## Both-ends Termination

Terminations exist to control ringing. Ringing (sometimes called overshoot or resonance) is the tendency for signals within a distributed transmission environment to slosh back and forth, bouncing from end to end and creating oscillatory ripples in the received digital data.

The best ways to control ringing on very long transmission lines are source termination, end termination, and both-ends termination. The both-ends termination is supremely tolerant of imperfections within the transmission system and within the terminators themselves.

Figure 1 depicts a time-space analysis of the both-ends termination. The graph depicts the evolution of one step edge from the time the driver injects it into the transmission line until it dissipates, bouncing back and forth.

The horizontal axis represents various physical positions along the transmission
line from the source position (at the far left) to the load (at the right). The
vertical dimension represents the flow of time, beginning at *t*_{0}, when the driver first impresses onto the line a rising step edge of
amplitude A.

As the step edge interacts with various obstacles along the way, each encounter
spawns a new reflected signal. The time-space diagram tracks the magnitude of all the
reflection products. Each arrow is labeled according to the attenuation factors
(reflection coefficients) it encounters. The four reflection coefficients Γ_{1} to Γ_{4} are schematically defined at the top of the figure. Assume for this simple example
that all four coefficients Γ_{1} to Γ_{4} are small, meaning that the line is well-terminated at both ends
(Γ_{1} and Γ_{4 }) and that the obstacle in the middle, whatever it is, generates only
mild reflections
(Γ_{2} and Γ_{3 }). In general, the amplitude of any step passing through* * obstacle *n* is multiplied by a factor
(1+Γ_{n }). For simplicity, the figure leaves out these
(1+Γ_{n} ) terms under the assumption that, in this discussion, Γ_{n} is small so
(1+Γ_{n }) must be reasonably close to one.

The first thing you should notice about the diagram is that all the first-order products (green arrows), having bounced one time, are heading from right to left. None of these products reach the endpoint. Only second-order products (blue arrows) and higher order even-numbered products can reach the endpoint. Because each reflection attenuates the signal, the higher order products are very small. In Figure 1 the higher order products appear in gray, denoting that they are too small to worry about.

The next thing to notice is that each of the second-order products has been attenuated
by *two* small coefficients. For example, both Γ_{4} and Γ_{3} attenuate the product arriving at time *t*_{2}.
Both Γ_{2} and Γ_{1} attenuate the product arriving at time *t*_{3}. In both cases, the surviving signal has been double-attenuated.
That's the beauty of a double-end-terminated net. All second-order reflection products
have been attenuated *twice*. It hardly matters what kind of
obstacle lies in the middle; the terminators always get a chance to damp out the
second-order-reflected products.

Contrast that behavior with what would happen on a plain end-terminated line. In that
case, the magnitude of the coefficient Γ_{1} would equal almost unity. (A powerful, low-impedance driver creates a reflection
coefficient at the source of approximately –1.) The second-order term at time *t*_{3} would then loom much larger.

Similarly, on a plain source-terminated line, the reflection coefficient Γ_{4} would be practically +1, enlarging the second-order term at time *t*_{2}.

The both-ends termination atenuates all second-order reflection products, improving
signal quality over any single termination. Mathematically, reducing the magnitude
of *both* Γ_{4} and Γ_{1} renders your design impervious to variations in Γ_{2} and Γ_{3}.

Of course, the big disadvantage of the both-ends termination is the half-amplitude received signal. The driver (whose source impedance matches the characteristic impedance of the transmission line) produces only a half-sized step. This half-sized step remains half-sized at the end-terminated endpoint. It takes an especially sensitive receiver to work with a both-ends-terminated transmission line.

The both-ends termination is an excellent choice for very high-speed serial links in which you anticipate encountering connectors, vias, or other impedance discontinuities in the middle of the line and for which you can afford a super-sensitive receiver.