# Constant power capacitor discharge

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#### Amirbaro

##### Newbie level 4
I'm trying to calculate or simulate capacitor charge/discharge behavior while connected to constant power load (DC-DC) and at the same time charged by a battery. (Battery, capacitor and DC-DC connected in parallel)
There are two power modes, low and high. Most of the time the load is in low power and the capacitor is fully charged. Once in a while there is high constant power pulse that causes a discharge.
What is the formula for constant power discharge?
Is it considered constant power discharge if it being charged by a battery simultaneously?
How to calculate the current from battery during this high power pulse?
And last question:
The battery type is Zinc air. Where I can find a pspice model for it?

Thanks

For your meaning of "constant power discharging", the average charging current will be equal to the average discharging current. This is the formula.

When a current pulse (Ip) of a short time (t) discharges a capacitor, the capacitor voltage will decrease by dV:
dV = Ip*t/C
If C is relatively small, the drop may become large in comparison to Vcc. For example:

Vcc = 5 V
Ip = 1 A
t= 1 ms
C= 1000 uF
dV = 1*1e-3/1000e-6 = 1V

at the start of the pulse is Vcc*Ip = 5*1 = 5 W
at the end of the pulse is (Vcc-1)*Ip = 4*1 = 4 W
This is not a constant power load (it is a constant currrent load).
But if the load power is indeed constant then the load current should increase with time to compensate the voltage drop. Is this your case?

The battery type is Zinc air. Where I can find a pspice model for it?
You rarely won't find an exact model. As a first order estimation, you can assume a voltage source with internal resistance. If not specfied by the manufacturer, you have to measure the resistance.

Assuming a voltage source with internal resistance is also the key to answer the other questions. You have to refer to electrical circuit theory.

You'll notice, that the capacitor voltage and current follow a differential equation, which solution is different from the standard RC discharge exponential function due to the constant power load.

Exactly, As the voltage goes down the current increaes.

Exactly, As the voltage goes down the current increaes.

Do you mean the way the capacitor is discharged on the pic attached?

Kerim

Note:
This is only the function of the capacitor voltage Vc(t) during its free discharge if its load happens to be of constant power instead of a resistor.

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You can find a battery model under Spice_Elem library(<installdir>/tools/capture/library/pspice/advanls/spice_elem.olb
This would allow you to choose AH & voltage of battery. You may not get exact discharge characteristic, but this would be close.

About simulation of constant power load: you need to model a variable resistance. This can be done using G device, Where current drawn is function of voltage, an voltage drop the current increases in same proportion to maintain constant power.

Hope this helps.

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