Visible Return Current

Current matters in a high-speed digital product because current represents the movement of electric charge. When the charges accumulate on the gate of a FET they make it switch, controlling other currents. Without current, an electronic machine could not function.

Of course, electrical current is not always a good thing. The flow of current, and its associated magnetic fields, are responsible for all our difficulties with ringing, crosstalk, ground bounce, power supply noise.

Engineers often have difficulty imagining how current moves through in a digital pcb. Particularly troublesome is the point about how, when you send high-speed current down a long pcb trace, an equal and opposite return current flows in the solid reference plane underlying that trace. A firm grasp of this return-current idea is crucial to understanding crosstalk and the effects of layer transitions (and split-plane boundaries) in digital products. The return-current concept is something I write about frequently (see references at the end of this article).

In my seminars, I sometimes encounter persons who, despite my best efforts at explaining the return-current concept, still experience doubts. These are not "slow learners"—they are very philosophical people who just require a very high standard of evidence before accepting what seems to them, at first, a counter-intuitive idea.

Well, if seeing is believing, then I may at last have found a way to demonstrate, in a direct (and dramatic) fashion, to any observer, where and how high-frequency current flows in a printed circuit board.

I would like to express my profound gratitude to Mr. Robert Trautman of Owego, NY for putting together the technical apparatus necessary for making this experiment and taking these extraordinary photographs.

How to Make Current Visible

Benjamin Franklin in his book, "Experiments and Observations on Electricity" (1769) reported a number of unusual experiments with electrical current. Using an electrostatic generator he forced current through various objects, including the gold-leaf design embossed on the cover of his old Bible. Each stroke of his generator enveloped the design with a shimmering trail of sparks.

Old Ben reasons that the gold, being a better conductor than the leather, confines the current mostly along the embossed design. The gold, also being a very thin leaf, contains numerous cracks. At every crack current arcs across the gap, producing the brilliant display of sparks.

Today these conclusions seems imminently reasonable, however, I should point out that at the time his work was published the world knew very little about electricity. In fact, the term "conductor" had not yet even been invented. Mr. Franklin seems to have been the first to coin that term, applying it at first only to metals and water, then gradually expanding his list of known conductive materials.

This simple experiment suggests a marvelous way of making current visible. One need only construct a pulse source having sufficiently large voltage amplitude, and apply it to network of conductors having a suitable number of small gaps. With this arrangement, you can see, directly and unambiguously, where current actually flows.

There are some fine points that determine whether such experiments may succeed. First, the sum total breadth of all the gaps in the experiment must be surmountable by the voltage of your generator.

Second, one must ensure that, at the frequencies associated with spark discharge (several MHz) the current will indeed be controlled by the mechanism one wishes to demonstrate. This constraint places some limits on the lengths and configuration of conductors used in the experiments.

Third, stand well away from the source when it fires…

A Good High-Voltage Pulse Source

Before we go any further, here are some pictures of the apparatus under discussion. In Figure 1, on the floor to the right of the unit you can see the power source. The tubes are high-voltage capacitors. The capacitors are connected in a formation called a Marx voltage multiplier. On the left, sparks fire into a dish of water.

Figure 1—The heart of Robert's high-voltage pulse generator is a ten-stage Marx voltage multiplier, driven by a 20,000 volt source.

The next picture documents the achievable spark length. I would not want to be holding the tape measure for this one.

Figure 2—Between the endpoints of two wires, Robert makes sparks more than seven inches long (roughly 150,000 volts). 

One of Robert's interests is in making these beautiful pictures of the sparks spreading into a dish of water.

Figure 3—Firing into water, the apparatus makes an impressive display.

Point of this Presentation

The specific demonstration I would like to make involves the flow of returning signal current on the nearest solid reference plane underlying a high-speed pcb trace.

[Excerpt from High-Speed Digital Design, p. 189]

At low speeds, current follows the path of least resistance. Referring to Figure 4, low-speed current transmitted from (A) to (B) returns to the driver along the solid reference plane. This returning signal current flows in wide arcs on its way back to the driver. The current density along each arc corresponds to the conductance of that portion of the overall path.

