# Passive Pi Filter Design and Simulation

*If you need a simple higher order passive filter, a pi filter is a good choice.*

Impedance matching, power regulation, EMI filtering… the applications of different filter circuits are varied. These filter circuits are critical in many applications, but they are quite simple to design. Although integration of filter circuits into many SoCs is simplifying circuit design and layout tasks, filters made from discrete elements are not going away and find their home in many important circuit designs.

If you’re looking to a simple higher order passive filter for use in impedance matching, EMI filtering, and power regulation, a pi filter provides strong rolloff without active circuit elements. The design principles for pi filter circuits are deceptively simple, and these filters can be easily adapted for many applications using discrete components. Here’s what you need to know about pi filter design and simulation.

## What is a Pi Filter?

A pi filter is a type of LC filter, where the LC filters are arranged to resemble the Greek letter “pi.” A pi filter can be configured as a high pass filter or a low pass filter. As these filters include three L or C elements, these filters are 3rd order in nature and provide strong rolloff above the cutoff (~20 dB/decade). The standard implementation is as a low pass filter, allowing this circuit to be used as a higher order filter for the input to DC power supplies.

The circuits below show the standard configurations as a low pass or high pass filter. The values of the L and C elements determine the cutoff frequencies for these circuits. When the capacitors are placed as shunt elements, they pass high frequency components in the input signal to ground. Similarly, when the inductors are placed as shunt elements, low frequency components in the input signal are passed to ground. Judicious selection of capacitors and inductors in pi filter circuits provides a way to easily manipulate signal behavior by providing low impedance and high impedance paths to ground or downstream to a load.

*The two common pi filter circuits as low pass or high pass filter circuits.*

### Low Pass Pi Filters in Power Supplies

The way in which the low pass version of a pi filter removes high frequency noise allows it to be used as a strong filter for an unregulated power supply. The low pass version can also be used as the input filter on a voltage regulator circuit. In both implementations, the low pass version of the pi filter is intended to suppress ripple on the output from a full-wave rectifier circuit.

The critical quantity to design for in this application is the ripple factor, which is defined as the RMS voltage fluctuation seen at the output from the pi filter divided by the desired DC output. The value of the ripple factor depends on the value of the downstream load R. For an unregulated power supply, this is just the load connected to the output. For a regulated power supply, this is just the input impedance of the regulator circuit in parallel with the downstream load. This can be calculated with the following equation:

*Ripple factor for a pi circuit in a power supply.*

A common practice is to use a ferrite choke as the inductor, which will have some equivalent series resistance (ESR). This ESR value can be adjusted with a series resistor on the ferrite choke, which will increase the damping in these circuits and will adjust the transient ringing. Due to ringing in these filters, they should only be used in switched-mode power supplies when there is a series resistor on the ferrite choke.

### High Pass Pi Filters in Impedance Matching

Pi filters are often used for high-to-low impedance matching with transceivers and antennas. If you want to use a pi filter for impedance matching, then you need to use the high pass version as you will normally be working at high frequencies. There are two ways to design these filters. First, the cutoff frequency needs to be determined using the formulas shown above. Next, the impedance of the matched circuit needs to be verified in the desired frequency range.

When you use the right simulation tools, you can determine the impedance spectrum of your pi filter when it is connected to your desired source/load components. An important point here is to match the antenna’s bandwidth to the bandwidth of the filter circuit, which then depends on the impedance spectrum of the antenna. This can be a complicated simulation, but if you know the impedance spectrum of your antenna, then you can easily model the antenna in a circuit simulation when designing a pi filter.

If these feel difficult to achieve, rest easier knowing that simulation tools are out there and available to meet your impedance, PI, and power supply concerns.

## Simulations in Pi Filter Design

Just like other circuits with reactive elements, these filters will have some transient response when the input voltage changes. Depending on the reactive impedance of the load and other elements in the circuit, these filters can have strong resonance. In the switched-mode power supply application, the transient response can be switched from underdamped to overdamped simply by placing the correct resistor on the ferrite choke. The important points to simulate in pi filter designs are shown in the following table.

The steps shown above have been discussed in the context of passive pi filter design, but pi filters can also be designed as active filters with an op-amp. In this type of simulation, you’ll need to use verified component models for your circuits. This will ensure your results are accurate and reflect the real behavior of your desired components.

Pi filter circuits are much easier to build when you use the best PCB design and analysis software. The SPICE simulator and circuit design tools in PSpice Simulator for OrCAD, and the full suite of analysis tools from Cadence, can help you design your pi filter circuit for low frequency or high frequency applications, such as power regulation, EMI filtering, and impedance matching. You’ll also have access to verified models directly from manufacturers for simulating circuit behavior.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts. You can also visit our YouTube channel for videos about Simulation and System Analysis as well as check out what’s new with our suite of design and analysis tools.