Return Current at Low Frequency: A Signal and Power Integrity Tutorial

Figure 3. Specially configured coax cable with
the front and back of the shield shorted together.

The following is excerpted from Professor Eric Bogatin's article in the Signal Integrity Journal, The Case for Split Ground Planes. Reprinted by permission of Signal Integrity Journal.

This section continues the discussion in Signal Return Paths of the equation,

Z = R + j𝛚L

Where:

Z is the loop impedance of the current loop path, 

R is the series resistance of the loop and 

L is the loop inductance of the path.

. . .

At low frequency, when the loop impedance is dominated by the R term, the current distribution in the return plane is NOT driven by the loop impedance, it is driven by the loop resistance. In the signal path, the current will spread out uniformly as any filament path in the signal conductor will have roughly the same resistance.

But the current filaments in the return path with the lowest R will be those which are shortest. This means that return currents will take the shortest paths, independent of the signal paths. As frequency increases, the return current will redistribute to transition from the path of lowest R to the path of lowest L. 

Signal Return Paths: A Signal and Power Integrity Tutorial

Figure 1. Current distribution in the signal and
return conductors at three different frequencies.
The current redistribution at higher frequency
is driven by the currents taking filament paths
with the lowest loop inductance. 

The following is excerpted from Professor Eric Bogatin's article in the Signal Integrity Journal, The Case for Split Ground Planes. Reprinted by permission of Signal Integrity Journal.

. . .

Why Continuous Return Path Planes

The first step in engineering interconnects to reduce noise is to provide a continuous, low impedance return path to control the impedance, which controls reflection noise, and reduce the cross talk between signals that also share the same return conductor. 

A wide, continuous ground plane adjacent to a signal trace will be the lowest cross talk configuration. Anything other than a wide plane means more cross talk between signal paths sharing this return conductor. This means, never add a split or gap in the return path. You would run the risk of a signal trace inadvertently crossing this discontinuity.

If a signal crosses over a split ground plane, there are two effects which compound each other. Crossing a split creates a higher impedance path for return currents that must cross the split and forces return currents from multiple signals to overlap through the same, higher impedance, common path. 

Situational Awareness: The Impact of the Interconnect

Fig 1. Coaxial cable has little effect on signal rise time,
but that's not true for every connection method.

How you connect a signal to your oscilloscope affects your measurements, and knowing the impact of different connection methods is an important part of your situational awareness.  

Using the same 40 ps fast edge signal we used for the risetime measurements in the last post, we’ll compare connections made using coaxial cable and a 10x passive probe, with and without different accessories.

Using 50-Ohm Coax From DUT to Oscilloscope

Figure 1: A coaxial cable presents high impedance at low
frequencies but acts as a transmission line at higher frequencies

In our recent exploration of 10x passive probes, we've determined that while these types of probes are great general-purpose tools, they're not necessarily going to do the job in specialized measurement circumstances. They're relatively low-bandwidth, low-SNR probes that impose some limitations and, in some scenarios, can deliver potentially misleading or erroneous measurement results if used without clear understanding of their capabilities.

Squeezing More Bandwidth From a 10x Passive Probe

Figure 1: Shown is a comparison of inherent oscilloscope
noise and noise at the shorted tip of a 10x passive probe

Now that we have a better understanding of what's happening under the hood of a 10x passive oscilloscope probe, we can sum up its key characteristics. The first thing to know about such probes is that they offer relatively low bandwidth (<100 MHz). This is largely a result of the probe's tip inductance.

How Tip Inductance Impacts a Probing System's Bandwidth

Figure 1: Shown are FFT plots of a 10-MHz, fast-edge square
wave reaching the oscilloscope via direct coax connection
(orange-yellow plot) and 10x passive probe fitted with a coax
tip adapter (straw-colored plot)

If you're using 10x passive probes with your oscilloscope, it's important to understand the bandwidth of your probing system and how it's affected by various methods of probing the signal of interest. There's a relatively easy way to determine this parameter by probing a fast-edge, 10-MHz signal from a square-wave generator. Doing so can also instruct us in the effects of tip inductance on the probe's bandwidth.

How Equalization Works in 10x Passive Probes

Figure 1: The adjustable equalization circuit on the oscilloscope
end of the coaxial cable compensates for the 10x passive
probe's inherent low-pass filter characteristics

We've been discussing 10x passive probes and their inner workings; our last post covered all the ways in which a 10x passive probe is apt to be a liability. They'd be basically unusable for any measurements at all but for one attribute: their equalization circuit (Figure 1). Without it, the 10x passive probe makes a pretty good low-pass filter, but the equalization circuit counters that with a high-pass filter to balance things out.