Figure 4—At low speeds, current follows the path of least resistance.

At high speeds, the inductance of a given return current path is far more significant than its resistance. High-speed return currents follow the path of least inductance, not the path of least resistance. 

The lowest inductance return path lies directly under a signal conductor, minimizing the total loop area between the outgoing and returning current paths.

Returning signal currents tend follow this direct path, close underneath a signal conductor. Figure 5 shows a typical high-frequency return current path.

Figure 5—At high speeds, return current stays tightly bunched under signal trace.

Experimental Setup

Let's test the return-current theory. On one side of an acrylic sheet, affix an array of tiny conductive squares. Leave uniform gaps between all the squares (Figure 6).

Figure 6—A uniform array of conductive squares, mounted on an acrylic sheet, makes a good reference plane for high-voltage signals.

The grid represents a "solid" reference plane, patterned with small gaps. When current from a high-voltage source traverses the grid, it should arc from square to square making a trail of light as it passes. On such a grid, we can perhaps see, visually, where current flows.

Robert's grid comprises a matrix of 570 foil squares. Each square is 1/8 in. x 1/8 in., with gaps of 1/8 in. between each square. To apply the squares, he first covered the entire sheet with sticky-backed foil. Then he scored the foil, removing narrow strips between the squares to create a grid pattern.

Conductors (copper strips) protrude from each end to provide a way for current to enter and leave the grid. You may leave one solid strip of conductor along the exit side of the reference grid, in order not to prejudice the current as to its precise point of exit from the reference grid.

Cover the grid with another sheet of acrylic, sandwiching it. The sandwich structure protects the grid from damage (Figure 7). The top side of this second sheet I call the "signal side" of the apparatus, the other side is the "grid side".

Figure 7—The topmost trace conveys current across the structure, from whence it returns through the reference grid.

On top side (signal side) of the topmost sheet of acrylic, affix a solid metallic conductor. This conductor represents a pcb trace. According to my theory, current flowing in the pcb trace should control where current flows on the reference grid.

The pcb trace conveys current from the high-voltage source (+) across the topmost acrylic sheet. On the right side of this diagram the solid conductor wraps over the edge of the acrylic sheet, dumping its current into the reference grid. Current then returns through the grid moving back towards the source. At the left side of the drawing, the (–) connection connects to the ground terminal of the high-voltage pulse generator.

IF the source produces a fast enough rise time (BIG IF...), the returning signal current in the grid will NOT spread out as would be its nature at DC, but rather it will concentrate under the solid trace. That's the theory, anyway.

The theory also says, "When you bend the signal trace into various shapes the current in the grid follows the signal trace."


Robert wrote to me when he completed his work saying, "To call this experiment a spectacular success would be a gross understatement." Both of us are excited to see this hair-brained idea, first published 236 years ago, resurrected in a format meaningful for today's engineers, at today's speeds.

The following pictures (Figures 8 and 9) were taken from the grid side (back side) of the apparatus. In the photos, current enters the apparatus at the bottom and makes it way to the top using a solid conductor pasted to the signal side of the acrylic (that side is turned away from the camera). The acrylic is transparent, though, so you can still dimly see the copper-colored signal-side conductor in places where it is not completely masked by the brilliant arcing, or by the grid squares.

At the top of the apparatus, the current flips over to the grid side (the camera side) of the Plexiglas sheet for its return journey through the grid. A solid collection strip at the bottom collects the returning current and conveys it to the ground terminal of the high-voltage generator.

The figures show two different arrangements of the signal-side conductor. In both photos, current on the reference grid clearly follows the position of the signal conductor.

Figure 8—Current flowing on the reference grid follows the signal conductor.

Figure 9—When you move the signal conductor, the reference-grid current moves with it.

In Figure 9, a spur of stray current jolts out from the signal trace, moving across the signal side of the acrylic layer to a screw location at bottom left. You can tell that this current moves on the signal side of the acrylic layer because it does not enter and exit each grid square at the corners, as does current on the grid side of the apparatus.

