# How to extend a power supply for droop compensation

Wouldn’t it be nice if the existing power design could easily be extended with the capability to compensate for the voltage drop across known cables and switches on load condition? This article describes the solution applicable for nearly all power designs where the feedback divider is accessible. For help with design, calculations are developed and given in a cookbook manner. The description is based on the practical example of a car’s centre console USB charging port, which is powered from the electronics located somewhere in the dashboard. To charge mobile digital devices, USB current capability has to be 2A or more. However, the stringent USB port supply voltage limits is often directly contradicted by the use of cheap thin cables, which experience a huge voltage drop.

**Voltage drop on power lines and connectors**

**Figure 1 Real Equivalent Circuit Diagrams**

According to the real equivalent circuit diagram Figure 1 the voltage drop in a system is illustrated. The voltage V_{load} is dependent on the current I_{load} , the wire resistance R_{wire} and the connector resistance R_{con}. Basically, everything that is in series with the power line – for example additional switches – needs to be taken into account and V_{load} will drop accordingly. Figure 2 illustrates this characteristic.

**Figure 2 Voltage Drop**

If R_{drop} is known and fixed in the system, with the following approach the power supply could be modified to compensate the voltage drop to keep V_{load} constant.

**Car Centre Console USB Port Charger Example**

Using the practical example of a car centre console USB-Port (Figure 3) the need for compensation is demonstrated. The Infotainment Head-Unit contains the electronics and is located in the dashboard. The USB-Port is a passive implementation and located in the centre console connected via a 3m cable. To keep cost and weight down the wire diameter or cross-sectional area of the cable needs to be minimized.

**Figure 3 Block-diagram Car Centre Console USB Charging Port**

The equivalent circuit of the car centre console USB charging port is shown in Figure 4. The power supply keeps the voltage constant on V_{out} because the feedback resistor divider is referenced to this point. For proper charge negotiation, a USB-Charging-Port-Controller and Power-Switch is needed. TPS2546-Q1 https://www.ti.com/product/tps2546-q1 provides the electrical signatures on D+/D– lines to support charging schemes. The switch is in series with the power line and highlights the resistivity that the power switch, connector and wire add to an unwanted voltage drop.

**Figure 4 Equivalent Circuit Car Center Console USB-Port**

**Voltage Drop Issue USB Port**

As per the USB definition the voltage limits of V_{Bus} are 4.75V and 5.25V. To cope with the voltage drop at maximum current the output of the DC/DC-Converter needs to be set to the maximum voltage. Assuming an accuracy of two per cent, the maximum allowable nominal voltage is 5.19V not to violate the 5.25V max. As a consequence of the tolerance the minimum voltage is 5.14V. What we have to take into account is the following: Minimum V_{out} voltage 5.14V minus minimum V_{Bus} voltage of 4.75V means that 390mV is the margin we have left as total acceptable voltage drop. Fast charging requires 2.1A. Looking in the data-sheet of the USB-Charging-Port-Controller and Power-Switch TPS2546-Q1 and considering the worst case conditions over temperature we find the R_{DSon} of the 120mΩ power switch translates to a further 252mV voltage drop. Deducted from the orginal 390mV window gives us 138mV margin as voltage drop over the cable and connectors. Plugging a 2.1A current into ohms law we find we have 66mΩ left for the cables and connectors. Based on that and the specific resistance of copper we can calculate for the wire, a 2mm2 cross sectional area, which is big, expensive and heavy. Incidentally, the rated current of such a wire is about 30A.

**Implementation Droop Compensation**

As shown in Figure 5 the droop compensation can be implemented by measuring the current with the current shunt monitor INA213. The voltage output V_{cs} feeds back via R_{m} to the feedback resistor network of the converter. The converter block P1 illustrates the very basic principal of the control loop. The feedback FB is compared to a reference voltage and V_{out} is adjusted via the actuator scheme that FB is V_{REF}. Therefor the feedback voltage FB is seen as constant and equal to V_{REF} of the converter, which is used as the base for all calculations. The inverse measurement of the load current I_{load} via the shunt resistor R_{s} is key for the application. To achieve a rise on V_{out} if load current I_{load} is increasing, the output voltage of the current shunt monitor V_{cs} needs to be decreased. Under no load condition V_{cs} is V_{REF}. If the load is increasing V_{cs} will decrease and V_{out} will rise accordingly. This is exactly what we want.

