Sporadic-E propagation is a topic which comes up relatively regularly here at Wireless Waffle. This increadible mode of propagation enables reception of radio signals, typically in the range 25 to 150 MHz, over very large distances - at least distances that are very large for those types of frequencies. Distances of up to 2000 km (1250 miles) are possible and, for example, distant FM radio stations can be received as strongly as local ones - sometimes so strong that they wipe-out the reception of the local stations.

Various articles exploring this unusual mode of propagation have graced these pages over the years, however as part of updating the FM DX Logbook a new analysis has been added. This takes the form of a bar-chart showing in which month Sporadic-E and Tropospheric propagation has caused reception of distant FM radio stations.

A number of publications state that Sporadic-E propagation tends to occur primarily in the summer months, and sometimes in the winter. Conversely, tropospheric propagation can occur at any time of the year. To test this hypothesis, the FM DX Logbook now produces a graph showing the month in which each of the logging took place.



So far the results support the hypothesis with Sporadic-E propogation occuring in January and then between May and July, with tropospheric propagation having been recorded throughout the year. Every time a logging is added to the page, the chart will be updated, so it will be interesting to see whether this pattern continues.

Part 5 of the series 'How not to design transmitters and receivers' discussed phase locked loops (PLL) and the fact that programmable dividers (divide by 'N') are required in order to make a PLL which can operate on different frequencies. Such a divider would need to be able to take radio frequency (RF) signals at its input before doing the dividing. Off-the-shelf CMOS logic chips in the 74HC series are generally capable of operating at frequencies up to 50 or 60 MHz (and in some cases up to 70 MHz). These could therefore be directly used as dividers in low frequency circuits where a solid 5 Volt signal can be fed into them, but anything operating at over about 70 MHz, or which produces a smaller output, requires some other technology.

This is then the realm of the 'prescaler'. A prescaler is basically a high frequency divider, often with a fixed division ratio, or in some cases with a limited number of fixed ratios. In most cases they are also designed to accept a low-level RF input rather than needing 5 Volts peak-to-peak.

There are an enormous number of prescaler IC's available, some dating back to the early 1980s. Thankfully, a useful look-up table of prescaler specifications is available online. The requirements for the Wireless Waffle lockdown project are that the prescaler must meet the following specifications:

• Be able to operate at frequencies down to around 25 MHz (so that the half-frequency oscillator can be used in Band-I, i.e. around 50 MHz, if needed).
• Be able to operate at frequencies up to around 600 MHz (so that future UHF designs can use the same chip).
• Have a division ratio of at least 40 (so that a 600 MHz input will be brought well within the frequency range of other digital components).
• Accept a reasonable and if possible wide range of input powers (to simplify the design of any circuitry feeding it).
• Be reasonably cheap (of course!)
• Be relatively widely available (so that there won't be any problems in getting hold of any for future projects).

It turns out that the most difficult of these requirements to meet is the combination of the lower operating frequency and being widely available. Most prescalers are, by nature, designed to divide very high frequencies and few are specified to operate below around 50 MHz at the lowest (no doubt due to the fact that the aforementioned high-speed CMOS chips can take over at this point). Some older prescalers (of the 1980s vintage) when frequencies in use were generally lower to begin with, are happy operating at low frequencies, however they fail the 'widely available' test as stocks are dwindling. Newer prescalers can operate at frequencies in excess of 10 GHz (10000 MHz) but are rarely specified below 1 GHz.

To find a suitable device, it was necessary to carefully peruse the exact specification sheets of various devices. Most have a 'guaranteed operating range' which is the combination of input frequency and input power over which they will perform perfectly. However, the specification sheets often contain performance curves which show input power and input frequency combinations that should work fine but are not guaranteed. A number of prescalers have guaranteed operating ranges which go as low as 50 or 70 MHz, but the datasheet shows that they will operate below this range, generally if they are driven with slightly higher input power.



Take, for example, the above chart taken from the datasheet for an SP8782 prescaler. The guaranteed operating window covers the frequency range from 200 MHz to 100 MHz with an input level of 200 mV peak-to-peak, descending to around 50 MHz (according to the datasheet, though the chart makes this look more like 70 MHz) if the input level is increased to 400 mV. However, even lower and higher frequency performance is possible. In the case of lower frequencies, it would appear to operate down to as low as maybe 25 MHz and as high as 1200 MHz if the input levels are suitably adjusted.

After much research, the MB501L was selected for the Wireless Waffle project. This has a guaranteed minimum operating frequency of 10 MHz, a maximum of 1100 MHz, and over this range will perform correctly with an RF input ranging from -4 to +6 dBm (1 milliWatt give or take). It has a pre-settable division ratio of 64, 65, 128 and 129. What's more one can be bought online for around £1.50 and seems relatively widely available despite originally being of mid 1980s vintage.

