The BLE ECO and WCO are already included in the kit (pre-installed in Ez-BLE Creator Module) and user need not solder it. These are part of the BLE module. Please refer to the "A.2.6.5 System Crystals" in the user guide.
Whether ECO is there or not is a secondary issue (BTW if you look at the picture you'll notice that it is not), the main question was about the capacitor values that do not match the formula from the application note and the data sheet. I simply wanted to understand why, that's all.
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In the PSoC 6 based module there is only the BLE ECO included, no WCO.
For low-power applications, with BLE using the low power modes or an accurate time is needed (RTC) a WCO should be added to the system. In case of BLE the WCO ensures that the timings are met while the device is in DeepSleep (Main clock is off).
An external ECO for the CPU is only needed if the IMO accuracy does not meet the project requirements.
Yes, it is using the alternative formula. I assume it is done because lower capacities will result in a lower power consumption, but I am not sure.
If I have to guess the formula in the Hardware Design Guide is wrong and should be C = 2*CL - CL/2
That way it returns the same results for 6pF and 12.5pf as the formula in the Crystal Oscillator Selection Guide (AN95089)
And basically it is just a complex way to say that C = 3/2 CL isn't it?
Considering: the 2:1 ratio, C1 = C and C2 = 2*C1 = 2*C
CL = (C*2*C)/(C+2*C) = (2*C²)/(3*C) = (2*C)/3 --> C = 3/2*CL
Crystal clear ! Thanks Achim !
There is still a small discrepancy: C2, i.e. C37 on the prototyping kit, is not exactly equal to 2*C1, i.e. C36 (33 and 18 pF respectively) but I got the idea. As long as C = 3/2 CL it does not matter if C1=C2 or C2=2*C1 right ?
Edit: I found this useful answering my own question : http://www.nkg.com.hk/pdf/NKG-TIT_OscFreqDeviations(E).pdf and this http://geyer-electronic.de/fileadmin/user_upload/box/GEYER-Crystal-or-Oszillator-how-to-apply.pdf
"C1 is smaller than C2 in order to enhance the start-up performance of the circuit"
Well after a bit more digging, here is what I found. Hopefully someone else may find that useful:
There are actually 2 ECO ! One is called "ECO for BLE" and is already included in the module as shown on the schematics page 20 of the datasheet (https://www.cypress.com/file/428336/download) and is connected to pins X0 and X1 (M5 and M4 on the 116-BGA package) The other is just call ECO, is optional and is connected to pins P12.6 and P12.7 (G5 and H5).
That's very confusing because it is not mentioned anywhere in and even some of Cypress' application specialists ignored it... So to summarise:
ECO-BLE ECO WCO
CYBLE-416045-02 y n n
PSoC63 BLE prototyping kit y n y