RTC backup by super capacitor estimation issue

I create a RTC backup circuit for a STM32L412CBT6. Circuit work but not as long as I estimate during design.

Here is the schematic (VBKP go directly to STM32 VBAT pin):

SC1 capacity is 0.33F

Here is my estimation :

CHARGE
Tc = RcxC
Tc = 100 * 0.33
Tc = 33 s
To fully charge the super capacitor at 5xTc I theoretically need 165 s (2 min 45 s)
I do measurement and It's OK, my super capacitor from 0V take about 2 min 30 to go to 3.2V.

DISCHARGE
To get the Rd, the internal resistance of the VBAT circuit of STM32, I see in datasheet RTC theoretically need 300nA at 3V, but when I take voltage across R17 during discharge I got 5mV, so current is 50µA (166 times more but it's an other problem so let's take 50µA)
Rd=3 / 0.00005
Rd = 60000 ohms (60 kohms)
Td = Rd x C
Td = 60000 x 0.33
Td = 19800 s
To fully discharge the super capacitor at 5xTd I theoretically need 99000 s (27 h 30 min)
To discharge super capacitor at 0.7xTd (50% is about VBAT min for RTC) I theoretically need 13860 s (3 h 51 min)

I do measurement and I'm totally out :

HOUR    SC1 Voltage [V]
22:00   3,21
22:12   2,62
22:22   2,44
22:33   2,29
22:49   2,10
22:59   2,00
23:12   1,86
23:24   1,74
23:34   1,64
23:47   1,52
0:15    1,25
0:24    1,16
0:42    0,99
0:55    0,86
1:26    0,58
1:35    0,51
1:53    0,37
2:34    0,18
2:56    0,14
3:03    0,13


I take about 5H to discharge the super capacitor (far away from 27H)

QUESTION

• I think my estimation problem is from Rd (internal VBAT circuit resistance of STM32) determination, but why I'm so far of my estimation ? Can you help me to find my error ?
• If someone got an idea for why my RTC sink 50µA instead of 300nA, let me known (Voltage measurement device error ?)
• If someone got an idea to connect (without regulator) the 3V3 of this circuit to a LiPo (3.7V) battery (charge at 4.2V), let me known.

EDIT 1 :

• I see no big deal here. Somewhere in the drawer I have 20yrs old PLC with a goldcap, external 64kB CMOS RAM and Dallas RTC, when new, it could hold data and time for about two weeks. I can't believe that in yr 2020 you don't have more than few hours autonomy even without the CMOS RAM. Commented Jul 1, 2020 at 11:20
• Have you seen this: community.st.com/s/question/0D50X00009XkdqpSAB/… Commented Jul 1, 2020 at 11:37
• Well really interesting post about leakage, thank you Marko Commented Jul 1, 2020 at 11:47

You should calculate the discharge time based on the voltage across the capacitor decaying to the minimum value that the RTC can survive on. That voltage might be (for a guess) 1 volt. If your charged voltage is 3 volts then you can say this: -

$$dv = \text{2 volts}$$

You also know the current (50 uA) and using this well-know capacitor formula: -

$$I = C\cdot \dfrac{dv}{dt}$$

You can rearrange for dt: -

$$dt = C\cdot\dfrac{dv}{I} = \text{13,200 seconds or 3 hours and 40 minutes}$$

This is based on a 0.33 F supercapacitor.

If someone got an idea for why my RTC sink 50µA instead of 300nA

It's most probably the DFLS130L-7 schottky diode. Take a look at this graph in the data sheet: -

With power removed, the anode will be at 0 volts and the capacitor diode will be reverse biased at around 1 to 3 volts. At 2.5 volts reverse, you would expect to see 50 uA discharge current flowing in the diode.

Choose a different diode is my advice.

• Many thanks Andy for correcting my point of view. Your method is simple and obvious for me now. An other big thanks for the DFLS130L-7 reverse current. It's a big miss, I think I need holiday....You save me a lot of time, your are really kind. Commented Jul 1, 2020 at 11:35