Next in the series of 'How not to design transmitters and receivers' we shall tackle the intermediate (IF) amplifier. This seemingly innocent little circuit is teeming with complexity and getting it right is not straightforward.

According to the calculations made in Part 15 of this series, the IF amplifier requires a gain of 19 dB or thereabouts (a few dB or so either way will not make too much difference). In addition, it needs to have an input and output impedance of 330 Ohms. This means that any ceramic filter used in the IF could be placed either before, or after, the amplifier and be correctly matched (or indeed two filters could be used). It is the combination of achieving a 330 Ohm input and output impedance, together with the requisite gain that makes the circuit more complex.



We shall use the circuit above as the basis for our amplifier. This is an untuned amplifier and will therefore provide gain across a wide range of frequencies which can sometimes cause problems as it will amplify both wanted and unwanted signals, however this has the major advantage that no tuning is required.

The gain of the circuit is primarily set by the ratio of Rc and Re, with gain being calculated as Rc divided by Re. However it needs to be remembered that Rc is in parallel with the load connected to the output, and that the transistor has an internal resistance in series with Re whose value is determined by the current flowing through the transistor (usually defined as 26 divided by the transistor emitter current (I_e in milliAmps).

Taking all this into account, the gain of the circuit can be (roughly) calculated by the equation:

Rc*R_load
(Rc+R_load)*(Re+26/I_e)

Note that this circuit also has additional negative feedback (via Rf) which will also impact (reduce) the gain, depending on the input impedance feeding the amplifier. The gain in this case will never exceed Rf/R_input. This effect will be marginal as long as the value of Rf is far above that of the input impedance of the circuit. As we are aiming for an input impedance of 330 Ohms, something over 10,000 Ohms (10K Ohms) will have only a small impact. Nevertheless, we should aim for the gain calculation above to produce a result slightly higher than that which we are aiming to achieve overall.

The input impedance of the circuit comprises three different values in parallel:

• Rb which is directly across the input of the circuit;
• The impedance of the emitter resistor Re (including the transistor's internal resistance) multiplied by the gain of the transistor (the Beta or h_fe); and
• The impedance of the feedback resistor Rf divided by the gain of the transistor circuit (not the gain of the transitor itself).

The input impedance of the amplifier can thus be calculated by the equation:

1
1/Rb+1/(h_fe*(Re+26/I_e))+1/(Rf/gain_circuit)

The output impedance of the amplifier is composed of the impedance presented by the transistor in parallel with Rc. The impedance presented by the transistor is approximately equal to the voltage between the collector and emitter divided by the current passing through the transistor. The output impedance of the amplifier can be calculated by the following equation, where V_cc is the voltage of the power supply:

Rc*(V_cc-Rc*I_e)
V_cc

This holds true as long as Rf is substantially larger than Rc.

One final consideration is the transistor bias. Ideally, the output of the transistor would be set to have a voltage roughly half of that of the supply (give or take). This ensures that the output of the amplifier can swing up and down as far as possible before 'hitting the rails' and no longer amplifying. The output voltage (at the transistor's collector) is determined by Rc and the current passing through the transistor. The current passing through the transistor is determined by the current flowing into the base of the transistor multiplied by its gain. In the case where the bias current is set through the feedback resistor from the collector (Rf), this calculation is iterative, as the base current is then related to the collector current.

Another kink is that the collector current can also impact the gain of the transistor, with very low collector currents reducing the gain. Similarly, currents too high can have similar effects. It is necessary to consult the datasheet for the transistor being used to determine how the current affects the gain. Usually over a relatively wide range, the gain will be roughly constant (and be at its highest) and this is often the point that should be aimed for.

Hopefully, by now, you can see why getting the various resistor values correct is complicated, and how changing one value (such as the emitter resistor, or feedback resistor) can change the gain and impedances of the circuit.

The following values therefore produce an amplifier which meets, so far as is possible, all the criteria which are required for the IF gain stage:

• Rb = 2.2K Ohms
• Rc = 560 Ohms
• Re = 8.2 Ohms
• Rf = 10K Ohms

Using these values, the collector current is roughly 7.5 mA meaning that the voltage at the collector, assuming a 9V supply, would be 4.7 Volts (i.e. giving the output a large peak-to-peak swing before hitting saturation). Knowing that the h_fe of the transistor at this current is approximately 110, and using the equations provided above, you should be able to confirm the fact that:

• The voltage gain of the amplifier is 17.8 (or 25 dB) before the reduction in gain caused by the feedback resistor Rf is taken into account;
• The input impedance of the amplifier is 331 Ohms;
• The output impedance of the amplifier is 299 Ohms.

