# Determining Impedance in PCB Microstrip Traces

August 30, 2018

I remember being told in grade school that the use of calculators was not allowed. This always seemed odd because people had access to calculators in the real world. Once I got into PCB design, I began to see the advantages and drawbacks of using circuit calculators. Some of these calculators can be major timesavers, while others are only narrowly applicable.

Whether you’re new to PCB design or you’ve made your career out of it, you are probably familiar with impedance matching. Under certain conditions, impedance matching needs to be performed in order to prevent signal reflection and ensure maximum power transfer between components. Impedance calculators can help under standard design configurations. But as your designs become more specialized, calculators might lose their usefulness.

## Impedance Calculators

Undoubtedly, you’ve noticed the number of online impedance calculators for different trace arrangements. Microstrips, striplines, and transmission lines in various geometries and combinations have their own impedance formulas. These values are usually only approximations and cannot be regarded as reliable except in specific cases.

Some impedance calculators also do not consider every special design case. Many calculators only consider FR4, but your design may require a substrate material with different dielectric and electronic properties. A good calculator will give you the ability to calculate the impedance for any dielectric constant for a thin microstrip. A decent calculator will also let you calculate the impedance of embedded microstrips

Impedance calculators also let you set a specific value for copper trace weight by specifying the thickness and width of the trace. Most calculators implement a standard formula under the approximation that the trace thickness is less than the thickness of the dielectric substrate. Once the copper becomes too wide compared to the substrate thickness, the often-cited formula for effective dielectric constant and the resulting impedance breaks down and can’t be used anymore.

It is important to note that the temperature rise and current carrying capacity of heavy copper depend nonlinearly on copper weight, temperature, and geometry. For example, it is not a simple matter where doubling the copper weight results in double the current carrying capacity.

While using a calculator or simulator to determine the impedance value of your microstrips is helpful, you will still need to compensate an impedance mismatch for any components at the ends of interconnects. Using surface or hole mounted capacitors and inductors is an old standby method to adjust impedance.

Smith chart for impedance matching

## Is Termination Required?

One important output from a microstrip impedance calculator is the effective dielectric constant of the microstrip. This parameter determines the propagation velocity of the signal, which can then be used to determine how long it takes for the signal to travel over the microstrip. This is known as line delay, transmission delay, or propagation delay (depending on who you ask).

Termination of digital signals becomes important when the rise time of the signal is less than about double the propagation delay. For analog signals, the rule is to take the rise time of the signal to be one quarter the oscillation period. The line should be terminated if the rise time is less than the propagation delay.

## Stub Matching

One way to impedance match analog signals using only printed copper is to use stub matching. This is tangentially related to via stubs in that microstrip stubs can act like resonators in certain conditions. This design technique refers to a rather simple impedance compensation method that involves creating an equivalent capacitor or inductor from a PCB trace. Copper stubs are commonly used by RF design community to build distributed element filters.

Instead of placing capacitors or inductors on the board to compensate impedance, which have broad response, a stub acts like a capacitor or inductor at a specific frequency that depends on its geometry. The stub acts like a resonator at other frequencies. These different conditions give you some flexibility for compensating impedance when placing shunt capacitors or inductors is inconvenient. The conditions are also easy to calculate using exact formulas.

There are two types of stub matching methods, known as single stub and double stub. Each stub in a transmission line can be used as either an open circuit or as a closed circuit. Short circuit stubs are generally preferable to the open circuit variety, as open circuit stubs have appreciable emission at RF and higher frequencies.

Stubs need to be placed at a specific location along the trace that requires compensation. For a given operating frequency, you can calculate the exact stub length required for compensation using exact formulas that do not require an approximation. Any standard scientific or engineering calculator can be used.

Keeping track of your traces with strong design software enables easier signal integrity management.

There are times where single stub matching requires the stub be placed somewhere that will not meet design requirements or will interfere with other components. In this case, double stub matching can be used. With double stub matching, the stubs need to be placed a specific distance apart, rather than being placed at a specific point along the trace.

Adding a capacitive stub in parallel with the interconnect will decrease the impedance, and vice versa for an inductive stub. More complicated stub arrangements include coupled stubs. Coupled stubs are not connected to the traces they compensate, and the stub is placed a distance away from the interconnect and arranged along the same direction.

Rather than running the risk of incorrectly designing a high-precision PCB using approximations, the built-in simulation tools and rules-driven design environment in Altium Designer® can help you avoid signal integrity problems that arise from incorrect impedance calculations. Now you can download a free trial and find out if Altium is right for you. If you want to learn more then talk to an Altium expert today.

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