Damping and Reflection Transfer with a Series Termination Resistor

Trace, source, and load impedance matching are important in boards that contain transmission lines. To reach these conditions, you may see some designs that use a series termination resistor on single-ended transmission lines. The reasoning for doing this is sometimes to slow down a signal, or sometimes to set the driver's output impedance, depending who you ask.

As surprising as it might be, the placement of series resistors for termination are sometimes misunderstood. Some of the questions that arise are:

• When do you need to manually place series resistors?
• When can you rely on simply designing a transmission line to a target impedance?
• What do you do on short vs. long transmission lines?
• How does load capacitance and ground bounce play a role in signal integrity with a series resistor?
• Is there a difference between single-ended and differential lines?
• What should be done if a signaling standard doesn't have an impedance requirement (e.g., SPI or I2C)

In this article, I'll look at some of the above questions from the perspective of fast GPIOs and serial buses. We often look at a standard like SPI, and it's easy to assume that termination is not needed because there is no impedance requirement specified, and the bus will be running slowly. This is not true in all cases, and the placement of any termination resistor will affect the injected signal rise time, the trace's input impedance, and reduction in overshoot on the line.

Two Functions of a Series Termination Resistor on Single-Ended Lines

Typical reasons to use series termination are as follows:

• The bus does not have an impedance specification
• The output impedance and signal level are being adjusted to a target value for specialty logic
• The push-pull driver switches very quickly (can be as low as a few ns)
• The rise time of the signal seen at the receiver depends on the load capacitance
• The output impedance from the driver is typically low
• There is ringing on the line

The last point could be caused by two factors: reflection on a long transmission line, or excitation of a transient response on a short line. The former is related to impedance mismatch, while the latter is instead related to the same factors that cause ground bounce.

Reflection on a long line: Series termination is sometimes used used at the source as the output impedance of the driver is always less than the single-ended impedance of the transmission line. In the ideal case the output impedance is 0 Ohms, but in general it will be a small non-zero value. The simplest way to size the value of the termination resistor is to subtract the output impedance from the transmission line impedance:

Damping on a short resonating line: A series termination resistor can be used to increase the damping constant in the equivalent circuit for a transmission line. If the series termination resistor takes just the right value, you can critically dampen any transient oscillation that can occur in a short line:

Note that Z(damping) is not always equal to Z(TL). Both cases rely on knowing the driver's output impedance.

For example, if the output impedance from your driver varies from 20 to 30 Ohms in the ON and OFF states, respectively, then the best series termination resistor to use is 25 Ohms. This will define an impedance of 45 to 55 Ohms at the source, which places you well within a +/- 10% variation of a 50 Ohms trace impedance target, assuming there are no other factors that cause output impedance variations. Thank you to Dr. Howard Johnson for pointing this out.

Series Resistor in a Short Resonating Single-Ended Lines

In a short single-ended transmission line, the signal is generally rising across the entire transmission line. This means that the load capacitance is charging while the signal is still being injected into the transmission line. In this case, we would say that the transmission line is below its critical length. In this case, the load capacitance will have two effects here:

1. The load capacitance contributes to the total capacitance seen by the signal
2. If there is excess inductance in the signal path, you can get strong ground bounce

In terms of modeling the response, you can treat the channel as a lumped RLC circuit as shown below. The lumped RLC circuit includes total inductance of L1 + L2 when switched OFF, or L3 + L2 when switched ON; the capacitance comes from the load capacitance and the trace capacitance. We generally ignore R1 when analyzing this as the resistance will be very low (mOhm value) in the ON state.

If you analyze the equivalent RLC model that defines a transmission line with a series termination resistor, you can quickly determine the level of damping provided by the presence of a series termination resistor. Because this is an RLC circuit, it can exhibit an oscillation that is superimposed on top of the ON or OFF signal level. This transient will be seen as a high frequency overshoot at the receiver, so it would be desirable to damp this overshoot if possible.

When the transmission line is critically damped, a transient oscillation will be completely suppressed and while still having the fastest rise time. How would you add damping? You would do it with a series resistor, and a correctly chosen series resistor will bring you to critical damping. If you calculate the transient oscillation frequency and damping in this RLC model, you can determine the value of the series termination resistor required to produce critical damping:

Is it actually possible to critically damp the response? The answer is "maybe"...