**Figure 5 INA213 Droop Compensation**

With that implementation the characteristics of the power supply is changed according to Figure 6.

**Figure 6 Voltage Drop Compensated**

Bi-Directional Current Shunt Monitor

For this application, the INA213A-Q1 https://www.ti.com/product/ina213a-q1 is used, a member of the INA21x family. These are well-suited devices for the implementation of droop compensation. It offers high-side current measurement with a common mode range extending the supply voltage. So V+ could direct connect to V_{out}. In addition the bi-directional feature is important to achieve the negative characteristic needed on the output. With the addition of Zero-Drift technology, these devices offer excellent accuracy and offset voltage down to 35µV (Max, INA210). This enables shunt drops of 10mV at full-scale, resulting in very low resistance current shunts. For different load currents, various fixed gain types are available. Quiescent current is as low as 100µA (max) and comes in small packages SC70 or THIN QFN. For the car centre console USB-Port charger example, automotive qualification is mandatory and is also offered by this family.

**Dimensioning and Calculations of the Components**

**Precondition Drop Resistance and Operating Points**

The precondition for a proper compensation of the voltage drop is the knowledge of the drop resistance R_{drop}. According to Figure 1 R_{drop} consists of all resistances in between the output voltage and the connection point where the voltage has to be kept constant. Which are wires, connectors, switches, etc. As such, the first step is to calculate the voltage drop that needs to be compensated for. This is calculated basically as per ohms law using R_{drop} and the maximum load current.

It is obvious with no load there is no drop. This gives us the first operating point OP1.

**OP1:**

The second operating point OP2 is determined at maximum system load.

**OP2:**

**Current Sensing**

The load current I_{load} is determined using the shunt resistor R_{shunt} and gained up with a differential amplifier. As seen in Figure 5 INA213 Droop Compensation, the current is sensed in the negative direction. Therefore the voltage output of the current sense amplifier V_{cs} is calculated as per equation 4.

V_{REFcs} derived from V_{out }via R3 and R4 voltage divider according to Equation 5.

To take advantage of full linear swing for OP1, V_{REFcs} should be set below the current shunt monitor limitations of the upper swing. As per datasheet of the INA213 (V+)-0.2V. R3 and R4 should be chosen accordingly.

Now the shunt resistor, in conjunction with the GAIN found by selecting the right current shunt monitor, can be calculated as per Equation 6 and OP2 to allow the maximum load current for minimum output. For V_{cs2} the limitations of the current shunt monitor for the lower swing needs to be taken into account. As per datasheet of INA213 (VGND)+0.05V.

**Feedback Divider Network**

Having the formula for the current sense output, the next step is to use the following formulas and calculations for the feedback divider network.

**Figure 7 Feedback Divider Network**

According to Kirchhoffs law:

Substitute Equation 8, 9, 10 in 7:

Re-position of Equation 11 and substitute the resistance with conductance:

**Linear System of Equations**

Equation 12 gives now the base for further development of a linear system of equations, defined by two operating points with the system current extreme values for OP1 and OP2. Equation 13 represents the linear system of equation in matrix notation.

V_{cs1} and V_{cs2} can be determined by Equation 4. Select a value for R_{2}. Best practice is to select the value already in the power design, as this helps ensure network stability. The feedback voltage V_{fb} of the converter is found in the datasheet of the regulator. With that the linear system of equations can be solved by hand or by a mathematical tool and the result is G_{1} and G_{M} conductance values. Just invert and the result is R_{1} and R_{M}.

**Conclusion**

The voltage drop on power lines can be compensated for if the drop resistance is constant in the system. By means of a bi-directional high-side current shunt monitor, the power-supply can be modified to rise V_{out} if I_{load} is increasing. Only minor changes to the existing application-tailored power supply are necessary. Simulations can also be made with the free SPICE-based analogue simulation program Tina-TI found here: https://www.ti.com/tool/tina-ti. In addition Design-Kits and Evaluation-Modules are available.

**Bibliography**

Automotive USB Charging Port Power Switch & Controller. https://www.ti.com/product/tps2546-q1

Bi-Directional Zero-Drift, Current Shunt Monitor. https://www.ti.com/product/ina213a-q1

SPICE-Based Analogue Simulation Program. https://www.ti.com/tool/tina-ti