8.2.1.2 Detailed Design Procedure

To limit the capacitor current, first connect the LMP8646 output to the feedback pin of the LM3102, as shown in Figure 28. This feedback voltage at the FB pin is compared to a 0.8V internal reference. Any voltage above this 0.8V means the output current is above the desired value of 1.5A, and the LM3102 will reduce its output current to maintain the desired 0.8V at the FB pin.

The following steps show the design procedures for this supercap application. In summary, the steps consist of selecting the components for the voltage regulator, integrating the LMP8646 and selecting the proper values for its gain, bandwidth, and output resistor, and adjusting these components to yield the desired performance.

Step 1: Choose the components for the Regulator.

Refer to the LM3102 evaluation board application note (AN-1646) to select the appropriate components for the LM3102 voltage regulator.

Step 2: Choose the sense resistor, R_SENSE

R_SENSE sets the voltage V_SENSE between +IN and -IN and has the following equation:

In general, R_SENSE depends on the output voltage, limit current, and gain. Refer to section Selection of the Sense Resistor, RSENSE to choose the appropriate R_SENSE value; this example uses 55 mOhm.

Step 3: Choose the gain resistor, R_G, for LMP8646

R_G is chosen from the limited sense current. As stated, V_OUT = (R_SENSE * I_LIMIT) * (R_G / 5kOhm). Since V_OUT = V_FB = 0.8V, the limited sense current is 1.5A, and R_SENSE is 55 mOhm, R_G can be calculated as:

Step 4: Choose the Bandwidth Capacitance, C_G.

The product of C_G and R_G determines the bandwidth for the LMP8646. Refer to the Typical Performance Characteristics plots to see the range for the LMP8646 bandwidth and gain. Since each application is very unique, the LMP8646 bandwidth capacitance, C_G, needs to be adjusted to fit the appropriate application.

Bench data has been collected for the supercap application with the LM3102 regulator, and we found that this application works best for a bandwidth of 500 Hz to 3 kHz. Operating outside of this recommended bandwidth range might create an undesirable load current ringing. We recommend choosing a bandwidth that is in the middle of this range and using the equation C_G = 1/(2*pi*R_G*Bandwidth) to find C_G. For example, if the bandwidth is 1.75 kHz and R_G is 50 kOhm, then C_G is approximately 1.8 nF. After this selection, capture the plot for l_LIMIT and adjust C_G until a desired load current plot is obtained.

Step 5: Calculate the Output Accuracy and Tolerable System Error

Since the LMP8646 is a precision current limiter, the output current accuracy is extremely important. This accuracy is affected by the system error contributed by the LMP8646 device error and other errors contributed by external resistances, such as R_SENSE and R_G.

In this application, V_SENSE = I_LIMIT * R_SENSE = 1.5A * 55 mOhm = 0.0825V, and R_G = 50 kOhm. From the Electrical Characteristics Table, it is known that V_OFFSET = 1 mV and Gm_Accuracy = 2%. Using the equations shown in Equation 8, the output accuracy can be calculated as 3.24%.

After figuring out the LMP8646 output accuracy, choose a tolerable system error or the output current accuracy that is bigger than the LMP8646 output accuracy. This tolerable system error will be labeled as I_ERROR, and it has the equation I_ERROR = (I_MAX - I_LIMIT)/I_MAX (%). In this example, we will choose an I_ERROR of 5%, which will be used to calculate for ROUT shown in the next step.

Step 6: Choose the output resistor, ROUT

At start-up, the capacitor is not charged yet and thus the output voltage of the LM3102 is very small. Therefore, at start-up, the output current is at its maximum (I_MAX). When the output voltage is at its nominal, then the output current will settle to the desired limited value. Because a large current error is not desired, ROUT needs to be chosen to stabilize the loop with minimal initial start-up current error. Follow the equations and example below to choose the appropriate value for ROUT to minimize this initial error.

As discussed in step 4, the allowable I_ERROR is 5%, where I_ERROR = (I_MAX - I_LIMIT)/I_MAX (%). Therefore, the maximum allowable current is calculated as: I_MAX = I_LIMIT (1+ I_ERROR) = 1.5A * (1 + 5/100) = 1.575 A.

Next, use Equation 14 below to calculate for ROUT:

Equation 14.

For example, assume the minimum LM3102 output voltage, V_{O_REG_MIN}, is 0.6V, then ROUT can be calculated as ROUT = [1.575A * 55 mOhm * (49.9k / 5k) - 0.8] / [ (0.8 / 2k) - (0.6 - 0.8) / 10k] = 153.6 Ohm.

Populate ROUT with a resistor that is as close as possible to 153.6 Ohm (this application uses 160 Ohm). If the limited sense current has a gain error and is not 1.5A at any point in time, then adjust this ROUT value to obtain the desired limit current.

We recommend that the value for ROUT is at least 50 Ohm.

Step 7: Adjusting Components

Capture the output current and output voltage plots and adjust the components as necessary. The most common components to adjust are C_G to decrease the current ripple and ROUT to get a low current error. An example output current and voltage plot can be seen in Figure 29.