Now that we know how to set the Si5351 to generate the FSK frequencies, we need to see about filtering (smoothing) the frequency transitions.

HF FM, using SSB:

• Audio FSK signal modulates SSB transmitter, creating upper-sideband signal. This is identical to FM
• Even with no explicit shaping, SSB transmitter audio filtering shapes the FM transient response
• WSPR and APRS have no filtering
• FT8/JS8 specify Gaussian filter, “BT = 2”, -3dB @ 12.5 Hz

With the Si5351 directly generating the transmit frequency there is no smoothing of the frequency shifts; the frequency change is a step function.  While this can still be received and decoded, the frequency steps create significant in-band interference:

FT8 spectrum with and without filtering

In addition, in some cases the receiver uses a filter that is matched to the transmit filter, and having mismatched filters impairs effective signal detection.

The filter specified for FT8 is a Gaussian filter.  This has a specific response, with characteristics that give good spectrum utilization.  These filters have a fairly gentle shape, smoother than a simple RC filter:

Gaussian Filter Step Response

Since we can’t use analog frequency-transition smoothing, we have to do this digitally, using small discrete frequency steps spread out over time.  The Si5351 divisors give us the small frequency steps, and the Drift Buoy software uses a timer-tick interrupt running at a 2.4 KHz frequency to chop the given Baudrate into many small timesteps.

The Gaussian filter runs at this 2.4 KHz rate and using the large frequency steps as an input, generates a smoothed sequence of small frequency steps, which are used to update the  Si5351 dividers.  This filter is implemented in software as a Finite Impulse Response filter (FIR).

The “standard” FIR looks like this:

The input data is shifted through the delay-register chain, and at each shift the register contents are multiplied by the fixed coefficients and summed, giving the output.  Many different filter responses can be obtained by selection of coefficients.

The Drift Buoy uses a simpler FIR structure, requiring no multiplications (there is one division operation for output scaling):

Each stage consists of two delay elements (these are 32-bit integer variables) and an addition.  Stages are cascaded as shown, and the resulting filter response is Gaussian.  The FT8 filter is clocked at 2.4 KHz and has 384 stages, which gives a -3dB response of 12.5 Hz.  The filter function takes about 50us per sample.

In the case of FT8, there are 40 available frequency steps from one of the eight tones to the next.  FT8 transmit data generates the eight tone values (0, 1, 2 … 7) . These are mapped to the values (0, 40, 80 … 280), which are sent to the filter.

Unfiltered frequency steps

Gaussian filtered frequency steps

 

Unfiltered (blue) and filtered (black) 8-FSK spectrum,
showing 1,6 KHz sample-rate artifacts

 The above plot shows the performance of an earlier version of the FIR, which was running at a 1.6 KHz sample rate.  Increasing this rate to 2.4 KHz pushed the sampling artifact further out and reduced its amplitude.  Updating the Si5351 at the 2.4 KHz rate required speeding up the I2C interface and optimization of the register updates — more on this to follow.

While WSPR and APRS have no filtering requirement, for these modes the Drift Buoy uses a four-stage Gaussian FIR, clocked at 2.4 KHz, to provide filtering similar to the audio bandwidth of a SSB transmitter.

Next:

• FSK with the Si5351 Clock Generator (Increasing the Si5351 register update rate)

This is a simplified illustration of the Si5351, as configured to to generate the WSPR frequencies used in the  Drift Buoy design.

The reference comes from a 10 MHz TCXO, which provides acceptable stability.  The TCXO has an initial frequency accuracy of +/- 2.5ppm, which gives a +/- 25 Hz accuracy at the 10 MHz transmit frequency.  Better initial frequency accuracy and secondary digital temperature compensation can be achieved in software, but this is not necessary for Drift Buoy operation

The output divider is programmed to divide the PLL VCO frequency by 64 (no fractional component), which provides the cleanest spectral output.  The output divisor must be chosen so that the PLL frequency is within the available 600-900 MHz range. The FSK is done using the PLL feedback divider to vary the PLL frequency.

Determining the  PLL divider values is fairly simple.  We start by taking the desired output frequency (in this case 10.1402 MHz) and multiplying it by the output divider value (here, 64).  This gives us a PLL frequency of 648.9728 MHz.  We then take this PLL frequency and find the feedback divisor that will give us our reference frequency (here, a divisor of 64.89728 matches our 10 MHz reference).

