# Linear Series DC-DC Converter

# DC-DC Converter

Dc-Dc converters are employed in a variety of applications, such as :

- Power supplies for personal computers
- Office equipment
- Spacecraft power systems
- Laptop computers
- Telecommunications equipment
- Dc motor drives.

The input to a dc-dc converter is an unregulated dc voltage Vg and the output is a regulated output voltage V, having a magnitude (and possibly polarity) that differs from Vg.

For example, in a computer off-line power supply, the 120 V or 240 V ac utility voltage is rectified, producing a dc voltage of approximately 170 V or 340 V, respectively. A dc-dc converter then reduces the voltage to the regulated 5 V or 3.3 V required by the processor ICs.

Several methods exist to achieve DC-DC voltage conversion. Each of these methods has its specific benefits and disadvantages, depending on a number of operating conditions and specifications.

Examples of such specifications are the voltage conversion ratio range, the maximal output power, power conversion efficiency, number of components, power density, galvanic separation of in- and output, etc.

## Linear Voltage Converters

The most elementary DC-DC converters are linear voltage converters.

They achieve DC-DC voltage conversion by dissipating the excess power into a resistor, making them resistive dividers. Clearly, this is not quite ideal for the power conversion efficiency .

Another implication of their operating principle is the fact that they can only convert a certain input voltage into a lower output voltage , having the same polarity. In other words, the value of their voltage conversion ratio is always between zero and one.

The advantage of linear voltage converters is that they are fairly simple to implement. Moreover, they generally do not need large, and space consuming inductors or capacitors, making them an attractive option for monolithic integration .

Therefore, the two types of linear voltage converters, namely the series and the shunt regulator, are discussed below .

## Series Converter

The operating principle of a linear series voltage converter is shown in Fig.1(a).

Fig.1 : (a) The principle of a linear series voltage converter and (b) a simple practical implementation

A variable resistor R_{series }is placed in series with the load R_{L}, lowering the input voltage U_{in} to output voltage U_{out}.

The resistance of R_{series} is controlled by the control system, which keeps U_{out} constant under varying values of U_{in }and R_{L}, by measuring U_{out}.

The control system also consumes power, which is illustrated by its supply current I_{cs}.

In this case the control system uses U_{in} as supply voltage, which can also be provided by U_{out}. However, the latter case will require a start-up circuit, as U_{out }is initially zero.

A practical implementation example for a linear series voltage converter is shown in Fig. 1(b).

In this example R_{series} is implemented as an NPN BJT and the control system as an OPerational AMPlifier (OPAMP), which performs the task of an error amplifier.

By doing so, U_{out} is determined as follows :

By examining the operating principle of Fig.1(a), the efficiency η_{lin} can be calculated as follows:

When I_{cs} is neglected and assumed to be zero, η_{lin} is equal to the voltage conversion ratio k_{lin }and thus independent of R_{L}. This is graphically illustrated by the black curve in Fig. 2(a). The gray curve illustrates the more realistic situation, where I_{cs }has a finite positive value. It can be seen that η_{lin }will tend to decrease when P_{out} decreases .

(a) (b)

Fig.2

Fig.2 (a) shows the power conversion efficiency η_{lin }as a function of the output power P_{out} for a linear

series voltage converter, at a constant voltage conversion ratio k_{lin } .

The black curve is valid for a zero control system supply current I_{cs } and the gray curve is valid for a non-zero I_{cs}

Fig.2 (b) shows the power conversion efficiency η_{lin} as a function of the voltage conversion ratio k_{lin }for a linear series voltage converter, at a constant output power P_{out}.

The black curve is valid for a zero control system supply current I_{cs} and the gray curve is valid for a non-zero I_{cs }.

Clearly, linear series voltage converters have an intrinsic advantage, in terms of power conversion efficiency, at high voltage conversion ratios. This is illustrated by Fig. 2(b), where the black curve is valid for I_{cs} = 0 and the gray curve for a finite, non-zero I_{cs}. The gray curve shows that the impact of the power consumption of the control system on η_{lin} becomes more dominant when k_{lin} approaches unity.

This type of converter is well suited for monolithic integration, due to its simple nature and lack of large passives. However, as the excess power is dissipated in R_{series}, the maximal P_{out} is limited by the allowed on-chip power dissipation. This limitation becomes more dominant for low values of k_{lin}.

This type of voltage converter are used in several designs in the work for start-up and rail-shifting .