amplitude.

Since antenna pairs B/C and A/D are the same distance from the transmitter we will get no glitch when we switch between those antennas.

As  you can see from the above operation, every time we make one "rotation", we'll get four glitches - but they will be in equal and opposite pairs - which is to say the A->B and the C->D are one pair with opposite polarity and B->C and D->A are the other pair with opposite polarity.  If we take the measured voltage of these pairs of glitches and subtract each set, we will end up with vectors that we can throw into our "atan2" function and get a bearing - and what's more, since we are getting the same information twice (the equal-and-opposite pairs) this serves to increase the effective amplitude of the glitch overall to help make it stand out better from modulation and noise that may be on the received signal.

Similarly, if we were receiving a signal from Transmitter #3 (in Figure 6) we could see that being at a 45 degree angle, each of our four glitches would have the same strength but differing polarities - with the vector pointing in that direction.  What's more, the magnitude of those glitches will be a bit lower than our example with Transmitter #1, above:  Since Transmitter #3 is shifted 45 degrees, this means that the apparent distance between any antenna switch will be about 71% as great as it would have been had it been Transmitter #1 or #2.  If you recognized that 71% - or 0.707 is the sine (or cosine) of 45 degrees, you would be exactly right!

A typical four-antenna ARDF unit will "spin" the antenna at anywhere between 300 and 1000 RPM - the lower frequencies being preferable as it and their harmonics are better-contained within the 3 kHz voice bandwidth of a typical communications-type FM receiver.

Figure 7:
Montreal "Dopplr 3" with compass rose,
digital bearing indication and adjustable switched-
capacitor band-pass filter running "alternate"
firmware (see KA7OEI link below).
Click on the image for a larger version.

Improving performance - filtering

As can be seen in the oscillogram of Figure 2, the switching glitches are of pretty low amplitude - and they are quite narrow meaning that they are easily overwhelmed by incidental audio and - in the case of weaker signals - noise.  One way to deal with this is to use a very narrow audio band-pass filter - typically something on the order of a few Hz to a few 10s of Hz wide.

In the analog world this is typically obtained using a switched-capacitor - the description of which would be worthy of another article - but it has the advantage of its center frequency being set by an external clock signal:  If the same clock signal is used for both the filter and to "spin" the antenna, any frequency drift is automatically canceled out.

It is also possible to use a plain, analog band-pass filter using op amps, resistors and capacitors - but these can be problematic in that these components - particularly the capacitors - are prone to temperature drift which can affect the accuracy of the bearing, often requiring repeated calibration:  This problem is most notable during summer or winter months when the temperature can vary quite a bit - particularly in a vehicle.

By narrowing the bandwidth significantly - to just a few Hz - it is far more likely that the energy getting through it will be only from the antenna switching and not incidental audio.

There is another aspect related to narrow-band filtering that can be useful:  Indicating the quality of signal.  In the discussions above, we are presuming that opposite pairs of antennas will yield equal-and-opposite "glitches" (e.g. A->B and C->D are mirror images, and B->C and D->A are also mirror images) - but in the case of multipath distortion - where the receive signal can come from different directions due to reflection and/or refraction - this may not be the case.  If the above "mirroring" effect is not true, this causes changes in the amplitude of the tone from the antenna spin rate (the "switching tone") which can include the following:

• The switching tone can decrease overall due to a multiplicity of random wave fronts arriving at the antenna array.   If multipath is such that one or more of our antennas gets no signal - or they get a delayed bounce that "looks" like one of the other antennas, you might get a missing glitch or one that has the wrong polarity.  A signal distorted in such a manner probably won't make it through our very narrow band-pass filter very well at all.
  

• The switching tone's frequency can double if each antenna's slightly-different position is getting a different portion of a multipath-distorted wave front.  If the multipath is such that every antenna as a different version of the bounced signal it may be that you don't get the "equal and opposite" glitches that you expect.  Again, if our switching tone is doubled, it won't make it through the band-pass filter.
  

• The switching tone can be heavily frequency-modulated by the rapidly-changing wave fronts.  Remember that Frequency Modulation is all about the rapid phase changes of the carrier with modulation - but if you are driving through an area with a lot of reflections, this can add random phase shifts to the received signal which can cause the switching tone of our antennas' rotation to be seemingly randomized.  Because the randomization will likely appear as noise, this will likely "dilute" our switching tone and there will be less of it to be able to get through our narrow band-pass filter.
  

If you have ever operated VHF/UHF from a moving vehicle, you have experienced all three of the above to a degree:  It's likely that you have stopped at a light or a sign, only to find out that the signal to which you were listening faded out and/or got distorted - only to appear again if you moved your vehicle forward or backwards even a few inches/centimeters.  Similarly, you've likely heard noise (e.g. "Picket Fencing") as you have driven through an area with a lot of clutter from buildings and/or terrain:  Imagine this happening to four antennas in slightly different locations on the roof of your vehicle, each getting a signal that is distorted in its own, unique way!