This stray current then passes through the screw hole to the back side (grid side, also the camera side in this photo) of the acrylic sheet and from there moves straight up about 1/8 inch to the collection strip. Surface dirt and other imperfections often cause current to follow stray pathways like this in high-voltage equipment.

Point To Remember

Every high-speed traces induces equal and opposite current on the nearest solid reference plane, directly under (or above) the trace.

Not convinced?

Drop by DesignCon 2006 in San Jose and let's talk about it.

I will be at the Xilinx booth showing my new movie, "Signal Integrity Techniques for Platform FPGA Design". The main topic of this film is crosstalk, specifically, the crosstalk that occurs underneath a BGA package in the spaces between the balls and your pc board. The presentation begins with a simple current-loop experiment illustrating the nature of magnetic (inductive) coupling, and then moves to a large-scale model of a BGA package where the principles of inductive crosstalk are easily observed. I get to modify, in real time, the pattern of power and ground pins within the package while observing the difference in crosstalk obtained with various patterns. I compare power-and-ground pin patterns for Xilinx Virtex-4 and Altera Stratix-II FPGA packages, and discuss the efficacy of using virtual ground, or soft-ground, connections to mitigate crosstalk.

Best Regards,
Dr. Howard Johnson

The inspiration for "Visible Return Current" came from comments reported by Benjamin Franklin in his book, "Experiments and Observations on Electricity". This book was originally printed by David Henry, and sold by Francis Newbery, at the Corner of St. Paul's Church-Yard in London, 1769. You may still be able to get a copy from The Classics of Science Library, Division of Gryphon Editions, 333 East Street, New York, New York 10016 (1996).

Related Discussions About return Current

Ground Current   Details the exact path of returning signal current when a chip switches HI or LO Newsletter v3-7 3/15/1999

High-Speed Return Signals   How do high speed return signals travel on a 4 layer pc board? Newsletter v1-15 10/27/1997

Interplane Capacitance   Follow-up to "High-Speed Return Signals" newsletter v1-15, discusses the effective useful radius of the interplane capacitance. Newsletter v3-21 8/30/1999

Minimum-Inductance Distribution of Current   Faraday, in his mind's eye, saw lines of force traversing all space. Newsletter v6_07 7/22/2003

Proximity Effect   Is there a "Proximity Effect" in strip lines or microstrips that is caused by currents flowing in adjacent conductors? Newsletter v4-1 3/10/2000

Proximity Effect II   Do you have any references dealing. with the current density distribution in a ground plane under a high frequency signal trace? Newsletter v4-3 6/1/2001

Proximity Effect III   Justification for crosstalk approximation (see High-Speed Digital Design p. 190, eqn. [5.1]) Newsletter v4-8 10/3/2001

Persistent Edge   Are there really any high-frequency currents still flowing in portions of a transmission line after those portions have been passed over by a voltage disturbance moving down the line? Newsletter v8_05 8/23/2005

Return Current in Plane   Distribution of return current on the solid plane underlying a high-speed signal trace. Newsletter v3-11 4/26/1999

Return Current Matters   Differential architectures sometimes tempt us to ignore return current issues. [but] even in a differential configuration, current flows on the planes under each trace separately. EDN 9/16/2004

Short-Term Impedance of Planes   Doesn't the returning signal current just pop between the planes through the parasitic capacitance of the planes themselves, you might ask? Newsletter v6_05 3/24/2003

TDR and Ice Cube Trays   The "Ice Cube Tray" model of distributed transmission. Newsletter v3-5 2/5/1999

Ten Layer Stack   Discussion of multi-layer board stack for system with multiple power voltages. Newsletter v2-11 4/27/1998

Terminator Crazy   The first clue as to whether a terminator is needed is the ratio of trace delay to rise time. ED 10/1/1996

Via Inductance   The inductance of a via depends on the path of returning signal current. Newsletter v6-04 3/15/2003