Resistance

What Is Resistance?

 

Resistance is a measure of the opposition to current flow in an electrical circuit. It is measured in ohms, symbolized by the Greek letter omega (Ω). Ohms are named after Georg Simon Ohm (1784-1854), a German physicist who studied the relationship between voltage, current and resistance. He is credited for formulating Ohm’s Law.

 

All materials resist current flow to some degree. They fall into one of two broad categories:

• Conductors: Materials that offer very little resistance where electrons can move easily. Examples: silver, copper, gold and aluminum.
• Insulators: Materials that present high resistance and restrict the flow of electrons. Examples: Rubber, paper, glass, wood and plastic.

 

Resistance vs. Reactance vs. Impedance

 

Some PCB designers only tend to pay attention to resistance when designing their power/ground planes and traces in their PCBs. This is appropriate in some cases, like in purely DC circuits or in very low frequency AC circuits. In other cases, where frequencies or switching speeds are higher, the reactance of a circuit becomes important.

A real PCB has some equivalent capacitance and inductance that depends on the arrangement of traces and power/ground planes. You should know that these elements produce reactance, which depends on the signal frequency. In a DC circuit, a capacitor acts like an open circuit once it charges, and an inductor doesn’t do anything, so you only need to worry about the resistance in closed circuits formed by your traces.

The resistance and reactance add together in quadrature to give you the impedance, and the impedance depends on the frequency and switching speed of signals in your circuits. Even if you are working with a high frequency or high speed device, the DC resistance of various elements on your PCB are still important and will affect the performance of your device. In PCB manufacturing, impedance measurement on test coupon is an important approach to inspect whether the controlled impedance meets requirement.

 

The Impact on the PCB Layout

 

There are some cases where impedance can be analyzed without including the resistive or real element. For example, when the reactance is much larger and resistance can be treated as negligible. However, in actuality, resistance plays a role for all electrical circuits as it impacts the level of current flow. For PCB design, the transmission lines or traces are relatively short and copper, which has one of the lowest resistivity, is most often the material used. Therefore, real power losses are typically not an issue; however, eddy current or I2R losses due to changing fields are a concern.

For board layout design, resistance is most often taken into account when performing design checks; such as power distribution (PDN) and/or thermal analysis. These analyses are typically done by simulating the board’s operation with desired inputs and with environmental conditions similar to what will be nominal for the assembled PCB or PCB Assembly deployment. Thermal analysis, in contrast to PDN simulations, has a primary goal to determine how heat is distributed along the surface and throughout the board. This is important to ascertain what thermal dissipation and/or distribution techniques and devices need to be implemented to ensure your board’s manufacturability and operation. Thermal analysis and PDN may be performed separately or using a single advanced tool.

The importance of resistance for power distribution and thermal analysis is based on the fact that changes in heat significantly alter material properties. Now, we know that both impedance and resistance are important for PCB layout design.

 

Calculation

 

Calculation of a trace is actually very easy when you assume that the temperature of your trace does not change during operation. This is actually a dubious assumption and is almost never realized in a real device without a complicated temperature regulation system.

Some trace calculations don’t include temperature effects, giving you a baseline resistance value at a certain reference temperature. Those calculators that do account for temperature require that you set a specific operating temperature for your traces. This operating temperature represents a design goal in your device. If you are designing your PCB for a specific temperature, you’ll need to take steps to ensure that your PCB doesn’t exceed this temperature.

If your PCB will be operating in an environment below room temperatures, most calculators can actually return a negative value, which is obviously incorrect. You’ll need to do more than just search the internet for a basic trace resistance calculator. Some application notes and research publications provide a very thorough view of trace resistance at very low temperatures.

The difference between an impedance calculator and a resistance calculator is that the trace impedance depends on the surrounding board material and trace arrangement with respect to nearby conductive planes or other traces. The board material also affects temperature rise, but calculating the actual temperature rise for a given power level is a much more involved problem.

 

Trace Resistance and Power Distribution

 

With all of this frequency dependence going on, why should the resistance in a DC circuit matter? We’re dealing with conductors, which already have small resistance. The resistance of a typical trace is about 0.03 Ohms, which is extremely small. This means that the current in some typical traces can be quite large, resulting in a large temperature change during operation.

The first reason the trace resistance is important has to do with IR losses in various elements throughout a PCB beyond just traces. Features like vias and solder points can have high resistance, and a significant amount of power can be lost as it is routed to critical components. These losses accumulate if your power lines are routed through a large number of vias or solder points, and downstream components might not receive the power they need to work properly.

As power is dissipated in various parts of your circuits, the temperature of these resistance elements increases, which then increases the resistance. Eventually, the thermal gradient between these resistive elements, the board substrate, and air causes heat to dissipate, and the temperature will saturate at its operating temperature.

The increased resistance at high temperature then affects power distribution, resulting in greater power loss as power is routed to downstream components. In order to ensure that the proper amount of power reaches downstream components, you’ll want to remove any unnecessary high resistance elements like vias from your power connections.