Each of the above cause the switching tone in the receiver to be disrupted and with the worse disruption, less of the signal will get through the narrow filter.  Of course, having a good representation of the antenna's switching tone does not automatically mean that it is going to indicate a true bearing to the transmitter as you could be receive a "clean" reflection - but you at least you can detect - and throw out - obviously "bad" information!

Improving performance - narrow sampling

In addition to - or instead of narrow-band sampling - there's another method that could be used and that is narrow sampling.  Referring to Figure 2 again, you'll note that the peaks of the glitches are very narrow.  While the oscillogram of Figure 2 was taken from the speaker output of the receiver, many radios intended for packet use also include a discriminator output for use with 9600 baud and VARA modes which has a more "pristine" version of this signal.

Because we can know precisely when this glitch arrives (e.g. we know when we switch the antenna - and we can determine by observation when, exactly, it will appear on the radio's output) we can do a grab the amplitude of this pulse with a very  narrow window (e.g. "look" for it precisely when we expect it to arrive) and thus reject much of the audio content and noise that can interfere with our analysis.  

Further discussion of this technique is beyond the scope of this article, but it is discussed in more detail here.

Improving performance - vector averaging

If you have ever used a direction-finding unit with an LED compass rose before, you'll note that in areas of multipath that the bearing seems to go all over the place - but if you look very carefully (and are NOT the one driving) you may notice something interesting:  Even in areas of bad multipath, there is likely to be a statistical weight toward the true bearing rather than a completely random mess.  This is a very general statement and it refers more to those instances where signals are blocked more by local ground clutter rather than a strong reflection from, say, a mountain, which may be more consistent in their "wrongness".

While the trained eye can often spot a tendency from seemingly-random bearings, one can bring math to the rescue once again.  Because we are getting our signal bearings by inputting vectors into the "atan2" function, we could also sum the individual "x" and "y" vectors over time and get an average.  

 

This works in our favor for at least two reasons:

1. It is unlikely that even multipath signals are entirely random.  As signals bounce around from urban clutter, it is likely that there will be a significant bias in one particular direction.
2. Through vector averaging, the relative quality of a signal can be determined.  If you get a "solid" bearing with consistently-good signals, the magnitude of the x/y vectors will be much greater than that from a "noisy" signal with a lot of variation.

In the case of #1, it is often that, while driving through a city among buildings that the bearing to a transmitter will be obfuscated by clutter - but being able to statistically reduce "noise" may help to provide a clue as to a possible bearing.

In the case of #2, being able to determine the quality of the bearing can, through experience, indicate to you whether or note you should pay attention to the information that you are getting:  After all, getting a mix of good and bad information is fine as long as you know which is the bad information!

Typically one would use a sliding average consisting of a recent history of samples.  If one uses the "vector average" method described above it is more likely that poor-quality bearings will have a lesser influence on the result. 

Antenna switching isn't ideal

Up to this point we have been talking about using a single receiver with a multi-antenna array that sequentially switches individual antennas into the mix - but electronic switching of the antennas is not ideal for several reasons:

• The "modulation" due to the antenna switching imparts sidebands on the received signals.  Because this switching is rather abrupt, this can mean that signals 10s and 100s of kHz away can raise the receive system noise floor and decrease sensitivity.

• The switching itself is quite noisy in its own right and can significantly reduce the absolute sensitivity of the receive system.  For this reason, only "moderate-to-strong" signals are good candidates for this type of system.

• In the presence of multipath, the switching itself can result in the signal being more highly disrupted than normal.  This isn't too much of a problem since it is unlikely that one could get a valid bearing in that situation, anyway, but it can still be mitigated with filtering as described above.

If one is actively direction-finding with gear like this, it should not be the only tool in their toolbox:  Having a directional antenna - like a small Yagi - and suitable receiver (one with a useful, wide-ranging signal level meter) is invaluable both for situations where the signal may be too weak to be reliably detected with a TDOA system and when you are so close to it that you may have to get out of the vehicle and walk around.

Doing this digitally

There is something to be said about the relative simplicity of an analog TDOA system:  You slap the antennas on the vehicle, perform a quick calibration using a repeater or someone with a handie-talkie, and off you go.  To be sure, a bit of experience is invaluable in helping you to determine when you should and should not trust the readings that you are getting - but eventually, if the signal persists, you will likely find the source of the signal.