One other thing to consider when using prescalers is that they often do a rather bad job of isolating their inputs from their outputs (and their power supply rails). This means that the divided signal can easily get into whatever they are connected to, and in particular the RF inputs, causing spurs on the RF signal at multiples of the divider output. Take an example of a 64 MHz oscillator, connected to a device such as the MB501L set to divide by 64. The output frequency of the divider will be 1 MHz, and if care is not taken, this will find its way back into the oscillator meaning that unwanted spurs 1 MHz from the oscillator (i.e. at 63 and 65 MHz) will be produced.

Solutions to this include a buffer between the oscillator and the prescaler, or the introduction of sufficient loss (i.e. through a resistor) between the two to minimise the impact of any lack of isolation in the prescaler. Unless there is an excess of RF power to play with, the best option is to use a buffer. There are a myriad of RF buffer schematics online to choose from. In this application, one of the main criteria is the amount of isolation between input and output as this is the purpose to which the buffer is being put. Another design criteria is for the buffer to produce the right level of output to drive the prescaler at its preferred input levels. Field effect transistor (FET) buffers are particularly good when it comes to input/output isolation, and a very simple buffer can be constructed with the minimum of components. Bipolar transistors (BJT) can also be used, but tend not to have such good isolation. Two such buffer circuits are presented below.



The Junction-FET (JFET) circuit has a very high input impedance (largely set by the value of the 220K resistor from its gate to ground) and good isolation. The input impedance of the BJT circuit will be much lower and isolation poorer, so what, you might ask, is the benefit of the BJT approach. The answer is simple: some companies who manufacture printed circuit boards (PCBs) can also assemble surface mount devices (SMD) on the board at very low prices, and the 2SC3356 shown in the schematic is a device which these manufacturers have in their low-cost stock room, whereas they rarely have JFETs available.

At this point we nearly have all the building blocks necessary to make a fully synthesised transmitter bar a couple - the 'divide by N' block, and the 'phase/frequency comparator'. More, then, to follow soon.

For some time, Wireless Waffle has published an FM DX Logbook. This logbook records any DX (distance) reception of FM broadcast stations that have been received, through whatever means (i.e. home FM tuner, car radio, software radio). Though an interesting exercise in itself, a recent update to the page to show the propagation mode which has been used also included some simple calculations to show the number of metres travelled divided by the number of Watts of transmitter power, and an additional calculation working out what the received signal power would be, assuming free space path loss between the transmitting and receiving location.

The use of free space path loss as the propagation model is definitely not applicable for any mode of propagation other than line-of-sight but it proved to be a useful exercise. Based on the frequency and power of the transmitter, and the length of the path, it is possible to determine how strong the received signal would be, if the path was line-of-sight. The results show an interesting trend.



With the exception of a few shorter paths (up to about 150 km), the theoretical signal strengths received from broadcasts received via troposhperic propagation are clustered around -40 dBm (which equates to about 67 dBuV/m). Similarly, the theoretical signal strength of transmissions received via Sporadic-E propagation are clustered around -65 dBm (42 dBuV/m). Note that these are not measured signal strengths, but a calculation of how strong the signals would be if they were being received via a line-of-sight path - which they are not.

A previous Wireless Waffle article identified that around 40dBuV/m is required at a receiver for FM reception. It is almost certainly true, that in the case of both the DX reception via the troposphere, or via Sporadic-E, the actual received signal strength would be similar, as in both cases the signal would need to be strong enough to be successfully received: the necessary signal would be nearer the -65 dBm level than the -40 dBm level. If this is true, then it must also be true that the additional loss caused by a signal travelling via ducts in the troposphere compared to via ionised clouds in the E-layer is around 25 dB, as this is the additional loss which the signal could tolerate and still be received.

This just goes to show how effective Sporadic-E propagation is and why it is (or indeed was) such a problem for VHF television and radio broadcasters during the summer months when it is most prevalent. It also suggests that the path loss via Sporadic-E must be close to the free space value, as if the received signal strength is around 42 dBuV/m based on free space path loss, this is only a couple of dB different to that needed for successful reception and the actual path could not be introducing much in the way of additional attenuation.

Parts 1 to 4 of this series have covered generating an RF signal, amplifying it, and providing the whole kit and caboodle with a nice clean power supply. In this part, we consider frequency stabilisation.

