Why are there many spurious signals around the carrier when generating 21 GHz in fractional mode using the ADF4371 PLL evaluation board?

The spurious signals around the carrier at 21 GHz in fractional mode are likely due to Fractional-N spurs. Reducing the charge pump current can help mitigate these spurs, which will also affect the bleed current. Additionally, using a phase word can be effective against fractional-N mode spurs. The datasheet recommends a phase word of 8388617. You can try a prime number close to 45°, 90°, or 180°.

How can I write SPI code to change frequencies using the ADF4371?

If you want to write your own code for SPI to change frequencies using the ADF4371, you can use the ADF4371's no-OS driver and also check the SDP-S part which is used on this part's EVAL board. The no-OS driver can be found at https://github.com/analogdevicesinc/no-OS/tree/master/drivers/frequency/adf4371. The SDP-S Evaluation Board documentation is available at https://www.analog.com/en/design-center/evaluation-hardware-and-software/evaluation-boards-kits/sdp-s.html#eb-documentation. These resources will provide the necessary information on how to update the registers and obtain the required values for frequency changes.