These days there are a number of SDR (Software-Defined Radio) systems - namely the earlier Kerberos and more recent Kraken SDRs.  Both of these units use multiple receivers that are synchronized from the same clock and use in-built references for calibration.

The distinct advantage of having a "receiver per antenna" is that one need not switch the antennas themselves, meaning that the noise and distortion resulting from the electronic "rotation" is eliminated.  Since the antennas are not switched, a different - yet similar - approach is required to determine the bearing of the signal - but if you've made it this far, it's not unfamiliar:  The use of "atan2" again:  One can take the vector difference of the signal between adjacent antennas and get some phasing information - and since we have four antennas, we can, again, get two equal and opposite pairs (assuming no multipath) of bearing data.

If you have two signals from adjacent antennas - let's say "A" and "B" from Figure 6 - we already know that the phasing will be different on the signal if the antenna hits "A" first rather than "B" first and this can be used in conjunction with its opposite pair of antennas ("C" and "D") to divine one of our vectors:  A similar approach can be done with the other opposite pairs - B/C and D/A.

This has the potential to give us better-quality bearings - but the same sorts of averaging and noise filtering must be done on the raw data as it has no real advantage over the analog system in areas where there is severe multipath:  It boils down to how it does its filtering and signal quality assessment and, more importantly, how you, the operator, interpret the data based on experience gained from having used the system enough have become familiar with it.

As far as absolute sensitivity goes between a Kerberos/Kraken SDR and an analog unit - that's a bit of a mixed bag.  Without the switching noise, the absolute sensitivity can be better, but in urban areas - and particularly if there is a strong signal within the passband of the A/D converter (which has only 8 bits) the required AGC may necessarily reduce the gain to where weaker signals disappear.

 

There are other possibilities when it comes to SDR-based receivers - for example, the SDRPlay RSPduo has a pair of receivers within it that can be synchronous to each other:  Using one of these units with a pair of magnetic loops can be used to effect the digital version of an old-fashioned goniometer!  This has the advantage of relative simplicity and can take advantage of the relatively high performance of the RSP compared to the RTL-SDR. 

Finally, there exist multi-site TDOA systems where the signals are received and time-stamped with great precision:  By knowing when, exactly, a signal arrives and then comparing this with the arrival time at other, similar, sites it is (theoretically) possible to determine the location of origin - a sort of "reverse GPS" system.  This system has some very definite, practical limits related to dissemination of receiver time-stamping and the nature of the received signal itself and would be a topic of of a blog post by itself!

Equipment recommendations?

 

My "go to " ARDF unit for in-vehicle use is currently a Montreal "Dopplr 3" running modified firmware (written by me - see the link to the "KA7OEI ARDF page, below) with four rooftop antennas.  Having used this unit for nearly 20 years, I'm very familiar with its operation and have used it successfully many times to find transmitters - both in for fun and for "serious" use (e.g. stuck transmitter, jammer, etc.) 

 

This unit has the advantage of being "grab 'n' go" in that it takes only a few seconds to "boot up" and it has a very simple, intuitive compass rose display. I believe that its performance is about as good as it can possibly be with a "switched antenna" type of ARDF unit:  For the most part, if a signal is audible, it will produce a bearing.

A disadvantage of this unit to some would be that it's available only in the form or a circuit board (still available from FAR circuits - link ) which means that the would-be builder must get the parts and put it together themselves.

"Pre-assembled" options for this type of unit include the MFJ-5005 which can sometimes be found on the used market and several options from the former Ramsey Electronics - along with the Dick Smith ARDF unit:  Information on these units may be found on the K0OV page linked below.

 

Comment:  Do NOT try to use ANY ARDF gear with inexpensive Chinese radios like BaoFengs.  The reason for this is that owing to their "receiver on a chip" having its own DSP processor, there are variations on how long the audio is delayed with respect to when the signal arrives at the antenna and this will certainly wreck any attempt at doing anything that requires consistent timing - which is true for all systems that use multiple antennas.  You will be much better off using a "conventional" (non-DSP) receiver:  Radios that are decades old - particularly if they don't have any features - are often ideal as they are typically robust and can be bought inexpensively.

Another possible option is the "Kraken SDR":  I have yet to use one of these units, but I'm considering doing so for evaluation and comparison - which I will report here if I am actually able to do so.

Final words

This (rambling) dissertation about TDOA direction finding hopefully provides a bit of clarity when it comes to understanding how such things work - but there are a few things common to all systems that cannot really be addressed by the method of signal processing - analog or digital:

• Bearings from a single fixed location should be suspect.  Unless you happen to have an antenna array atop a tall tower or mountain, expect the bearing that you obtain to be incorrect - and even if you do have it located in the clear, bogus readings are still likely.
  

