For predictable PCBs, stop thinking in terms of voltage and current and start thinking about energy propagation with field containment.
They called me “Professor” when I worked part-time as an electronics engineer at Sundstrand, for two reasons: one, I was a professor of electrical and electronics engineering technology, and two, I dished out a lot of advice.
I recently wrote about the advice I gave my old cubemate Dave on the importance of decoupling capacitors in PCB design. We kept in touch after he left, but even though we were no longer coworkers, I was still the Professor. Over drinks one night, I gave him a new lecture on PCBs that taught him the right way to think about electrical energy.
You’re thinking about circuits wrong
Light and electrical energy both travel at 3×108 meters per second in a vacuum and nearly that in air. They are both electromagnetic waves that differ only in frequency. Light is measured in terahertz while electrical energy can be in gigahertz.
Suppose we have the theoretical situation provided in the image below. A lamp is connected using ideal wires that are 3×108 meters long. One second after the switch is closed, the lamp illuminates.
If we apply the “normal” circuit analysis thinking, we might say the current flows from the source to the lamp and then returns to the source (ground). Wouldn’t that take two seconds for the lamp to illuminate? That will not happen. So, we need to correct our thinking.
The forward wire is connected to the positive terminal of the voltage source and the return wire goes to the negative (ground) terminal. When the switch is closed, electromagnetic energy is launched toward the lamp. The image which follows reminds us of the relationship between the electric and magnetic fields in the direction of propagation. The electric field causes electron movement (current) and the resulting current produces a magnetic field. (This video gives an excellent visualization of electromagnetic waves.)
As the EM wave propagates, it will generate forward and return currents simultaneously in the conductors. This occurs when the EM wave reaches a given point. This is indicated in the next image. (It is flawed thinking to imagine forward current reaching the load and then returning to the source.)
“So, what does this have to do with circuit analysis?” Dave interrupted. “I could use another beer by the way!”
I reminded Dave about wavelengths. “Dave, remember λ=c/f? As frequency increases the wavelength shortens. When the wavelength becomes short compared to the distance the wave must travel, we move into the realm of transmission lines, wave guides and microstrips. As you know, the speed of digital integrated circuits has increased dramatically over the years. Similarly, analog systems are operating at higher frequencies—think cellphones, for example. High band 5G uses frequencies of 24 to 47 gigahertz. This permits download speeds in the gigabit per second range.”
Smiling, Dave responded, “Yeah, back in 1981 we were working with stone knives and bear claws. We were a simple people.”
The critical viewpoint is we are now dealing with electrical energy for signal conveyance.
Energy in review: COMETMAN
Energy is defined as the capacity to perform work, and work means movement or molecular interactions. Energy is neither created nor destroyed but can be converted from one form into another. The various sources of energy are captured by the acronym COMETMAN: Chemical, Optical, Mechanical, Electrical, Thermal, Magnetic, Acoustic, Nuclear.
When dealing with printed circuit boards, if we have a signal trace and a ground trace or plane, the signal electrical energy exists between them. The energy moves through the dielectric material (like FR4 at about c/2).
Dave put down his glass of beer and uttered a single “Huh?”
I replied, “Electrical and light energy are the same. In the outer space lamp example, you had no problem with energy propagating through a vacuum. Vacuum is the perfect dielectric.”
I continued, “It is important to note the energy is not on the copper. The E (electric) and H (magnetic) fields form a wave that carries the energy. The voltage and current do not.” These underpinnings serve as the basis for well-behaved PCB design.
Forward path, return path and the path of least impedance
The signal traces and the ground trace or ground plane make up a waveguide that steers the energy between two points. The signal trace can be regarded to be the forward path while the ground trace or plane can be thought of as the return path. The energy follows the path beneath the trace since it provides the path of least impedance. This occurs as the frequency increases (typically beyond 20 kilohertz).
Dave remarked, “So, the transmission-line effects become significant when we are dealing with signal frequencies about 20 kilohertz?”
“That’s about it,” I replied.
In a PCB design it is critical to consider carefully the space between the forward signal traces and the (ground) return path. Otherwise, coupling between circuits can occur which can cause crosstalk and other problems.
Frequency and rise time
The signal frequency affects the path the return signal takes. To illustrate that fact, the “experimental” test circuit is provided in the image below. (The idea for this example is derived from a presentation by Rick Hartley called How to Achieve Proper Grounding.)
The additional ground wires are the same gauge and essentially the same length as the return wire in the twisted pair. If a DC (0Hz) input is applied to the twisted pair, the current will divide equally between the three wires. This illustrates a point demonstrated on a PCB: DC current tends to spread out.
As the frequency of the input increases, the current in Additional Ground 2 will decrease. As the frequency is raised further, the current through Additional Ground 1 will also decrease. At a high enough frequency (e.g., 20kHz) the current through the additional grounds will be zero and all the return current will flow through the return wire of the twisted pair.
Energy takes the path of lowest impedance when the frequency is above the audio frequency range. In the case of a PCB, the path of lowest impedance is the ground trace that lies directly under the signal trace. The circuit operation in the image above demonstrates the salient points.
If a ground plane is used, the energy will spread out. This is true particularly at low frequencies. At high frequencies, the return signal energy will self-route. (If that were not true, ground planes would not work.) A ground plane offers an infinite number of paths, but the return energy will take only the one path that offers the lowest impedance—the path directly under the signal trace.
Dave inquired, “I assume this discussion applies to analog systems with frequencies greater than 20 kilohertz and in digital systems.”
I replied, “You’re correct, but in digital systems, the pulse risetime is significant rather than frequency. Let me explain.”
When dealing with digital waveforms, it is not the frequency so much as it is risetime (tr), the time it takes the leading edge of a pulse to go from 10% to 90% of its maximum value. The shorter the rise time, the higher the spectral content. There is a simple but powerful relationship that relates risetime to the high-end corner frequency (fH). The analysis is detailed in the image that follows.
Dave looked a little like a puppy dazed from being scolded. I apologized to him for getting into the weeds.
Do’s and don’ts in PCB design
I finished my impromptu lecture with some simple PCB design rules.
- Signals should not occupy the same dielectric space. This will couple the signals into one another creating havoc.
- To contain fields, the ground should lie directly under the signal trace. However, be aware that low-frequency fields tend to spread out.
- Separate analog and digital grounds are only necessary if the analog section is operating under 20 kilohertz.
“Dave what do you think?” I asked.
“No one should drink (or even be near) beer when you present this material,” he replied, adding “Can you give me a ride home?”
“Sure, too much beer?”
With a grin he said, “No, too much lecture!”