One can immediately see that the source output impedance and series termination resistor could be nearly double the equivalent imepdance of the channel in order to reach critical damping, particularly when the source impedance is very small. Note that we have the following parameters that give us the total inductance and impedance:

• C(line) - Typically 2 to 3 pF/inch
• C(load) - Anywhere from 1 to 10 pF (could be larger)
• L(line) - Typically 5 to 10 nH/inch
• L(1) and L(3) - Order of ~1 nH due to any vias and lead frame
• Z(source) - Maybe up to 20 Ohms for a typical push-pull bus that does not have an impedance specification

Since these parameters add together in the numerator and the denominator, we can see that we need to have the series resistor be at least equal to the characteristic impedance to reach critical damping. Obviously, given power loss over the series resistor, you might not have enough signal left at the receiver to toggle the logic state. In my opinion, smaller resistors (22 or 33 Ohms) are better and I commonly see them on many designs.

Example on an Electrically Short (1 inch) Line

Let's look at an example:

1. Suppose in the above example, ground and power have via connections with L(via) = 1 nH. If we have a 1 inch line with C(load) = 4 pF, L(line) = 7.5 nH/inch, and C(line) = 3 pF/inch. The total source resistance required to hit critical damping will be 70 Ohms.
2. If the I/O's output impedance is 10 Ohms, then the series resistor would need to be 60 Ohms
3. The damped resonant frequency will be 646 MHz, resulting in an underdamped oscillation period of 1.55 ns.

Because the line's characteristic impedance is targeting 50 Ohms, and you see the resonance on an oscilloscope, it might be natural to assume that the ringing is from reflections and a 40 Ohm series resistor termination series termination will eliminate the ringing. In reality, because the ringing is actually due to an excited resonance in the short line, complete damping of the ringing does not occur unless you over-size the series resistor.

Damping and Matching Have a Tradeoff

The above illustrates that there is a tradeoff between damping and impedance matching: one cannot critically damp the response and perfectly match impedance simultaneously without losing some power on the series resistor. If you match the source impedance exactly to the transmission line impedance, then you will create two issues:

• You produce an underdamped oscillation when the driver switches.
• You drop some power over the series resistor and you might not register the correct voltage at the load unless the load is high-impedance as defined by its load capacitance.

This is why we instead opt for a bypass capacitor as a solution to this problem. The resulting model would look like that below, where the bypass capacitor is effectively in series to compensate transient oscillation and ground bounce.

Do bypass capacitors eliminate the need for a series resistor? Again, this one has a "maybe" answer. I would argue that you should go through the following process:

1. Apply the recommended or calculated bypass capacitor first
2. The datasheet for your single-ended driver should include a rise time vs. receiver load capacitance value
3. Based on the receiver load capacitance in your design, determine whether the edge rate will be too fast to ensure low noise
4. If the edge rate is too fast, you are longer than the critical length, or you would still have excess overshoot at low load capacitance, add in a small series resistor.

These points are important as some processors become more advanced with smaller form factor. These devices will show a continued trend in lower load capacitances, resulting in faster edge rates on simple buses like SPI.

Finding Compromise

The point from the above discussion is: there will always be a bit of oscillation on the rising edge of a signal, and the overshoot can be greater when the edge rate is faster. This can be slowed with manually-placed series termination, but probably not totally eliminated by just using a series resistor. Instead, we prefer a bypass capacitor as the first step to reducing transient responses, then we might use a series resistor, but only if the bus does not have an impedance specification.

Determining the right compromise between damping and impedance matching really requires considering the noise margin at the receiver. If the receiver has a large noise margin, then most likely you can design to the characteristic impedance without worrying about overshoot; you won’t induce involuntary switching or enter the undefined region for your logic family. If the noise margin is narrow, then you may need to allow a slight mismatch and power transfer reduction from the source and use a larger resistor, which will bring the response closer to critical damping. Although this reduces the amplitude of the transient oscillation, it also increases the rise time somewhat, which might violate the receiver's setup and hold time.

Because of the issue mentioned earlier, where the output impedance of a driver can be different in the ON and OFF states, you might be able to critically damp one edge of the pulse, while the other edge exhibits some ringing during switching. If the load is a high-Z receiver that does not require termination, then you can even have a reflection that produces a stair-step response on one or both edges of the pulse.

Always test transmission lines in your prototype for signal integrity

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