• Having multiple sources of bearings is a must.  Having more than one fixed location - or better yet having one or more sources of bearings from moving vehicles is very useful in that this dramatically decreases the uncertainty.
  

• The most important information is often just knowing the direction in which you should start driving.  Expecting to be able to located a signal with a TDOA system with any reasonable accuracy is unrealistic.  It is often the case that when a signal appears, the most useful piece of information is simply knowing in which direction - to the nearest 90 degrees - that one should start looking.
  

• The experience of the operator is paramount.  No matter which system you are using, its utility is greatly improved with familiarity of its features - and most importantly, its limitations.  In the real world, locating a signal source is often an exercise in frustration as it is often intermittent and variable and complicated by geography.  No-one should reasonably expect to simply purchase/build such a device and have it sit on the shelf until the need arises - and then learn how to use it!

 * * *

Footnote:

1. On systems like this where one switches between (or uses) multiple antennas - it is necessary that adjacently-compared antennas be less than a quarter wave apart at the highest operational frequency.  While it is possible to get better resolution by increasing the spacing between antennas, the directional response will have multiple lobes meaning that there can be an uncertainty as to which "lobe" is being detected.
   

Having more than 1/4 wavelength spacing can be useful if you have means of resolving such ambiguities.  Spacing antennas closer than 1/4 wavelength can work, but the phase difference also decreases meaning that differences between antennas reduces making detection of bearing more difficult and increasingly susceptible to incidental signal modulation and the uncertainty that those factors imply.  From a purely practical stand point, the roof of a typical vehicle is only large enough for about 1/4 wavelength spacing on 2 meters, anyway.

Related links:

• Part 1 of this article -  "'TDOA' direction finder systems - Part 1 - how they work, and a few examples." - LINK.

• KA7OEI ARDF page - link - This page deals mostly with "Doppler" (TDOA) direction-finding gear.
  

• K0OV's Direction Finding page - link - By Joe Moell, this covers a wide variety of topics activities related to ARDF. 
  

• WB2HOL's ARDF Projects - link - This page has a number of simple, easy to build antenna/DF projects.
  

• KrakenSDR page - link - This is the product description/sales page for the RTL-SDR based VHF/UHF SDR.
  

 

This page stolen from ka7oei.blogspot.com

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Adding a useful signal strength indication to an old, inexpensive handie-talkie for transmitter hunting

A field strength meter is a very handy tool for locating a transmitter, but a sensitive field strength meter by itself has some limitations as it will respond to practically any RF signal that enters its input.  This has the effect of limiting the effective sensitivity of the field strength meter, as any nearby RF source (or even ones far away, if the meter is sensitive enough...) will effectively mask the desired signal if it is weaker than these "background" signals.

Figure 1:
The modified Icom IC-2A/T HT with a broadband
field strength meter paired with the AD8307-based field
strength meter mentioned and linked in the article, below.
Click on the image for a larger version.

This property can be mitigated somewhat by preceding the input of the meter with a simple tuned RF stage and, in most cases, this is adequate for finding (very) nearby transmitters.  A simple tuned circuit does have its limitations:

• It is only broadly selective.  A simple, single-tuned filter will have a response encompassing several percent (at best) of the operating frequency.  This means that sensitive meter preceded by a 2 meter filter will respond to nearly any signal near or within to the 2 meter band.
• A very narrow filter can be tricky to tune.  This isn't usually too much of a problem as one can peak on the desired signal (if it is close enough to register) or use your own transmitter (on the same or nearby frequency) to provide a source of signal on which the filter may be tuned.
• The filter does not usually enhance the absolute (weak signal) sensitivity unless an amplifier is used with it.

An obvious approach to solving this problem is to use a receiver, but while many FM receivers have "S-meters" on them, very few of them have meters that are truly useful over a very wide dynamic range, most firmly "pegging" even on relatively modest signals, making them nearly unusable if the signal is any stronger than "medium weak".  While an adjustable attenuator (such as a step attenuator or offset attenuator) may be used, the range of the radio's S-meter itself may be so limited that it is difficult to manage the observation of the meter and adjusting the signal level to maintain an "on-scale" reading.

Another possibility is to modify an existing receiver so that an external signal level meter with much greater range may be connected.

Picking a receiver:

When I decided to take this approach I began looking for a 2 meter (the primary band of interest) receiver with these properties:

• It had to be cheap.  No need to explain this one!

• It had to be synthesized.  It's very helpful to be able to change frequencies.

• Having a 10.7 MHz IF was preferable.  The reasons for this will become apparent.

• It had to have enough room inside it to allow the addition of some extra circuitry to allow "picking off" the IF signal.  After all, that's the entire point of this exercise.