It is very straightfoward to produce a radio frequency (RF) signal that does not drift from the wanted frequency. Using a quartz crystal oscillator, it is possible to maintain an accuracy of a few parts per million, or a couple of Hz per MHz of output frequency. However, the output from a crystal is so stable that it's just about impossible to move it. If you want to modulate the frequency by more than a few kHz, using a crystal is therefore not feasible. For a wideband FM transmitter, where the required deviation (i.e. the amount by which the frequency changes) is +/- 75 kHz, using a crystal is therefore a non-starter. Instead it is necessary to use a voltage controlled oscillator (VCO) and surround this by some kind of feedback loop which samples the output frequency and corrects it if it has drifted off the wanted frequency. Such a feedback loop is called a phase locked loop or PLL (or indeed a frequency locked loop).



A simple PLL would just compare the frequency being produced by an VCO with some reference, determine the difference between the two, and if the two are different, provide an error voltage to the VCO to bring it back onto frequency. In the block diagram above, the error voltage is added to the modulation voltage as both of them affect the frequency of oscillation. This system would be great, and work a treat, if it was only necessary to operate on one frequency. However, if it is necessary to tune the VCO to different frequencies, some additional jiggery pokery is necessary.

To make a tuneable PLL, an additional stage is added to the loop. The output from the VCO is divided by a number (let's call it 'N') and instead of having a reference frequency the same as the wanted output frequency, a much lower reference frequency is used. For example, if the reference frequency is 100 kHz, and we wanted the VCO to be on 89.6 MHz, we would divide the VCO output by 896 to give 100 kHz, and compare this to the 100 kHz reference. The rest of the circuit then operates as before. If we now change the division ratio to 900 instead of 896, the circuit would now attempt to retune the output to 90.0 MHz (assuming that the VCO was able to tune to that frequency). Thus, by changing the division ratio, we can lock the output frequency to any multiple of the reference frequency that we desire.



One difficulty of using a PLL in the case where we are trying to modulate the VCO (for example with audio or data) is that the PLL will see any modulation as a frequency error and try and correct it. To circumvent this problem it is normal to filter the error voltage produced by the PLL such that it cannot act upon the VCO at any frequency we are interested in modulating. If we are interested in audio frequencies which may descend as low as 20 Hz, we therefore need to low pass filter the error signal so that it cannot have any effect on modulation frequencies above 20 Hz and thus cannot try and 'correct' the audio being modulated onto the VCO.

This low pass filter is known as the loop filter. In addition to ensuring that the response of the loop is slow enough not to impact any low frequency modulation, it has the dual purpose of removing any of the reference frequency that might be present on the error voltage as the output of the comparator output will often just be a square wave whose mark-space ratio changes depending on the difference between the VCO frequency and the reference. If the required loop response time is slower than 20 Hz, and the reference frequency is 100 kHz this is not a difficult job, however having such a difference between the loop response time and the reference frequency leads to another difficulty: overshoot.



Imagine the situation...

• We switch on the PLL and the output frequency of the VCO is too low. The comparator recognises this and outputs a positive voltage to tell the VCO to increase its frequency. This positive signal is filtered by the loop filter which has the effect of slowing down the response time, and the VCO slowly begins to respond and its frequency rises.
• At some point the VCO output and the reference will now be the same and the comparator will stop producing a positive correction, however the loop filter, being very slow in comparison, has not yet finished acting upon its previous 'increase frequency' instruction and so instead of the PLL settling down, the output frequency continues to rise above the wanted one.
• The comparator now recognises that the frequency is too high and outputs a negative voltage to tell the VCO to reduce its output frequency. This instruction is slowed down by the laggard of the loop filter.
• Eventually the VCO output matches the reference and the comparator stops issuing its correction. But the loop filter has not yet finished the 'reduce frequency' instruction it was given and so the VCO frequency continues to go down.
• The comparator recognises this and outputs a positive voltage to tell the VCO to increase its frequency...

And so we enter a situation where the loop never settles down. The output frequency continuously oscillates around the wanted frequency but never actually ends up on that frequency. The loop, as the saying goes, never 'locks', it just goes up and down like a yo-yo.

One solution to this is to speed up the loop filter response, but this would then mean that lower modulating frequencies would be corrected by the PLL. Another solution is to reduce the reference frequency so that the loop frequency and the reference frequency are sufficiently close that one does not lag the other too much. This, however, often means that the loop filter will not be able to filter out the comparator output sufficiently, leading to the reference frequency modulating the VCO and causing 'spurs' in the RF output that are separated from the VCO output by the reference frequency.

A common solution to the yo-yo problem is to use a 'lead-lag' filter instead of just a low-pass for the loop filter. A lead-lag filter is a low pass filter whose frequency response is flattened at some point in its frequency range. The advantage of this is that it can provide the filtering necessary to slow down the loop and get rid of the comparator output, whilst providing protection against the yo-yo-ing by having a flatter phase response. This can then be combined with a seperate filter to specifically remove the comparator output and together the two can ensure good performance and a clean VCO output.