# Linear Shunt DC-DC Converter

# Linear Shunt DC-DC Converter

The alternative for a linear series voltage converter is a linear shunt voltage converter. The principle of operation for this type of DC-DC converter is shown in Fig. 1 (a).

Fig. 1: The principle of a linear shunt voltageconverter and (b) a simple practical implementation

U_{in }is lowered to U_{out} by means of the resistive division between the fixed input resistor R_{in} and both the load R_{L} and the variable shunt resistor R_{shunt }, where U_{out} is calculated through as follows :

R_{in }can either be the intrinsic output resistance of U_{in}, an added resistor or the combination of both.

U_{out} is kept constant under varying R_{L} and U_{in} conditions by adapting the value of R_{shunt}.

This operation can be performed by a control system, providing feedback from U_{out}. The control system consumes a certain amount of power by drawing a current I_{cs} from U_{in} or U_{out}. The fact that U_{out }can also be directly used to supply the control systems is due to the self-starting nature of this circuit, as opposed to the linear series voltage converter.

The voltage used for supplying the control system will depend on whether U_{out } has a sufficiently large value. In the following analysis it is assumed that U_{in} is used for this purpose, for which the results merely differ little from the other possibility.

Feedback of U_{out} is however not always required, as illustrated by the simple practical implementation of Fig. 1(b). For this implementation the shunt resistor is replaced by a reverse-biased zener diode D. In this way a quasi constant U_{out} can be achieved, if the current through D is kept large enough for it to operate in the zener-region.

For a shunt converter η_{lin } is calculated as below :

Fig. 2 graphically illustrates η_{lin} as a function of the output power P_{out}, for a constant voltage conversion ratio k_{lin}.

Fig.2

The black curve is valid for the ideal case, where I_{cs} is zero and the gray curve is valid for a finite non-zero I_{cs}. As opposed to a linear series converter, η_{lin} is intrinsically linear dependent on P_{out} . It can be seen that η_{lin} is zero for P_{out} = 0 and that it has a maximal value equal to k_{lin}, occurring at the maximal output power P_{out_max} which is given below :

For a given U_{in }and U_{out}, P_{out_max} is determined by the inverse of the value of R_{in}.

Unlike a linear series converter, where η_{lin} is ideally independent of P_{out}, a linear shunt converter only achieves its maximal η_{lin }at P_{out_max}. This behavior makes a linear shunt converter inferior compared to a series converter, in terms of η_{lin}.

However, its simple practical implementation makes it suitable for applications that require a small and quasi constant P_{out} .

Furthermore, a linear shunt converter can prove to be more practical than a linear series converter in applications that have a low value for k_{lin} and η_{lin}.

In such a case the voltage difference U_{in} − U_{out} will only be present over the passive resistor R_{in} rather than over an active device, of which the maximal voltage is limited.

The simple nature of a linear shunt voltage converter, and its lack of large passives, makes it suitable for monolithic integration in non-critical applications.

Obviously, the problem of on-chip power dissipation remains and becomes more limiting than for linear series voltage converters.