• It had to be easy to use.  Because one may not use this receiver too often, it's best not to pick something overly complicated and would require a manual to remind one how to do even the simplest of tasks.

• The radio would still be a radio.  Another goal of the modification was that the radio had to work exactly as it was originally designed after you were done - that is, you could still use it as a transceiver!

Based on a combination of past familiarity with various 2 meter HTs and looking at prices on Ebay, at least three possibilities sprang to mind:

• The Henry Tempo S-1.  This is a very basic 2 meter-only radio and was the very first synthesized HT available in the U.S.  One disadvantage is that, by default, it uses a threaded antenna connection rather than a more-standard BNC connector and would thus require the user to install one to allow it to be used with other types of antennas.  Another disadvantage is that it has a built-in non-removable battery.  It's power supply voltage is limited to under 11 volts.  (The later Tempo S-15 has fewer of these disadvantages and may be better suited for this application, but I am not too familiar with it.)

• The Kenwood TH-21.  This, too, is a very basic 2 meter-only radio.  It uses a strange RCA (e.g. phono) like threaded connector, but this mates with easily-available RCA-BNC adapters.  Its disadvantage is that it is small enough that the added circuitry may not fit inside.  It, too, has a distinct limitation on its power supply voltage range and requires about 10 volts.

• The Icom IC-2A/T.  This basic radio was, at one time, one of the most popular 2 meter HTs which means that there are still plenty of them around.  It can operate directly on 12-15 volts, has a standard BNC antenna connector, and has plenty of room inside the case for the addition of a small circuit.  (The "T" suffix indicates that it has a DTMF numeric keypad.  The "non-T" version such as the IC-2A is a bit less common, but would work just fine for this application.)

Each of these radios is a thumbwheel-switch tuned, synthesized, plain-vanilla radio. I chose the Icom IC-2AT (it is also the most common) and obtained one on Ebay for about $40 (including accessories) and another $24 bought a clone of an IC-8, an 8-cell alkaline battery holder (from Batteries America) that is normally populated with 2.5 amp-hour NiMH AA cells.  With its squelched receive current of around 20 milliamps I will often use this radio as a "listen around the house" radio since it will run for days and days!

"Why not use one of those cheap Chinese radios?" Upon reading this you may be thinking "why spend $$$ on an ancient radio when you can buy a cheap chinese radio that has lots of features for $30-ish?" The reason is that these radios have neither a user-available "S" meter with good dynamic range or an accessible IF (Intermediate Frequency) stage.  Because these radios are, in effect, direct conversion with DSP magic occurring on-chip, there is absolutely nowhere that one could connect an external meter - because that signal simply does not exist! While many of these "single-chip" radios do have some built-in S-meter circuitry, the manufacturers of these radios have, for whatever reason, not made it available to the user - at least not in a format that would be particularly useful for transmitter hunting. Unfortunately these radios can overload quite easily when near a strong signal.  This property - and the fact that they use audio processing that can vary based on signal quality - make many of these radios generally unsuitable for direction-finding!

Modifying the IC-2A/T (and circuit descriptions):

This radio is the largest of those mentioned above and has a reasonable amount of extra room inside its case for the addition of the few small circuits needed to complete the modification.  When done, this modification does not, in any way, affect otherwise normal operation of the radio:  It can still be used as it was designed!

An added IF buffer amplifier:

This radio uses the Motorola MC3357 (or an equivalent such as the MP5071) as the IF/demodulator.  This chip takes the 10.7 MHz IF from the front-end mixer and 1st IF amplifier stages and converts it to a lower IF (455 kHz) for further filtering and limiting and it is then demodulated using a quadrature detector.  Unfortunately, the MC3357 lacks an RSSI (Receive Signal Strength Indicator) circuit - which also explains why this radio doesn't have an S-meter.  Since we were planning to feed a sample of the IF from this receiver into our field strength meter, anyway, this isn't too much of a problem.

Figure 2:
The source-follower amplifier tacked atop the IF amplifier chip.
Click on the image for a larger version.

We actually have a choice to two different IFs:  10.7 MHz and 455 kHz.  At first glance, the 455 kHz might seem to be a better choice as it has additionally amplified and it is at a lower frequency - but there's a problem:  It compresses easily.  Monitoring the 455 kHz line, one can easily "see" signals in the microvolt range, but by the time you get a signal that's in the -60 dBm range or so, this signal path is already starting to go into compression.  This is a serious problem as -60 dBm is about the strength that one gets from a 100 watt 2 meter transmitter that is clear line-of-sight at about 20 miles (about 30km) distant, using unity-gain antennas on each end.  What this means is that if we were to use this signal tap, we might still be a fair distance away from the transmitter we were seeking when its signal saturated the meter.

