RaspberryPi Software FM and APRS

RaspberryPi FM Transmitter

RaspberryPis have a GPIO pin that can be connected internally to a clock divider of a number of source clocks. This isn't a simple divider, rather, it's a dithering fractional divider, with 12 integer bits, and 12 fractional bits. First, this means that the frequency is only correct when averaged. Since it's digital, there will be many harmonics as well.

As an example, a 500MHz PLL clock(from PLLD on the older boards) can be divided by the ratio (22285/4096) to reach 91.9004MHz, this is somewhat of a best-case, since the divider lines up well.

To make broadcast FM, we can change the divider(or have the chip's DMA do it rapidly for us) to generate other tones within the broadcast FM bandwidth, which is 100-150KHz(channel spacing is 200KHz). For our example 91.2MHz station, we can use dividers from (22303/4096) at 91.826MHz to (22266/4096) at 91.978MHz, which is 37 discrete tones at maximum volume(roughly 4kHz spacing between tones). If we switch(modulate) between them rapidly enough, we can generate something like FM audio at the receiver, which low pass filtering in the receiver should help us clean up.

Why RaspberryPi FM will not work for APRS

However, things get more interesting at 144.390MHz, for two reasons. First, since the transmit frequency is higher, a single increment or decrement of the divider moves the transmit frequency further, about 10KHz now. But also, the bandwidth of 2 meter FM voice is only around 12kHz. When we work out the dividers, we get (14184/4096) at 144.388MHz and (14183/4096) at 144.398MHz, which is far enough from 144.390MHz that receivers are likely to filter it out or at least significantly attenuate it.

Cludging it all together

Because square waves have a lot of odd harmonics, with appropriate filtering, we can tune to 144.390MHz/3, or 48.130MHz, and filter out unwanted harmonics like 96.260MHz(2x) and 192.520MHz(4x). It's easiest to use a bandpass filter centered on 144.390MHz, with cuts set between 2x and 3x, and again between 3x and 4x harmonics. We could also tune lower, perhaps to 144.390MHz/5, but this will reduce out transmit power on target frequency more, and make filtering more difficult, as the nearest unwanted harmonics become closer together(4*144.390MHz/5 and 6*144.390MHz/5).

Bandwidth calculation also needs scaled. +/-6KHz at 144.390MHz is only +/-2KHz at 48.130MHz, however, we can fit four tones there, where we could only fit 1 at 144.390MHz, specifically we can divide 500MHz by (42553/4096) to (42550/4096).

When we do this, we can indeed hear some sort of audio, but it's still pretty terrible. Dithering and increasing the sample rate might help, but it's never going to work well.