Introduction to Transmission Lines
In high speed digital design, signals are often transmitted over controlled impedance traces on a PCB known as transmission lines. As data rates increase into the gigabit per second range and rise/fall times decrease into the sub-nanosecond regime, these interconnects must be treated as transmission lines to minimize signal integrity issues like reflections, ringing, crosstalk, and power loss.
A transmission line is a pair of electrical conductors – the signal trace and its reference plane – that carry a signal from source to destination. The key properties that define a transmission line are:
- Characteristic impedance (Z0) – determined by trace geometry and dielectric properties
- Propagation delay (tpd) – time for signal to travel the length of the line
- Frequency dependent losses – due to skin effect and dielectric loss tangent
At low frequencies, interconnects can be modeled as simple lumped capacitance and resistance. But at high frequencies, the transmission line effects dominate. The transition between lumped and distributed behavior occurs when the rise time of the signal is less than about 2.5 times the propagation delay of the line:
tr < 2.5 * tpd
When this threshold is crossed, reflections will occur at any impedance discontinuities along the line, such as connectors, vias, or improper terminations. These reflections cause ringing, overshoot, undershoot, stair-stepping waveforms, and false triggering of receivers. Proper impedance matching and termination is required to mitigate these issues.
Types of Transmission Lines
The three most common types of transmission lines used in PCB design are:
Microstrip
Microstrip is a trace routed on the outer layer of a PCB, with a solid reference plane below. It has higher impedance than stripline and coplanar waveguide.
| Parameter | Effect on Z0 |
|---|---|
| Increasing trace width | Decreases Z0 |
| Increasing trace thickness | Decreases Z0 |
| Increasing dielectric thickness | Increases Z0 |
| Increasing dielectric constant | Decreases Z0 |
Stripline
Stripline is a trace embedded within the PCB, with reference planes above and below. It provides better isolation and less crosstalk than microstrip.
| Parameter | Effect on Z0 |
|---|---|
| Increasing trace width | Decreases Z0 |
| Increasing dielectric thickness | Increases Z0 |
| Increasing dielectric constant | Decreases Z0 |
Coplanar Waveguide
Coplanar waveguide (CPW) has the signal trace and reference planes on the same layer, with the references on either side of the signal. It allows convenient placement of components.
| Parameter | Effect on Z0 |
|---|---|
| Increasing trace width | Decreases Z0 |
| Increasing gap width | Increases Z0 |
| Increasing dielectric constant | Decreases Z0 |
The choice of transmission line type depends on the design constraints such as available board space, layer count, and required impedance.
Impedance Matching
For maximum power transfer and minimum reflections, the impedance of the source (ZS), transmission line (Z0), and load (ZL) should all be equal:
ZS = Z0 = ZL
When this condition is met, the line is said to be matched. Any impedance mismatch will result in a reflected wave propagating back to the source. The greater the mismatch, the greater the reflected voltage.
The reflection coefficient Γ quantifies the amount of reflection:
Γ = (ZL – Z0) / (ZL + Z0)
- Γ = -1 for a short circuit
- Γ = 0 for a matched line
- Γ = +1 for an open circuit
The percent reflection is Γ * 100%. For example, a 60 ohm load on a 50 ohm line has a 9% reflection.
To minimize reflections, the impedance of the transmission line should be controlled along its entire length, especially at transitions like connectors and vias. Discontinuities that are small compared to the rise time can be tolerated. A good rule of thumb is that the round-trip delay of the discontinuity should be less than 1/4 of the rise time.
Termination Techniques
When the impedances of the source, line and load are not perfectly matched, termination networks can be added to minimize reflections. The termination resistor(s) provide a matched impedance and absorb the reflected energy as heat. The four main termination styles are:
Series
A resistor is placed in series with the signal near the source. The resistor value is:
Rs = Z0 – ZS
This reduces the amplitude of the forward wave, allowing a full voltage swing at the load. It is simple but has high frequency attenuation.
Parallel
A resistor is placed in parallel with the signal near the load. The resistor value is:
Rp = Z0
This doubles the current drawn from the source. It is well suited for point-to-point links.
AC
A resistor and capacitor are placed in series near the load. At low frequencies, the capacitor blocks DC current. At high frequencies, it acts like a parallel termination. The resistor and capacitor values are:
Rac = Z0
Cac > 10 / (2 * π * Z0 * fknee)
where fknee is the highest frequency of interest. This reduces DC power consumption.
Differential
For differential transmission lines, each side is terminated to its complement through a resistor:
Rdiff = 2 * Z0diff
This provides good common mode rejection and noise immunity. A center tap can be added to control the DC bias.
FAQ
What is ringing in a transmission line?
Ringing is an oscillation or ripple on a signal caused by reflections at impedance discontinuities. Under-damped ringing can cause false triggering of receivers.
How do I choose the right termination scheme?
The best termination depends on the application. Series is the simplest but has the most attenuation. Parallel is better for point-to-point. AC saves power. Differential provides the best noise immunity. Simulate or measure the waveforms to optimize.
What causes crosstalk between transmission lines?
Crosstalk is caused by electromagnetic coupling between adjacent traces. As the edge rates increase, so does the coupling. Increase the spacing between lines or route them perpendicular on adjacent layers to minimize crosstalk.
Do I need to terminate lines in both directions?
It depends on the round-trip delay compared to the rise/fall times. If the delay is much less than the transition times, reflections will settle out and you only need to terminate at the load. If the delay is comparable or greater, you need bi-directional termination, e.g. at both ends of a cable.
What is the bandwidth of a transmission line?
The bandwidth depends on the acceptable amount of loss/attenuation. A rule of thumb is that the knee frequency is:
fknee ≈ 0.5 / tr
For example, a 1 ns rise time has a knee frequency of 500 MHz. The 3dB bandwidth is typically 2-3 times higher than this.
Conclusion
As digital speeds increase, transmission line effects become significant even on short PCB traces. If left unterminated, impedance mismatches cause reflections which degrade signal quality and limit performance. By understanding transmission lines and applying proper terminations, designers can reliably push data rates into the multi-gigabit regime. Simulating, measuring and optimizing waveforms is essential to minimize signal integrity issues and ensure a robust high speed design.
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