The other choice is to tap the signal at the 10.7 MHz point, before it goes into the MC3357.  This signal, not having been amplified as much as the 455 kHz signal, does not begin to saturate until the input reaches about -40 dBm or so, reaching full saturation by about -35 dBm.  Given our example, above, -35 to -40dBm is roughly equivalent to a line-of-sight 100 watt 2 meter transmitter at 1-3 miles (approx. 1.6-5km) - which means that we'll get much closer before the signal path saturates - but we can easily deal with that as we'll discuss shortly.

One point of concern here was the fact that at this point, the signal has less filtering than the 455 kHz, with the latter going through a "sharper" bandpass filter.  While the filtering at 10.7 MHz is a bit broader, the 4 poles of the crystal filter do attenuate  a signal 20 kHz away by at least 30 dB - so unless there's another very strong signal on this adjacent channel, it's not likely that there will be a problem.  As it turns out, the slightly "broader" response of the 10.7 MHz crystal filters is conducive to "offset tuning" - that is, deliberately tuning the radio off-frequency to reduce the signal level reading when you are nearby the transmitter being sought and it starts to saturate the IF stages.

To tap this signal without otherwise affecting the performance of the receiver requires a simple buffer amplifier, and a JFET source-follower does the job nicely (see figure 6, below for the diagram).  Consisting of only 6 components (two resistors, three capacitors and an MPF102 JFET - practically any N-channel JFET will do) this circuit is simply tack-soldered directly onto the MC3357 as shown in figures 2 and 3.  This circuit very effectively isolates the (more or less) 50 ohm load of the field strength meter from the high-impedance 10.7 MHz input to the MC3357 and it does so while only drawing about 700 microamps, which is only 3-4% of the radio's total current when it is squelched.

Figure 3:
A wider view of the modifications to the radio.
Click on the image for a larger version.

As can be seen from the pictures (figure 2 and 3) all of the required connections were made directly to the pins of the IC itself, with the 330 pF input capacitor connecting directly to pin 16.  The supply voltage is pulled from pin 4, and pins 12 and/or 15 are used for the ground connection. 

A word of warning:  Care should be taken when soldering directly to the pins of this (or any) IC to avoid damage.  It is a good idea to scrape the pin clean of oxide and use a hot soldering iron so that the connection can be made very quickly.  Excess heat and/or force on the pin can destroy the IC!  It's not that this IC is particularly fragile, but this is care that should be taken.

Getting the IF signal outside the radio:

The next challenge was getting our sampled 10.7 MHz IF energy out of the radio's case.  While it may be possible to install another connector on the radio somewhere, it's easiest to use an existing connector - such as the microphone jack.

One of the goals of these modifications was to retain complete function as if it were a stock radio, so I wanted to be sure that the microphone jack would still work as designed, so I needed to multiplex both the microphone audio (and keying) and the IF onto the tip of the microphone connector as I wasn't really planning to use the signal meter and a remote microphone at the same time.  Because of the very large difference in frequencies (audio versus 10.7 MHz) it is very easy to separate the two using capacitors and an inductor:  The 10.7 MHz IF signal is passed directly to the connector with a series capacitor (such as 100pF) while the 10.7 MHz IF signal is blocked from the radio's internal microphone/PTT line with a small choke:  Anything from 4.7uH to 100uH will work fine.

Figure 4:
The modifications at the microphone jack.
Click on the image for a larger version.

The buffered IF signal is conducted to the microphone jack using some small coaxial cable:  RG-174 type will work, but I found some slightly smaller coax in a junked VCR.  To make the connections, the two screws on the side of the HT's frame were removed, allowing it to "hinge" open, giving easy access to the microphone connector.  The existing microphone wire connected to the "tip" connection was removed and the choke was placed in series with it, with the combination insulated with some heat-shrinkable tubing.

The coax from the buffer amp was then connected directly to the "tip" of the microphone connector.  One possible coax routing is shown in Figure 4 but note that this routing prevents the two halves of the chassis from being fully opened in the future unless it is disconnected from one end.  If this bothers you, a longer cable can be routed so that it follows along the hinge and then over to the buffer circuit.  Note:  It is important to use shielded cable for this connection as the cable is likely to be routed past the components "earlier" in the IF strip and instability could result if there is coupling.

Interfacing with the Field Strength meter:

Using RG-174 type coaxial cable, an adapter/interface cable was constructed with a 2.5mm connector on one end and a BNC on the other.  One important point is that a small series capacitor (0.001uF) is required in this line somewhere as a DC block on the microphone connector:  The IC-2A/T (like most HTs) detects a "key down" condition on the microphone by detecting a current flow on the microphone line and this series capacitor prevents current from flowing through the 50 ohm input termination on the field strength meter and "keying" the radio.

