Electrical Properties of Interconnects
4.8 Electrically Short and Electrically Long
For additional information on the properties of transmission lines, see the book Bogatin’s Practical Transmission Line Design and Characterization for Signal Integrity Applications.
While the distributed transmission line models are the most accurate interconnect models over the widest bandwidth, they are sometimes complicated to use correctly. Transmission lines are an advanced topic. If you expect to advance in circuit design and deal with the highest-performance systems, understanding transmission lines must be in your future.
If interconnects are electrically short, their electrical properties can be approximated by the lumped circuit elements. These circuit models dramatically simplify the electrical analysis and are the focus of this book.
The condition for an interconnect to be considered electrically long, where transmission line properties dominate interconnect
performance, is that the electrical properties of the interconnects can only be accurately approximated by transmission line models.
Lumped element models are not an accurate description of the interconnects when the interconnects are electrically long.
There are a number of ways of estimating this transition, but they should all be considered just estimates or rules of thumb and not a hard limit. This transition between electrically short and long is just about which is the better equivalent circuit model to use.
While distributed transmission line models are an accurate
representation of all interconnects from DC to some high bandwidth, they carry a higher cost in complexity to understand and to use and not all simulators have accurate transmission line models. This is especially the case when describing cross talk between an aggressor and victim signal-return path loop.
4.8 Electrically Short and Electrically Long
Being electrically short does not mean the interconnects are transparent. Being electrically long does not mean they must be
terminated for acceptable performance. This condition just refers to the appropriate equivalent circuit model to use.
Once we determine if an interconnect is electrically long, we can use the model of the interconnect and a simulation to evaluate whether a termination strategy is required based on the combination of driver models, routing topology, and reflection noise generated compared to what is acceptable.
The condition for electrically short depends on both the rise time of the signals and the length of the interconnects. In the last section, we estimated this connection between physical length of the
interconnect and the rise time of the signal based on when the length was shorter than 1/10th a wavelength. This condition was:
Lenlong[in] 1.7 RT[n sec]
Another way of evaluating this threshold of when an interconnect is electrically long and transmission line analysis is important is by looking at the impact from ringing noise due to reflections based on the transmission line properties of the interconnects.
As the signal rise times decrease or lengths increase, the ringing noise from the reflection properties of the transmission line behavior of the electrical long interconnects on the interconnects due to the distributed transmission line effects become more pronounced and a transmission line description becomes essential.
This is one of the conditions that can be used to describe the threshold for an interconnect to be electrically long.
For example, Figure 4.17 shows the measured signal at an
oscilloscope input as a receiver from a fast, low impedance source as the length of the interconnect increases. Above a threshold, as the interconnect length increases, the ringing noise from transmission line effects increases.
4.8 Electrically Short and Electrically Long 113
Figure 4.17 An example of the reflection noise in an interconnect from the signal source on a microcontroller board to the input to a scope for three interconnect lengths. The
longer the interconnect, the more the reflection noise.
Reflections on interconnects from impedance changes will always happen. However, when an interconnect is short enough and its time delay is short compared to the rise time of the signal, the resulting reflection noise may be low enough to not be a concern.
The magnitude of the reflection noise depends not just on the rise time of the signal and the time delay of the interconnect. It also depends on the output impedance of the driver. As the starting place, we make the assumption that the output impedance is very low compared to 50 ohms.
The signature of reflection noise looks like a damped sine wave. The period of the sine wave voltage noise is related to the time delay, TD, of the signal to propagate from the transmitter pin to the receiver pin. The signal reflects from the high impedance RX, heads to the TX, reflects and changes sign from the low impedance of the TX, hits the RX again, then heads back to the TX, reflects and changes sign and
comes back to the RX again with a positive peak. The period of ringing is four one-way time delays:
Period= 4 TD
When the rise time is long compared to the ringing period, the reflections will smear out during the rising or falling edge of the signal. In this case, the reflections will always happen, but they may not be visible and would play no role affecting signal quality at the receiver. In this case, the transmission line properties of the
interconnect can be approximated by the lumped circuit elements.
The amount of ringing depends on many details. It can overwhelm any signal, or it can be insignificant. An example of a typical case and the resulting signal at the receiver for three different rise times is shown in Figure 4.18.
Figure 4.18 Top: example of a simple transmission line circuit with a signal source with a 10 ohm source impedance, driving a transmission line with a high impedance receiver.
Bottom: the simulated voltage at the receiver as the rise time of the signal increases compared to the time delay of the transmission line. Simulated with Keysight’s ADS.
