# How to Design and Simulate an Impedance Matching Network

When you’re first learning about circuit design and you are just trying to get the thing laid out so that it looks professional, you probably aren’t thinking about things like crosstalk, power integrity, or impedance matching. Once I learned more about matching networks for antennas and other RF devices, I realized the importance of impedance matching in high speed and high frequency circuits.

This begs the question: when should you use an impedance matching network, and which network is appropriate for your device? The answer is a solid “it depends.” If you are designing an interconnect between two components where the source and load have mismatched impedance, then there is a chance you will need a matching network.

## Do I Need an Impedance Matching Network?

The answer depends on the rise time for the signal and the propagation delay along an interconnect. If the propagation delay is longer than approximately 50% of the signal rise time (for digital signals), or longer than one-quarter of an oscillation period (for analog signals), then you will need to take impedance matching into account.

With amplifiers that need to output a range of analog signals, you will need to consider the maximum required output frequency when determining the need for impedance matching. This is usually done by taking the maximum output frequency (fmax), converting this to an oscillation period, and converting this to an equivalent rise time (teq). This equivalent rise time is equal to 35% of the oscillation period for the maximum output frequency. Once the propagation delay is longer than 50% of this rise time, then impedance matching becomes necessary.

*Condition for impedance matching with amplifiers*

## Some Impedance Matching Networks

First, it is important to note that you generally only need to design an impedance matching network for the load or the source components, but not both. This is because the impedance of the transmission line can be adjusted by adjusting its geometry. This allows you to immediately match the trace impedance to either the source or load, and a matching network will be connected to the other component.

Normally, each single-ended transmission line is impedance matched to the source, and a matching network is connected to the load. The goal is to change the impedance of the equivalent circuit formed by the load+matching network so that it matches the impedance of the transmission line.

There are several possible impedance matching networks to choose from. The simplest matching networks place a resistor in series or in parallel (connected to ground) with either the load. For example, if the source and transmission line have the same impedance, but the input impedance of the load is very small, you can connect a resistor to the input port of the load so that its impedance increases to match the impedance of the transmission line.

With a parallel resistor, you have the opposite effect. The parallel resistor effectively reduces the equivalent impedance of the load+terminating resistor parallel circuit so that it matches the transmission line impedance. Six useful impedance matching networks are shown in the figure below:

*Some common impedance matching networks with source and load impedances*

Note that the circuit models for sources and loads shown above include the output and input reactance values, which are typically just due to capacitance. The output/input capacitance can typically be found in data sheets for the components of interest. The output/input capacitor in the component model will need to be placed in parallel with the output/input resistor, and the resistor value will need to be chosen to match the exact impedance value at the frequency of interest.

## Designing and Simulating an Impedance Matching Network

Impedance matching networks are generally simulated at a specific frequency or with a specific waveform. When you’re working with an analog signal, some designers find it easier to work in the frequency domain. However, if you are not familiar with frequency domain SPICE simulations, you can work in the time domain using a sinusoidal voltage source. When working with digital signals or an arbitrary waveform, you’re much better off working in the time domain because a frequency domain simulation will need to approximate the power spectrum for these signals.

Your simulation begins with a source in series with an equivalent resistor with defined impedance. This will then be connected in series to a resistor with defined impedance, which is intended to model the transmission line. Finally, this will be connected in series to the load, which is represented using a resistor with defined impedance.

To determine whether your network properly matches the load impedance to the transmission line, you will need to measure the current that flows through the network and the voltage drop across the network. The magnitude of the voltage to current ratio will tell you the impedance. You can also calculate the phase difference that accumulates in the matching network.

*Equations for the magnitude and phase difference between voltage and current in a parallel resistor impedance matching network*

Once you have built a model for determining the impedance of the load, you can adjust your values for your circuit elements in the impedance matching network to determine when your matched load has the desired impedance value. You will need to iterate through successive circuit element values. You can then determine the exact component values required to match the impedance using Optimizer.

## A Note on Impedance Controlled Routing

Impedance controlled routing is a great way to ensure that most of the interconnects in your board are impedance matched as this will ensure the impedance values of your traces match the impedance of various sources and loads in your board. Many components that are designed for specific signaling standards will accommodate a specific impedance value, and you will only need to worry about designing your trace geometry to match a specific impedance.

However, even in the case where you are working with a certain signaling standard, not all components may be impedance matched, and controlled routing will not eliminate impedance mismatch in particular interconnects. You should always check the input/output impedances of loads/sources, respectively, in order to identify which interconnects require an impedance matching network.

Working with the right circuit simulation and analysis package is much easier when you work with OrCAD PSpice Simulator from Cadence. You’ll be able to analyze the frequency domain behavior of a particular impedance matching network and its transient behavior when working with digital signals. This unique package is specifically adapted to complex PCB designs.

If you want to learn more about the solutions Cadence offers, talk to us and our team of experts.