# Which Transmission Line Impedance is Used for Termination?

November 4, 2019 These connectors will create some return loss and insertion loss when used with high speed or high frequency signals.

Transmission line impedance matching is a critical part of any layout for reasons that will be seen shortly. Whenever you are routing traces, there are several important points to check in order to ensure signal integrity throughout your board. Without further adieu, let’s look at which transmission line impedance you need to consider for termination.

## The Real Scoop on Transmission Line Impedance

Before getting into the topic of determining which transmission line impedance to use for termination, you should read this article, which describes the different impedances used to describe real transmission lines in a PCB. For the moment, we will only consider an isolated transmission line; meaning the transmission line is not coupled in any way to any other nearby transmission lines (again, read the aforementioned article to understand why this is important).

There is something that the PCB community won’t tell you (or won’t accept) about transmission lines and their critical length; all interconnects that do not run at DC will behave as transmission lines. The issue is whether the effects of a transmission line impedance mismatch are noticeable at different frequencies or different signal rise times. This brings up the question of when it is worthwhile to match a transmission line. As a result, designers have defined various values for a critical length below which you do not need impedance matching. As a general rule, if you are working with razor thin noise margins, then you should always match impedances between a driver, load, and source, even in electrically short transmission lines.

This so-called critical length is actually quite important beyond just determining when to impedance match a transmission line to the source and load. Here is how this is quantified. If you calculate the voltage V and current I along a transmission line with length ℓ, you’ll find that the impedance seen by a signal (analog or digital) that reflects off a mismatched load depends on the length of the transmission line and its capacitive and inductive characteristics. This is shown in the equation below. The final equation defines the lossy transmission line input impedance seen by a signal that is input to the line.

For more information on determining the propagation constant, see this article. Essentially, when the transmission line is very small compared to the wavelength (i.e., at low enough frequency), the impedance seen by a travelling signal will reduce to the load impedance because tanh(0) = 0. Note that this applies to both lossy and lossless transmission lines.

This explains why we have a critical length: when the transmission line is short enough that tanh(γℓ) ~ 0 (or tan(γℓ) ~ 0 for a lossless line), then the input signal are only sees the load impedance. The source and load impedance should be matched to ensure maximum power transfer into the load.

The situation changes when the line length is long or when it takes specific lengths, and whether there are losses in the transmission line:

### Long or Short Lines

The author, being something of a mathematical purist, is a proponent of taking this approach in all situations. First, simply calculate the value of γ and the characteristic impedance. Next, plug in the length and γ into the equation shown above. The impedance value you calculate is the transmission line impedance the signal sees as it reflects off the mismatched load and travels on the line.

In the limit of a very long transmission line (such as when the line length is many multiples of the wavelength), then tanh function eventually converges to 1. In this case, the input impedance is just the transmission line’s characteristic impedance.

For transmission lines with sufficiently low losses (i.e., Re(γ) = 0), the tanh(x) function above must be replaced with the function jtan(x), where j is the imaginary constant. You will have certain cases where Im(γ)ℓ = mπ/2, where m is an integer. In this case, you will be evaluating tan(mπ/2) in the above equation. The result reduces to: These are the impedances that a signal sees as it reflects backwards along the transmission line. If the source, load, and transmission line are all mismatched, then there are repeated reflections along the length of the line, which leads to a stair-step response seen in digital signals, or standing waves with analog signals.

Matching the transmission line’s characteristic impedance and the load prevents reflection at the load end, and the input impedance will just be the characteristic impedance. In this case, there are no reflections at the load, but you do not have maximum power transfer down the line if the source is unmatched. If you go a step further and match the source to the characteristic impedance, you now ensure maximum power transfer across the line.

### Coupling Between Nearby Transmission Lines

All groups of transmission lines in a PCB have some mutual capacitance and inductance. This is a parasitic effect and is unavoidable, even on the most carefully designed boards. This coupling produces the even and odd mode impedance values for a transmission line, depending on how both lines are driven. In this case, relevant impedance that should be considered for matching is the odd mode (coupled lines driven commonly) or even mode (coupled lines driven differentially) impedance. In the above discussion, just replace the term “characteristic impedance” with the other relevant term.

## Analog vs. Digital Signals

We should make a distinction here regarding the value of γ. In distinguishing the effects of a transmission for different types of signals, think of transmission lines (either isolated or coupled) as filters with some transfer function. With an analog signal oscillating at a single frequency, γ is just the complex wavevector multiplied by the effective dielectric constant (i.e., pi divided by half the wavelength inside the trace) plus the attenuation per unit length along the line.

For frequency modulated analog signals, the characteristic impedance of a transmission line has a constant value throughout the signal’s frequency spectrum as long as the relevant frequency range is high enough. At lower frequencies, and with amplitude modulated signals, this may not be the case, and the other relevant impedance values will depend on frequency and driving mode, i.e., they will have some associated spectrum (again, read this article to understand why this is the case). Modulation should be considered when impedance matching

With digital signals, one must remember that the source and load impedances are not consistent at all frequencies. The relevant bandwidth to consider for transmission line impedance matching is the range extending from the pulse repetition rate to the knee frequency (approximately 0.35 divided by the signal rise time). As long as the component’s bandwidth is flat within this range of frequencies, then you can consider a single value for impedance matching with your transmission line.

### A Note on Ringing

The ringing seen on a transmission line will also be a function of its length relative to the length the signal travels during its rise time. For slowly rising signals, i.e., where the signal reaches the end of the transmission line before the signal rises to full strength, the signal will still ring even with perfect transmission line impedance matching. However, the strength of ringing may be so small as to be unnoticeable when compared to the noise margin as long as the transmission line’s impedance spectrum is flat up to the knee frequency. This is discussed beautifully by Dr. Howard Johnson. This is one reason why some designers encourage routing traces with the shortest possible length.

In essence, the ringing amplitude depends on the voltage difference between the two ends of the line. If the signal rises faster, the voltage difference across the line will be larger, leading to larger ringing amplitude for a given line length. In order to compensate ringing, you need to shift the resonance frequency of the transmission line to much higher than the knee frequency while ensuring impedance matching to eliminate reflection, or you need to critically damp the response with a series resistor.

## When In Doubt: Check Your Datasheets!

Many components are designed to specific signalling standards and have specified input and output impedance values. These components are designed to operate with a specific transmission line impedance, where the impedance is normally specified in terms of the characteristic, common (for parallel data transfer), or differential impedance (for differential signalling standards like LVDS). These signalling standards will also specify the line lengths you should use for different applications and how components that use different standards (or no standard at all) should be terminated in order to ensure compatibility. Check your datasheets to determine the impedance you should use for termination

If you are not working with a specific signalling standard, you will have some work ahead of you to ensure compatibility when connecting components. DRCs are generally not designed to account for potential intermixing between components with different signalling standards, and you’ll need to check the component data sheets to see how exactly components should be matched to the transmission line impedance.

Transmission line impedance matching is a critical part of ensuring signal integrity, and you can ensure your interconnects are designed properly when you use the right PCB design and analysis software package. Allegro PCB Designer and Cadence’s full suite of analysis tools make it easy to determine the various transmission line impedance values and perform important signal integrity simulations in your circuits.

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