Issue link: https://resources.pcb.cadence.com/i/1480205
APPLICATION NOTE 3 Where: E_Cell signifies the PSpice call to a VCVS named E_Cell +OUT and -OUT are the output nodes of the VCVS TABLE is the PSpice behavioral modeling TABLE directive {V(x)} is the controlling voltage for the table (0,1.5) (0.5,1.3) (1.0,0.0) are the table pairs that are output to +OUT and -OUT based on the value of V(x). If V(x) is 0, signifying 0% discharge, E_Cell will have the first table pair value of 1.5 Volts. If the cell is 50% discharged, the second table pair will be used and so on. For in-between discharge values, PSpice uses linear interpolation between the table pairs. Note: The actual lookup tables are composed of 30 or more pairs of data to provide finer granularity of the resulting discharge voltage curve. Modeling Discharge Current Sense and Cell Resistance To model the discharge current sense and the cell resistance, add a zero-valued voltage source in series with the output voltage. The cell resistance is modeled as a simple resistor for NICD or Lead-Acid cells and as a more complex variable resistance that depends on the cell's state of charge for Alkaline cells. Modeling the State-of-Charge To model the state-of-charge (SOC), use a simple and appropriately sized capacitor as the charge storage element that simulates the available charge of the cell. Size this capacitor so that it has a value of 1 Volt at 100% cell capacity and 0.5 Volts at 50% cell capacity. This capacitor is given the following value at the start of the simulation by PSpice's Parameterization function: C_CellCapacity 50 0 {3600*CAPACITY*FudgeFactor} The capacitor, C_CellCapacity, is connected between nodes 50 and 0 and is given a value of the Amp-hour capacity of the cell times a conversion from hours to seconds (3,600 seconds = 1 hour) times a fudge factor (FudgeFactor). If a cell has a 10 Amphour capacity, C_CellCapacity equals10 * 3,600 or 36,000 Farads; this is a big capacitor, but a workable value that is easy to understand. FudgeFactor adjusts for the difference in the manufacturer's listed Amp-hour capacity (i.e., some cutoff voltage with some capacity remaining at the cutoff) and the simulated capacity of 0 Volts output at 0% remaining capacity. To correct for this, and still allow the model user to use the manufacturer's listed capacity, a FudgeFactor value of 1.01 to 1.1 is included. The actual usable capacity of a cell depends on the rate at which it is being discharged. Most manufacturers list the capacity at the most favorable rate, usually, at greater than 20 hours discharge. At any faster rate, the cell is less efficient and results in a nonlinear function of the discharge rate. This must be characterized as a lookup table at many discharge rates. This inefficiency is modeled as a VCVS in series with the output voltage of the battery state-of-charge node (the voltage on C_CellCapacity). This VCVS subtracts a given amount of capacity from the cell during discharge. The amount subtracted depends on the rate at which the cell is being discharged. To determine the rate at which the cell is being discharged, it is convenient to normalize the discharge rate in Amps to a more conventional cell rate called the C rate. The C rate is defined as the capacity of the cell in Amp- hours when it is discharged completely in one hour. This normalization makes it easy to determine the cell inefficiency at different rates, and between different cell sizes, because it converts discharge in Amps to discharge in "C" units of the battery capacity at one hour. This conversion is done in the model by the VCVS, E_Rate, as follows. E_Rate RATE 0 VALUE = {I(V_Sense) / CAPACITY}