# Power Supply Filters With Low-Z Loads

When you dig into all of the different types of power supply filter circuits, both on the input and output sides of a power supply, you find that they are very similar. All power supply filters use series and shut elements together to filter noise, as well as to provide stable power output. This is usually done to provide power at DC, but the same concept applies in AC power delivery, such as for digital circuits.

No matter what type of power you need to deliver, the use of a power supply filter on the output side of a power supply needs to consider the size of the load in order to ensure both regulation and stability of the system’s transfer function. As we will show below, once the connected load becomes low enough, you will find that your power supply filter starts to behave differently. Fortunately, some simple simulations can help you understand how your power supply will operate in low load versus high load conditions.

## Filter Circuits at With Low-Z Loads

Consider the LC filter circuit with a load impedance (single resistor) as shown below. We input some arbitrary voltage source, the L and C elements provide low pass filtering, and the connected load receives some output voltage as described by a transfer function.

A typical situation for a filtration stage on a switching converter is shown below. This represents the output L and C elements in a buck converter, but it could equally represent a discrete LC filter circuit placed after the output stage of any switching converter. The voltage across the load can be determined by finding the transfer function.

PSpice model for a power supply circuit. The LC frequency for this circuit at infinite load impedance is 500 kHz.

What is the transfer function of this circuit as a function of the load impedance Z? If you take the ratio of the input and output voltages, you will get the next expression for the transfer function:

Normally when analyzing a power supply filter, particularly the filter on the output of a DC supply, we look at the magnitude of the transfer function as defined below.

Now with this there is a direct expression for the output voltage in terms of the load impedance. The expression above does not include series resistances from the switching FET stage, or any ESR value in the inductor and capacitor, but these can be easily added in and will be left for an exercise for the reader.

But in the general case where we examine the above expression for the extreme values of load impedance, the result is a gradual drop in the output voltage that is delivered to the load impedance as it draws more current. We can see this from a SPICE simulation of the above circuit.

## SPICE Results

The results below show the function of the filter with capacitor ESR = 1 Ohms and inductor ESR = 2 Ohms. The added resistance on the inductor represents both R_ON for the switcher and the winding inductance of the inductor. Together, they provide LC circuit damping when the load is very low.

As the load resistance is swept from high value (1 kOhm) to low value (1 Ohm), the voltage measured at the load steadily decreases. This is due to voltage drop across the series ESR values becoming comparable to the output voltage drop.

So how does the supply maintain output up to higher powers? Its feedback loop needs to compensate for the output voltage drop and restore it to the target value. This could mean the duty cycle needs to drop (in the case of a buck converter), or the design goes into discontinuous mode.

If you are designing a power supply and need to select a switcher that attempts to regulate the output voltage delivered to small load impedances, the switcher will need to adjust its PWM driver to compensate for the reduced voltage delivered to the load. When selecting the gate driver, be mindful of the potential voltage reduction for the target load when the design is operating at the higher end of its power output.

Anytime you need to simulate the effects of adding filters to a power supply circuit, use the complete set of circuit simulation features in PSpice from Cadence. PSpice users can access a powerful SPICE simulator as well as specialty design capabilities like model creation, graphing and analysis tools, and much more.