When the rise time is shorter than 4 x TD, the reflections can be significant, and the transmission line properties of the interconnects are important. This is the condition for an electrically long
interconnect when transmission properties are important.
4.8 Electrically Short and Electrically Long 115
But, if the rise time is longer than 4 x TD, the transmission line properties are not important. This is the condition for an electrically short interconnect when transmission line effects are not important.
Generally, in a printed circuit board, the typical laminate materials have a dielectric constant of about 4 and the speed of a signal is about 6 inches/nsec. For an interconnect of length, Len, the time delay, TD, is:
Len[in] Len[in]
TD[n sec]
v 6 in / n sec
= =
As a rough rule of thumb, an interconnect is electrically short when the transmission line properties of the interconnect are not
significant when:
Len[in]
RiseTime[n sec] 4 TD 4 0.7 Len[in]
6 in / n sec or
Len in 1.4 RT n sec
= =
For example, if the rise time is 3 nsec, an electrically short
interconnect, when transmission line effects are not important and a lumped circuit model is adequate to describe the interconnect, is for an interconnect length shorter than 1.4 x 3 nsec = 4.2 inches.
The electrical properties of interconnects shorter than 4.2 inches can be accurately described with lumped circuit elements.
This is remarkably close to the estimate of an electrically short interconnect based on when the interconnect length is 1/10th of a wavelength. This suggests that a good rule of thumb for when interconnects are electrically long is roughly:
Lenlong[in] 1.5 RT[n sec]
If you worry whether this relationship should have a 1.4 or 1.7 or even a 1 as the scaling term, then don’t use this criterion. You should assume the interconnect is electrically long and use a transmission
line model to evaluate the impact of the interconnect on electrical performance.
This relationship between the interconnect length and the rise time for when transmission line properties play a role is shown in Figure 4.19.
Figure 4.19 The boundary for when interconnects are electrically long, based on the criteria of Len[in] > 1.5 x RT[nsec].
For example, when the rise time of the signal is 10 nsec,
interconnects shorter than about 15 inches are electrically short.
This does not mean that if rise times are 5 nsec and the interconnect lengths are longer than 15 inches, the interconnect will cause a problem. It just means you will get a better estimate of the reflection noise using transmission line models of the interconnect.
Whether ringing self-aggression noise is significant depends on:
✓ The rise time of the TX
✓ The output source impedance of the TX
✓ The length of the interconnects
✓ The characteristic impedance and uniformity of the interconnects
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✓ The routing topology of the interconnects
✓ The impedance of the RX
✓ The noise margin: how much noise is too much
When interconnects are electrically long, transmission line analysis should be performed to determine whether it is necessary to implement some of the design guidelines to reduce reflection noise to an acceptable level, such as designing the interconnects as uniform, controlled impedance transmission lines, implementing a termination strategy, reducing the branch lengths in the routing topology, or even limiting the routing topology as point to point or daisy chain.
The first step in any design is to determine whether your
interconnects are transparent or not and then if they are not, can they be approximated with lumped circuit elements or distributed transmission line elements. Which regime a product is in depends on the rise time of the signals and the interconnect lengths. These relationships are shown in Figure 4.20.
Figure 4.20 Mapping design space into the three regions of transparent, where lumped elements can be used and when transmission line elements are needed.
Another way of identifying the range of electrically long or electrically short interconnects is to consider the behavior of the signal propagating on the transmission line.
When the signal is originally launched on the interconnect, the voltage between the signal and return path increases with the rising edge. As the voltage turns on and increases, the signal launched on the transmission line will begin to propagate down the line at the speed of light in the materials, v.
Once the rising edge has reached its peak, the signal stops changing, and the edge continues to propagate down the transmission line.
This rising edge, as it propagates, has a spatial extent on the transmission line, as illustrated in Figure 4.21.
Figure 4.21 An illustration of the spatial extent of the rising edge of the voltage wave on a signal-return path interconnect.
In the time of the rising edge, the beginning of the edge has moved down the interconnect a distance of RT x v. This is the spatial extent of the rising edge.
When the length of the interconnect is longer than the spatial extent of the rising edge, the interconnect is considered to be electrically long: the interconnect is long compared to the spatial extent of the rising edge of the signal.
This condition for an electrically long interconnect translates to:
Len RT v RT c ~ RT 6in / n sec Dk
=
This condition for electrically long means Len[in] > 6 x RT[nsec].