
Keywords: tricklecharger,trickle,charger,supercap,super cap, app note 3517
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Estimating Super Capacitor Backup Time on TrickleCharger RealTime Clocks
© May 24, 2005, Maxim Integrated Products, Inc.


Abstract: The Maxim realtime clock (RTC) family includes a number of parts with integrated tricklecharging 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 V_{CC} is absent. The energy stored in the capacitor will maintain clock operation for a period of time that is determined by several factors. This application note discusses methods used to calculate backup time based on capacitor size.
Also see application note 3816, "
Selecting a Backup Source for RealTime Clocks."
The Charging Circuit
A typical tricklecharger circuit diagram is shown in
Figure 1. A specific fourbit pattern in the upper nibble of the tricklecharger register is used to enable the trickle charger. The lower four bits are used to select a voltagedropping diode and currentlimiting 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 data sheet for details). The capacitor is connected from V
_{BACKUP} to ground (
Figure 2).
Figure 1. Typical tricklecharging 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 data sheet for chargingcurrent limits.
ChargingCurrent Calculations
The maximum charging current can be calculated as follows: assume that a system power supply of 3.3V is applied to V
_{CC}, 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:
I
_{MAX} = (V
_{CC}  diode drop)/R2
= (3.3V  0V)/R2
≈ (3.3V  0V)/2kΩ
≈ 1.65mA
As the voltage on V
_{BACKUP} 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 V
_{BACKUP}, then calculating the worstcase backup time in hours would use the formula:
[C(V_{BACKUPSTART}  V_{BACKUPMIN})/I_{BACKUPMAX}]/3600
Where:
C is the capacitor value in farads
V
_{BACKUPSTART} is the initial voltage in volts (the voltage applied to V
_{CC}, less the voltage drop from the diodes, if any, used in the charging circuit)
V
_{BACKUPMIN} is the ending voltage in volts (the minimum oscillator operating voltage)
I
_{BACKUPMAX} is the maximum data sheet V
_{BACKUP} current in amps
Given that C = 0.2F, V
_{BACKUPSTART} = 3.3V, V
_{BACKUPMIN} = 1.3V, and I
_{BACKUPMAX} = 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 I
_{BACKUP} typical value (I
_{BACKUPTYP})for I
_{BACKUP} maximum (I
_{BACKUPMAX}).
Therefore, if V
_{BACKUPTYP} is 3.3V (typ) and I
_{BACKUPTYP} 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 I
_{BACKUP} is constant, regardless of the voltage on V
_{BACKUP}. The oscillator on 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 in
Figure 3) 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 farads
Rearranging the equation to solve for t, we get:
ln(V/E)(RC) = t
From the RTC data sheet, we can get the minimum oscillator operating voltage as well as the maximum V
_{BACKUP} current (I
_{BACKUPMAX}). To estimate the load resistance, R, we divide the data sheet V
_{BACKUPMAX} by I
_{BACKUPMAX} (because the worsecase current occurs at the maximum input voltage). For this example, V
_{BACKUPMAX} is 3.7V and I
_{BACKUPMAX} is 1000nA, or 3.7/1e6 or 3,700,000Ω. Assuming that the capacitor value is 0.2F and has been charged to 3.3V, that the I
_{BACKUPMAX} is 1000nA, and that the minimum oscillator operating voltage is 1.3V, the backup time would be calculated as:
ln(V_{BACKUP}MIN/V_{BACKUP}MAX)[(V_{BACKUPMAX}/I_{BACKUPMAX}) × C] =
ln(1.3/3.3)(3,700,000 × 0.2) =
689,353s (191.5hrs)
By changing the value of C, the estimated operating time while running from the backup capacitor can be determined.
These calculations can be done using the
online calculator. This Supercapacitor Calculator implements the three equations shown above.
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APP 3517: May 24, 2005
APPLICATION NOTE 3517,
AN3517,
AN 3517,
APP3517,
Appnote3517,
Appnote 3517