Dealing with L.O. leakage:

As soon as it was constructed I observed that even with no signal, the field strength meter showed a weak signal (about -60 to -65 dBm) present whenever the receiver was turned on, effectively reducing sensitivity by 20-25 dB.  As I suspected when I first noticed it, this signal was coming from two places:

• The VHF local oscillator.  On the IC-2A/T, this oscillator operates 10.7 MHz lower than the receive frequency.  In other words, tuned to 146.520 MHz, the local oscillator is running at 135.82 MHz.
• The 2nd IF local oscillator.  On the IC-2A/T this oscillator operates at 10.245 MHz - 455 kHz below the 10.7 MHz IF as part of the conversion to the second IF.

The magnitude of each of these signals was about the same, roughly -65 dBm or so.  The VHF local oscillator would be very easy to get rid of -  A very simple lowpass filter (consisting of a single capacitor and inductor) would adequately suppress it - but the 10.245 MHz signal poses a problem as it is too close to 10.7 MHz to be easily attenuated enough by a very simple L/C filter without affecting it.

Figure 5:
The inline 10.7 MHz bandpass using filter using a ceramic
filter.  The diagram for this may be seen in the upper-right
corner of Figure 6, below.
Click on the image for a larger version.

Fortunately, with the IF being 10.7 MHz, we have another (cheap!) option:  A 10.7 MHz ceramic IF filter.  These filters are ubiquitous, being used in nearly every FM broadcast receiver made since the 80s, so if you have a junked FM broadcast receiver kicking around, you'll likely have one or more of these in them.  Even if you don't have junk with a ceramic filter in it, they are relatively cheap ($1-$2) and readily available from many mail-order outlets.  This filter is shown in the upper-right corner of the diagram in Figure 6, below.

The precise type of filter is not important as they will typically have a bandpass that is between 150 kHz and 300 kHz wide (depending on the application) at their -6 dB points and will easily attenuate the 10.245 MHz local oscillator signal by at least 30 dB.  With this bandwidth it is possible to use a 10.7 MHz filter (which, themselves, vary in exact center frequency) for some of the "close - but not exact" IF's that one can often find near 10.7 MHz like 10.695 or 10.75 MHz.  The only "gotcha" with these ceramic filters is that their input/output impedances are typically in the 300 ohm area and require a (very simple) matching network (an inductor and capacitor) on the input and output to interface them with a 50 ohm system.  The values used for matching are not critical and the inductor, ideally around 1.8uH, could be anything from 1.5 to 2.2 uH without much impact of performance other than a very slight change in insertion loss.

While this filter could have been crammed into the radio I was concerned that the L.O. leakage might find its way into the connector somehow, bypassing the filter.  Instead, this circuit was constructed "dead bug" on a small scrap of circuit board material with sides, "potted" in thermoset ("hot melt") glue and covered with electrical tape, heat shrink tubing or "plastic dip" compound, with the entire circuit installed in the middle of the coax line (making a "lump.")  Alternatively, this filter could have been installed within the field strength meter itself, either on its own connector or sharing the main connector and being switchable in/out of the circuit.

Figure 6:
The diagram, drawn in the 1980s Icom style, showing the modified circuity and details of the added source-follower JFET amplifier (in the dashed-line box) along with the 10.7 MHz bandpass filter (upper-right) that is built into the cable.
Click on the image for a larger version.

With this additional filtering the L.O. leakage is reduced to a level below the detection threshold of the field strength meter, allowing sub-microvolt signals to be detected by the meter/radio combination.

Operation and use:

When using this system, I simply clip the radio to my belt and adjust it so that I can listen to what is going on.

There's approximately 30 dB of processing gain between the antenna to the 10.7 MHz IF output - that is, a -100 dBm signal on the antenna on 2 meters will show up as a -70 dBm signal at 10.7 MHz.  What this means is that sub-microvolt signals are just detectable at the bottom end of the range of the Field Strength meter.  From a distance, a simple gain antenna such as a 3-element "Tape Measure Yagi" (see the article "Tape Measure Beam Optimized for Direction Finding - link) will establish a bearing, the antenna's gain providing both an effective signal boost of about 7dB (compared to an isotropic) and directivity.

While driving about looking for a signal I use a multi-antenna (so-called) "Doppler" type system with four antennas being electrically rotated to get the general bearings with the modified IC-2AT being the receiver in that system.  With the field strength meter connected I can hear its audio tone representing the signal strength without need to look at it.  As I near the signal source and the strength increases, I have both the directional indication and the rising pitch of the tone as dual confirmation that I am approaching it.

