Estimating DC/DC Converter Efficiency with Different Input Voltage

Wahyu Pamungkas, S.T

Background:

A DC/DC converter is usually fed by constant voltage battery charger in parallel with associated battery when the load is categorized as critical and a regulated voltage is required. It means, when main supply is failed, the battery will take over to energize the critical load. In its autonomy time duration, the battery’s voltage is going lower. The voltage reduction will impact to DC/DC converter’s efficiency

Defining the limitation

As we are understood, the best efficiency of DC/Dc converter can be achieved when input voltage is closest with output voltage [1]

. At this condition the Dc/Dc converter’s manufacturer is sometimes confident to warranty efficiency until 95%. Commonly, the efficiency at the best is high as 90%. The ideal condition can’t be always maintained especially when load shall be fed by battery. This situation is illustrated by figure 1.

Figure 1: A modeled regulated output Dc/Dc converter with dual input

In figure 1, the converter is fed by a constant current DC source, such as battery charger in parallel with battery banks. In this configuration, battery charger is set at floating charge voltage of the battery; therefore the output voltage (V out) shall set closest to input voltage (V in) to get the best efficiency of the converter. In practical application, the setting of Vout shall also consider the range of load’s input

voltage. The setting of Vin will impact the number of battery’s cells. In this very early design, these factors shall be considered.

In scenario where constant voltage DC source is failure, the critical load is fed by battery. Depend on the rate of discharged current; the battery terminal will be drop soon. Usually during battery sizing, we have set the lowest battery voltage base on required autonomy. In this point we must define the efficiency of the converter and define its impact to the heat dissipation and then to temperature increase.

The equation of efficiency can be described as below

휂 =푃표푢푡푃푖푛

(1)

휂 =푃표푢푡푃푖푛

(2)

Where Pin0 is power input when DC/DC converter is fed by floating charge voltage (Vin0) of constant voltage DC source. This is ideal situation, where the highest efficiency can be achieved. The input current associated with Pin0 is Iin0.

Pin1 is power input when DC/DC converter is fed by the lowest voltage from battery (Vin1). The input current associated with Pin1 is Iin1

The losses power in both situations,

푃푙표푠푠 = 푃푖푛 − 푃표푢푡 (3) 푃푙표푠푠 = 푃푖푛 − 푃표푢푡 (4) In both conditions the critical load is always kept the same; so Pout is same in both conditions.

The dissipative component, resistance, of the input part of converter can be calculated.

푅푖푛 =

푃푙표푠푠퐼푖푛

(5)

From equation 1 and 3, the input resistance can be described as

푅푖푛 =

푃표푢푡 1 휂 − 1퐼푖푛

(6)

In this step we have succeeded to develop the internal characteristic of dissipative component of the converter.

Now, when we feed the converter from lowest voltage from battery, Vin1, the Ploss1 can be represented as combination of equation (5) and (6)

푃푙표푠푠 = 퐼푖푛 .

푃표푢푡 1 휂 − 1퐼푖푛

(7)

푃푙표푠푠 =

푃표푢푡휂 .푉푖푛

.푃표푢푡 1 휂 − 1

퐼푖푛 (8)

푃푙표푠푠 =

휂 푉푖푛휂 .푉푖푛

.푃표푢푡 1 휂 − 1 (9)

Suppose the ratio of floating charge voltage and battery lowest voltage is depicted as

훽 =푉푖푛푉푖푛

(10)

Equation (9) now can be simplified

푃푙표푠푠 =

휂휂 .훽 .푃표푢푡 1 휂 − 1 (11)

In equation (11), we have defined Ploss1 as function of Pout0, or Ploss1=f(Pout0). Now, It is turn to define new efficiency at lowest battery’s voltage (η1) as a function of Pout0. We know that η=Pout/(Pout+Ploss), so η1 can be described as below

휂 =1

1 +휂휂 .훽 1 휂 − 1

(12)

To simplify, we assume

퐾 = 휂 .훽 1 휂 − 1 (13) Then, equation (12) become

휂 =1

1 + 1휂 .퐾

(14)

And it is a simple quadratic equation

0 = 휂 − 휂 + 퐾 (15) The solution for above equation (15),

휂 =

1 + √1 − 4퐾2

(16)

Equation (16) will have solutions, when K < ¼. This limitation will help us to define maximum limit β.

휂 .훽 1 휂 − 1 <14

(17)

훽 <1

2휂 1휂 − 1

(18)

Defining System

As we have knew the limitation factor, now we can develop flowchart for sizing the system

Conclusion

In this document, a proper estimating efficiency of DCDC converter at final voltage is presented. A flowchart to define battery sizing calculation, load balance and temperature increase inside DCDC converter is also introduced.

Note:

1. The complement of equation (16), 휂 = √ , is not applied, since it will result lower value

than 50%. A value that hardly to exist when ratio input voltage is limited at β.

Source

1. Source Resistance: The Efficiency Killer in DC-DC Converter Circuits, Maxim, 2004