Estimating Super Capacitor Backup Time on Trickle-Charger Real-Time Clocks
Abstract: The Maxim real-time clock (RTC) family includes a number of parts with integrated trickle-charging circuitry. The trickle charger can be used to charge a secondary battery or capacitor. The battery or capacitor is used to maintain operation of the clock when the supply voltage on VCC is absent. The energy stored in the capacitor will maintain clock operation for a period of time, determined by several factors. This application note discusses methods used to calculate backup time, based on capacitor size.
A typical trickle-charger circuit diagram is shown in Figure 1. A specific four-bit pattern in the upper nibble of the trickle-charger register is used to enable the trickle charger. The lower four bits are used to select a voltage-dropping diode and current-limiting resistor. In the diagram below, either one diode or no diode can be inserted into the charging path, and the resistor values that can be selected are 250Ω, 2kΩ, or 4kΩ. Some devices provide different diode and resistor configurations (check the device datasheet for details). The capacitor is connected from VBACKUP to ground (Figure 2).
Figure 1. Typical trickle-charging circuit.
Figure 2. Typical circuit.
The user determines the diode and resistor selection according to the maximum current required for capacitor charging. Contact the manufacturer of the capacitor or check the capacitor datasheet for charging-current limits.
Charging-Current Calculations
The maximum charging current can be calculated as follows: Assume that a system power supply of 3.3V is applied to VCC, and that the trickle charger has been enabled with no diode and a 2kΩ resistor. The maximum current, when the capacitor voltage is zero, would be calculated as:
As the voltage on VBACKUP increases, the charging current decreases.
Calculating Backup Time
Now we need to determine how large the capacitor needs to be. Given the desired backup time, we need to know several other parameters: The starting and ending voltage on the capacitor, the current draw from the capacitor, and the capacitor size.
If we assume that the RTC draws a constant current while running from VBACKUP, then calculating the worst-case backup time in hours would use the formula:
C(VBACKUPSTART - VBACKUPMIN)/IBACKUPMAX/3600
where C is the capacitor value in farads.
VBACKUPSTART is the initial voltage in volts. The voltage applied to VCC, less the voltage drop from the diodes, if any, used in the charging circuit.
VBACKUPMIN is the ending voltage in volts (the minimum oscillator operating voltage).
IBACKUPMAX is the maximum datasheet VBACKUP current in amps
Given that C = 0.2F, VBACKUPSTART = 3.3V, VBACKUPMIN = 1.3V, and IBACKUPMAX = 1000nA, then:
Hours = 0.2(3.3-1.3)/(1e-6)/3600 = 0.2(2.0)(1e-6)/3600 = 111.1
If we want to know what the typical backup time should be, we would substitute the IBACKUP typical value for IBACKUP maximum.
Therefore, if VBACKUP is 3.3V (typ) and IBACKUP is 600nA (typ), then:
Hours = 0.2(3.3-1.3)/(600e-9)/3600 = 0.2(2.0)(600e-9)/3600 = 185.2
These calculations assume that IBACKUP is constant, regardless of the voltage on VBACKUP. The oscillator on Dallas/Maxim RTCs tends to act more like a resistor, so that backup current tends to decrease with the backup voltage. It should therefore be possible to calculate a more realistic backup time.
>From basic electronics, the formula to determine the voltage across a capacitor at any given time (for the discharge circuit below) is:
V(t) = E(e-τ/RC)
Figure 3. Discharge circuit.
Where τ is the time in seconds
E is the initial voltage in volts
V is the ending voltage in volts
R is the resistive load in ohms
C is the capacitor value in farad
Rearranging the equation to solve for t, we get:
-ln(V/E)(RC) = t
>From the RTC datasheet, we can get the minimum oscillator operating voltage as well as the maximum VBACKUP current (IBACKUP). To estimate the load resistance, R, we divide the datasheet VBACKUP maximum by IBACKUP maximum (because the worse-case current occurs at the maximum input voltage). For this example, VBACKUP maximum is 3.7V and IBACKUP maximum is 1000nA, or 3.7/1e-6 or 3,700,000 ohms. Assuming that the capacitor value is 0.2F and has been charged to 3.3V, that the IBACKUP current maximum is 1000nA, and that the minimum oscillator operating voltage is 1.3V, the backup time would be calculated as:
-ln(VBACKUPMIN/VBACKUPMAX)(VBACKUPMAX/IBACKUPMAX) =
-ln(1.3/3.3)(3,700,000*0.2) =
689,353 seconds, or 191.5 hours
By changing the value of C, the estimated operating time while running from the backup capacitor can be determined.
The supercapacitor calculator implements the three equations shown above.
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