These are well within the range that we are trying to achieve and so will 'do the job nicely'.

Another set of values which yields the correct input and output impedances is:

• Rb = 1K Ohms
• Rc = 470 Ohms
• Re = 22 Ohms
• Rf = 4.7K Ohms

In traditional academic style, and armed with the knowledge that the collector current in this example would be 5.5 mA, it is left to the reader to do the maths and work out what the gain and input and output impedance would be.

Note that in reality there are various additional factors which will impact the performance of the circuit, especially at radio frequencies. In particular, various capacitances within the transistor will tend to limit the high frequency performance. Choosing a transistor whose transition frequency (f_t - the frequency at which the transistor's gain drops to unity) is significantly above the required amplifier frequency minimises these issues. According to its datasheet, the 2N3904 used in the amplifier has an (f_t) of 300 MHz, and as we want the amplifier to operate at 10.7 MHz, this is sufficient margin to largely ignore these other factors.

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.

There seems to have been a lot of interest in the Wireless Waffle series entitled 'How Not to Design Transmitters and Receivers'. One or two (or, indeed, a few more) people have asked about a printed circuit board (PCB) layout and even whether it might be possible to put a kit of parts and set of instructions together for experimenters who wanted to try and build a 1 Watt FM transmitter/exciter for themselves. In that vein, a PCB has been designed for a simple synthesised PLL transmitter which has the following characteristics. It:

• Uses a half-frequency oscillator, to get round the feedback problems that an at-frequency oscillator can suffer from in RF hot environments
• Is built from the minimum sub-set of components, to keep the cost of getting all the parts together as low as possible
• Doesn't use lots of obsolete, expensive or difficult-to-get-hold-of parts
• Can accommodate different output transistors (such as the 2N4427, MRF237 and similar)
• Can use a range of transistors for most of the parts (such as the BF199, MPSH10 and similar)
• Will produce around 1 Watt across the band with as little fiddling as possible (or more depending on the output transistor)
• Has an output that is legally clean enough to either be connected directly to an antenna, or amplified to high power (nothing over 60dB below the carrier)
• Keeps the digital and analogue parts of the circuit as seperate as possible to minimise digital noise on the modulation
• Doesn't require any micro-controllers and thus does not require any software to be written/blown
• Has out-of-lock power-down to stop transmissions on unwanted frequencies whilst the phase lock loop is settling down
• Is straightforward to set onto the desired frequency
• Can be easily tested and maintained (to the extent that it could be built in stages, testing each along the way)
• Has a flat modulation frequency response from around 3 Hz to at least 100 kHz, providing superlative audio
• Does not need any tuning (other than setting the VCO frequency)
• Can have its output quickly disabled (i.e. for connection to a high SWR detector)
• With some component changes, can be made to work on Band-I too (the final design will work down to about 52 MHz)

Together with the good people at Zynq who have provided the PCB design and manufacture, we present the FM 3.05K (the 'K' stands for 'kit'). It's a very straightforward circuit based on the use of a 4046 as the phase detector and a diode based divide-by-N counter and uses three 74HC4020's, one each for the reference oscillator, divide-by-N and pre-scaler. This means only two types of IC's are needed: a 4046 and three 74HC4020s (oh, and an LM317 for the power supply), together with a handful of transistors.

There are no surface-mount parts on the PCBs, making it easy to assemble even for the relatively cack-handed, and the ICs can be socketted for those not confident enough to solder the chips directly to the board. The only complexity is that there are a number of coils to be manually wound, including one on a small toroid.

The circuit diagram is below and those who have followed the series will recognise the various elements which go together to make up the overall design.



Three options are available for anyone who wishes to have a go a building this design:

• PBC's for this project are available on their own for those who wish to assemble the various components required themselves, or who have a large junk-box full of suitable components. This is £4.99 plus postage.
• In addition, a minimalist kit is available which contains the PCB, as well as the ICs, transistors and the toroid and wire for winding the coils as these are the parts least likely to be in a typical junk box. This is £24.99 plus postage.
• Finally, a full kit of parts is available including the PCB, semi-conductors, toroids and all the resistors, capacitors and diodes needed to complete the project. This is £34.99 plus postage.

