# What Determines Differential Pair Via Impedance in a PCB?

### Key Takeaways

• Impedance determines signal propagation behavior, and every feature on an interconnect will have some impedance.

• For differential signals, vias can have their own differential impedance, just like the traces in a differential pair have a specific impedance.

• The factors that influence differential pair via impedance will affect the input impedance seen at the vias.

The vias on these differential pairs have their own impedance, which can create signal integrity problems on long interconnects

High speed PCBs and signaling standards almost entirely use differential pairs with precise impedance, length matching, skew compensation, and loss budgets. Designers need tools to help them design to these important differential signal integrity goals. This is about more than just accurate impedance calculations; it requires understanding how differential signals interact with every feature on an interconnect. This includes connectors, cables, components, and vias.

Among these features on an interconnect, vias should appear in a differential arrangement, just like a pair of traces. The via pair will have its own differential impedance, thus it will also have its own set of network parameters (i.e., S-parameters). If you’re designing a very high speed board with differential via routing, keep reading to see what factors affect differential pair via impedance.

## Understanding Differential Pair Via Impedance

Just like a trace on PCB, vias have their own impedance, which is often described using lumped circuit models, similar to a transmission line. By understanding how a via can act like a simple inductor, LC circuit, and as a pure capacitor, it’s easier to spot how the structure of a via and nearby parasitics will influence the via’s differential impedance.

The following factors will combine to determine the characteristic impedance of a single via:

• Via inductance: All vias are like small inductors filled with a weakly magnetic core. Although they don’t create the same fields as large electromagnets, they have inductive impedance.

• Parasitic capacitance to nearby planes: The directionality of wave propagation requires that waves interact with different impedances at different types. An interaction at one impedance will affect the interaction at the next impedance.

• PCB laminate material: The dielectric constant of the PCB laminate will also influence the impedance of an individual via.

Once two vias are driven with differential signals, their differential impedance will be determined by their parasitic capacitive and inductive coupling, just like even and odd mode transmission lines. Once we know the differential impedance, we now need to worry about the input impedance of the (differential pair) + (via) arrangement, as this will determine the S-parameters in the interconnect.

## Input Impedance of Differential Vias

The procedure for calculating the differential impedance of an interconnect with a differential via transition is iterative; you calculate the input impedance from the receiver end and work backwards to the load end. To see how this works, consider the diagram below. We have a differential pair being routed through a via mid-way between driver and receiver components.

Each section of the interconnect will have its own input impedance. The differential input impedance at each section depends on the differential impedance in all downstream sections, similar to a standard transmission line. We can write the following iterative equation relating the input impedance in section i to the next section along the interconnect:

Input impedance equation

This input impedance will determine reflection at each section of the transmission line. For differential signals traveling through a via pair, the input impedance at the via pad might look like the differential impedance of Pair 2, depending on the length of the via and the propagation delay.

Just like transmission lines, differential vias will have a critical length that determines whether they require precise impedance matching to the differential pairs on each side. If the via length is short, then the tanh function will approximate to 0 and the input impedance will be the differential impedance of section (i + 1). This will be the case in low speed/low frequency signals, so we typically don’t worry about the differential impedance on protocols like 10/100 Ethernet, low-speed USB, or similar differential protocols. For other protocols, like gigabit Ethernet or MIPI protocols, the via length will matter and steps should be taken to understand how differential pair via impedance affects losses on an interconnect.

## Challenges With Differential Vias

If it’s not evident from the above discussion, we can summarize the above points as follows:

• When the differential via pair is very short, its impedance will not matter; the input impedance at the via pair will be the input differential impedance from Pair 2.

• When the via pair is very long, such as in a thick backplane, the differential pair via impedance will determine impedance mismatch seen by a propagating signal.

• Via stubs create another source of impedance mismatch and will create differential resonances when the stubs are long.

### Use Short Vias and Short Stubs

Determining when each condition applies requires looking at the critical electrical length of the vias. In general, for signals with bandwidths spanning up to ~100 GHz, you will need both short differential via pairs and backdrilled via stubs. This solves two problems, but it creates more complexity in routing and stackup design, and it increases the total cost of the system.

### Use Differential Mode S-Parameters

To fully summarize the behavior of the via pair, we need the differential mode S-parameters. When the differential pair via impedance creates a mismatch with the section’s input impedance, there will be some return loss. The total loss (return loss plus insertion loss) in a high speed channel needs to be compared with the loss budget in the differential channel, and the loss budget will be specified in your receiver specifications. The best PCB design software will include a 3D field solver you can use to calculate S-parameters and other network parameters directly from your PCB layout.

When you need to calculate or simulate differential pair via impedance and S-parameters, use a set of PCB design and analysis tools with integrated field solvers and analysis features. Cadence offers a range of applications that automate many important tasks in systems analysis, including signal and power integrity analysis through an integrated set of field solvers.