So how do we set our “A + B/C” fractional divider to give us a ratio of 64.89728?  The “A” value is easy, that’s just 64.  We could set B = 897,728 and C = 1,000,000 — that would work, and setting C to one million makes the math easy.  But WSPR FSK tone spacing of 1.4648 Hz requires precise frequency control, and with a denominator of 1,000,000, incrementing the numerator by one gives a frequency change of 0.15625 Hz and you can’t get a 1.4648 step with that increment.  You can get close, probably close enough, but with a little math we can select divisor values that work much better.

Here’s a useful (very simple) equation for finding a PLL fractional-divider denominator when you are searching for a particular frequency step:

Fx = reference oscillator frequency in Hz,
OutDiv = output stage divisor.  This can be an integer or a fractional division,
Fdelta= desired output frequency step in Hz.
PLLdenom = PLL fractional divider denominator (the “c” in a + b/c)

Here’s the relationship.  Fdelta= Fx / (OutDiv * PLLdenom).

Rearranging this, we get:  PLLdenom = Fx / (OutDiv * Fdelta).

So for WSPR,  we have:

• Fdelta = 1.4648
• OutDiv = 64
• Fx = 10e6

Which results in PLLdenom = 106669.8525

Since the “C” denominator can only hold integer values, we could round up to 106670, but we can do better.  The “C” value in the Si5351 fractional divider can be any value up to 1,048,575 (which is 2^20 – 1), so we can multiply this PLLdenom by 8, giving a rounded-up “C” of 853,359 (we could also multiply by 9 and still stay within the limits, but for some unknown reason I am using 8).  With this numerator we have a minimum frequency step of 0.18309996 Hz.  Incrementing the “B” numerator by 8 gives steps of 1.46479969 Hz — well within a microHz of the WSPR spec.  We will use these small steps later, when we do Gaussian filtering of the FSK modulation.

So what about the “B” numerator?  With B set to zero, the output frequency will be Fx * A  / (output divider), or in this case 10MHz * 64 / 64, or 10 MHz.  To get the desired 10.1402 MHz we need to set the “B” numerator to  (10,140,200 - 10,000,000) / 0.183099961, which equals 765702 (rounded).  Alternately, we can take the original 64.89728 divisor from our first calculation, and multiply the fractional part by  C/1,000,000 which also equals 765702 (rounded).

There are ways to achieve even finer frequency resolution, by changing both the “B” and “C” values — see the “Farey Sequence” — but the simple method used here requires only one parameter change, allowing for faster configuration of the Si5351 (more on that later.)

This example was for WSPR modulation, but the principles apply to the other FSK modes.

 

Next: FSK with the Si5351 Clock Generator (Gaussian FSK)

The Si55351 Clock Generator chip  is a real workhorse.  Give it a clock reference  (10 – 40 MHz), or a crystal (25 – 27 MHz) and it can generate three different output frequencies, between 2.5 KHz and 200 MHz.  There are two internal PLLs that can run from 600 MHz to 900 MHz, with fractional synthesis feedback dividers that can provide extremely high resolution.  Each of the three output pins is driven by a fractional divider, and a smoothing filter that significantly reduces the frequency transients caused by the digital dividers, providing quite a spectrally pure output for such an inexpensive device (about $1).  There are more features such as spread-spectrum dithering, and phase offset control (the phase offset can be used to drive quadrature modulator and demodulator architectures.)

With the fractional dividers used in both the PLL feedback and the three output stages, with some restrictions milli-Hertz frequency resolution can be obtained over the full frequency range.   Frequency accuracy is determined by the accuracy of the reference or crystal input. Configuration of the chip is done using a I2C interface.

In the drift-buoy I am using the Si5351 to generate the 30-meter (10.10 – 10.15 MHz) CW and FSK carrier frequencies.  The 3.3V logic level output of this chip feeds a small 1W class-E power amplifier, which drives a short whip antenna.  The FSK modes being used are APRS (2-FSK, 300 Baud, +/- 100 Hz), WSPR (4-FSK, 1.4648 Baud, 1.4648 Hz tone spacing), and FT8/JS8 (8-FSK, 6.25 Baud, 6.25 Hz tone spacing).

Given all the options and flexibility of the chip, there are many ways to generate a specific output frequency.  When generating the FSK frequencies there are many factors to consider.  In the following posts I will cover:

• Selecting and setting the fractional divider values
• Generating Gaussian Frequency Shift Keying
• Increasing the Si5351 register update rate

Next: FSK with the Si5351 Clock Generator (Fractional Dividers)