The major advantage of using the HT as tunable "front end" of the field strength meter means that the meter has greatly enhanced selectability and sensitivity - but this is not without cost:  As noted before, this detection system will begin to saturate at about -40 dBm, fully saturating above -35 dBm - which is a "moderately strong" signal.  In "hidden-T" terms, it will "peg" when within a hundred feet or so of a 100 mW transmitter with a mediocre antenna.

When the signals become this strong, you can do one of several things:

• Detune the receiver by 5, 10, 15 or even 20 kHz.  This will reduce the sensitivity by moving the signal slightly out of the passband of the 10.7 MHz IF filters.  This is usually a very simple and effective technique, although heavy modulation can cause the signal strength readings to vary.

• Add attenuation to the front-end of the receiver.  The plastic case of the IC-2A/T is quite "leaky" in terms of RF ingress, but it is good enough for a step attenuator on the antenna lead to work nicely and will thus extend usable range to at least -10dBm dBm.  I use a switchable step attenuator for this and I have found that I can drive to the location (house, yard, park) where the transmitter is located and still have sufficient adjustment range.

• When you are really close (e.g. 10s of yards/meters) to the transmitter being sought you can forgo the receiver altogether, connecting the antenna directly to the field strength meter!

If you want to be really fancy, you can build the 10.7 MHz bandpass filter and add switches to the field strength meter so that you can switch 20 dB of attenuation in and out as well as routing the signal either to the receiver, or to the field strength meter using a resistive or hybrid splitter to make sure that the receiver gets some signal from the antenna even when the field strength meter is connected to the antenna.

What to use as the field-strength meter:

The field strength meter used is one based on the Analog Devices AD8307 which is useful from below 1 MHz to over 500 MHz, providing a nice, logarithmic output over a range that goes below -70dBm to above +10dBm.  It is, however, broad as the proverbial "barn door" and the combination of this fact and that its sensitivity of "only" -70dBm is nowhere near enough to be useful with weak signals - especially if there are any other radio transmitters nearby - including radio and TV stations within a few 10s of miles/kilometers.  The integration of this broadband detector with the narrowband, tuneable receiver IF along with its gain makes for a complete system useful for signals that range from weak to strong.

The description of an audible field-strength meter may be found on the web page of the Utah Amateur Radio club in another article that I wrote, linked here:  Wide Dynamic Range Field Strength Meter - link.  One of the key elements of this circuit is that it includes an audio oscillator with a pitch that increases in proportion with the dB indication on the meter, allowing "eyes-off" assessment of the signal strength - very useful while one is walking about or in a vehicle.

There are also other web pages that describe the construction of an AD8307-based field strength meter (look for the "W7ZOI power meter" as a basis for this type of circuit) - and you can even buy pre-assembled boards on EvilBay (search for "AD8307 field strength meter" or "AD8307 power metetr").  The downside of most of these is that they do not include an audible signal strength indication to allow "eyes off" use, but this circuit could be easily added, adapted from that in the link above.

Another circuit worth considering is the venerable NE/SA605 or 615 which is, itself, a stand-alone receiver.  Of interest in this application is its "RSSI" (Receive Signal Strength Indicator) circuit which has both good sensitivity, is perfectly suited for use at 10.7 MHz,  has a nice logarithmic response and a wide dynamic range - nearly as much as the AD8307.  Exactly how one would use just the RSSI pin of this chip is beyond the scope of this article, but information on doing this may be found on the web in articles such as:

• NXP Application note AN1996 - link (see figure 13, page 19 for an example using the RSSI function only)
  

Additional comments:

• At first, I considered using the earphone jack for interfacing to the 10.7 MHz IF, but quickly realized that this would complicate things if I wanted to connect something to the jack (such as pair of headphones or a Doppler unit!) while DFing.  I decided that I was unlikely to be needing to use an external microphone while I was looking for a transmitter!

• I haven't tried it, but these modifications should be possible with the 222 MHz and 440 MHz versions (the IC3 and IC4) of this radio - not to mention other radios of this type.

• Although not extremely stable, you can listen to SSB and CW transmissions with the modified IC-2A/T by connecting a general-coverage/HF receiver to the 10.7 MHz IF output and tuning that receiver to about 10.7 MHz, +/- a few kHz.  Signals may be slightly "warbly" - but they should be easily copyable!

Finally, if you aren't able to build such a system and/or don't mind spending the money and you are interested in what is possibly the best receiver/signal strength meter combination device available, look at the VK3YNG Foxhunt Sniffer - link.  This integrates a 2 meter receiver (also capable of tuning the 121.5 MHz "ELT" frequency range) and a signal strength indicator capable of registering from less than -120dBm to well over +10dBm with an audible tone.

Comment:  This article is an edited/updated version of one that I posted on the Utah Amateur Radio Club site (link) a while ago.


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