A full set of assembly and test instructions will be provided (as an online PDF download), though a certain level of skill is assumed (i.e. it won't tell you how to solder components into a board - there are plenty of tutorials for this on YouTube).

To get hold of your FM 3.05K kit, please leave a postcard with your name and address, together with £10,000 in unmarked £20 notes in a rucksack in a dustbin of your choice at Piccadilly railway station in Manchester at 23:15 any sunny Tuesday night in March.

Alternatively, fill in the contact form, stating which version of the kit you wish to purchase, and where it needs posting to, and we'll get back to you with a final price (including the postage) and how to pay (this will be via PayPal).

The Wireless Waffle FM DX Logbook has been updated to automatically calculate the theoretical signal levels, following a previous article that discussed whether any conclusions could be drawn about whether sporadic-E and tropospheric propagation produced different path losses. As a result of the update, the logbook page now draws the chart which shows the theoretical signal level produced by different transmitters.



With all of the logs now included in the calculations, the difference in propagation loss is smaller than that which was original posited, however it shows that the theoretical average signal from a radio station received via tropospheric propagation is around -48 dBm, whereas one received via sporadic-E propagation is around -64 dBm, a still not insubstantial 16 dB difference, suggesting that tropo propagation is more lossy than sporadic-E (as the received signal strengths are very similar).

What also stands out from the chart is the single outlying value in the blue, tropospheric values. One dot exists at around -66 dBm which is over 6dB lower than for any other station. This dot represents the theoretical signal from TOP Radio, from its 105.7 MHz FM transmitter in Ypres (Belgium), which has a supposed transmitter power (according to FM Scan, and the ITU GE06 database) of 100 Watts. This station has been logged on more than one occasion so it is not just a one-off freak of reception that it appears on the chart.

There are several possible explanations for the anomoly:

• The transmitter site is at a particularly elevated location, improving the coverage of the station. However, according to various sources it is only 40 to 43 metres above sea level, which isn't particularly high.
• The antenna is mounted very high above the ground. Again, according to FM Scan, it is only 30 metres above ground level, which isn't an outstanding lofty height, as the picture on the right of the transmitter site shows.
• The transmitter power is not the stated 100 Watts. For the 'dot' on the chart to be better grouped with the other stations received, the transmitter power would have to be at least 6dB higher, i.e. 400 Watts, or even higher.
• There is some freak propagation path from Ypres to the UK that occurs on regular occasions, and to different UK receive locations, which gives TOP Radio an advantage over other stations in its neighbourhood.
• There is an alien spacecraft hovering mid way between the UK and Belgium which is reflecting or relaying the signal with surprising effectiveness.

It is not easy to see from the picture above and to the right, however using Google Street View it is possible to get a side look at the mast. Mounted on top are two, three element, vertically polarised antennas pointing roughly north west (as they would need to, to provide coverage in Ypres from the transmitter site). Again, it is difficult to tell, but a working assumption might be that these are the antennas used for TOP Radio, not least as they are the only ones that would be near the 30 metre height that the records suggest that they should be mounted at. It may be that the '100 Watt' power restriction has been interpreted as 100 Watts to the antenna, rather than 100 Watts e.i.r.p.

If we presume that:

• 100 Watts is being fed up the coax to the antennas; and
• the gain of each 3 element antenna is 6 dB relative to a dipole (a reasonable figure); and
• the additional gain from stacking 2 dipoles is 3 dB;

then the e.i.r.p. would be 9 dB above 100 Watts, or just shy of 800 Watts. However, the radiation pattern from the 3 element yagis would be 3 dB down at roughly +/- 50 degrees from the main beam and would drop off rapidly around the back of the antenna, however the locations in the UK where TOP Radio from Ypres has been recieved are less than 20 degrees from the main beam of the yagis and as such, the e.i.r.p. would be close to the maximum.

If the e.i.r.p. of TOP Radio is closer to 800 Watts than 100 Watts, this would account for the anomoly in the received signal chart, and so the mystery is, at least partially, solved. Let's just hope that the authorities in Belgium responsible for regulating FM radio transmitters don't read this!