# Common Mode vs Differential Mode Signals

Introduction

In the realm of signal integrity and high-speed circuit design, understanding the behavior of differential pairs is crucial. A fundamental aspect of differential pairs is the concept of even mode and odd mode propagation, which governs how signals travel along the pair. Additionally, various impedance parameters play a significant role in characterizing the differential pair's behavior. This includes even mode impedance (Zeven), odd mode impedance (Zodd), differential impedance (Zdiff), common mode impedance (Zcom), and characteristic impedance (Zo). By comprehending these concepts and equations, engineers can design differential pairs with optimized performance and ensure reliable signal transmission in their electronic systems.

Definition:

Even mode propagation: Signal propagation on a differential pair (P & N traces) where the signals have equal magnitude and polarity.

Odd mode propagation: Signal propagation on a differential pair (P & N traces) where the signals have equal magnitude but inverted polarity.

Even mode impedance (Zeven):

Zeven = Zo (P/N) + Mutual Impedance (P&N)

The even mode impedance is determined by the characteristic impedance (Zo) of each individual differential pair line and the mutual impedance between the P and N traces.

Odd mode impedance (Zodd):

Zodd = Zo (P/N) - Mutual Impedance (P&N)

The odd mode impedance is determined by the characteristic impedance (Zo) of each individual differential pair line and the mutual impedance between the P and N traces.

Differential impedance (Zdiff):

Zdiff = 2 x Zodd

In an ideal differential pair, the differential impedance (Zdiff) is equal to twice the value of the odd mode impedance (Zodd).

Common mode impedance (Zcom):

Zcom = 0.5 x Zeven

The common mode impedance is half of the even mode impedance (Zeven) and represents the impedance seen by the common mode voltage driver across the differential pair.

Characteristic impedance (Zo):

It is the impedance of a single trace seen by a single-ended driver, which is determined by the transmission line's inductance and capacitance.

Application

Differential impedance, odd mode propagation, and odd mode impedance are key concepts in differential high speed signals design, where differential pairs are used in board layout.

In real design, we are given a differential impedance of 100 ohms which is measured by Time Domain Reflectometry (TDR). TDR will given both a odd and even impedance.

Due to the fact differential traces are tightly coupled to reference ground planes in PCB stripe line design, Zdiff=2xZodd=2xZo

A differential driver A (e.g. H-Bridge) transmits complementary signals on a communication interface usually postfixed as _TX_P and _TX_N

Q&A

Q: How do even mode impedance relate to characteristic impedance of each differential pair line?

A: Zeven = Zo (P/N) + Mutual Impedance (P&N). The even mode impedance is determined by the characteristic impedance (Zo) of each individual differential pair line and the mutual impedance between the P and N traces.

Q: How do odd mode impedance relate to characteristic impedance of each differential pair line?

A: Zodd = Zo (P/N) - Mutual Impedance (P&N). The odd mode impedance is determined by the characteristic impedance (Zo) of each individual differential pair line and the mutual impedance between the P and N traces.

Q: How does differential impedance (Zdiff) relate to odd mode impedance in an ideal differential pair?

A: Zdiff = 2 x Zodd. In an ideal differential pair, the differential impedance (Zdiff) is equal to twice the value of the odd mode impedance (Zodd).

Q: When does Zodd equal to Zo?

A: The odd-mode impedance of the loosely coupled pair equals the characteristic impedance (Zo) of the single-ended (SE) trace, which is typically observed in PCB designs for coupled traces. In tightly coupled traces where the differential P and N traces are routed closer to each other, the mutual impedance is higher, resulting in a lower Zodd value.

Summary

Differential pairs in high-speed circuit design exhibit even mode and odd mode propagation.

Even mode impedance (Zeven) and odd mode impedance (Zodd) are parameters that describe the behavior of a single trace in a differential pair.

Differential impedance (Zdiff) represents the impedance seen by the differential driver across the pair and is equal to twice the odd mode impedance.

Common mode impedance (Zcom) is the impedance seen by the common mode voltage driver and is half of the even mode impedance.

Characteristic impedance (Zo) is the impedance of a single trace seen by a single-ended driver, determined by the transmission line's properties.

Reference and Further Reading:

For more detailed information on the topics of Time Domain Reflectometry (TDR) and differential impedance, you can refer to the provided reference and further reading links: "The basics of Time Domain Reflectometry" at https://hvtechnologies.com/blog/basics-time-domain-reflectometry-tdr and "What is Differential Impedance and Why do We Care?" at https://www.signalintegrityjournal.com/blogs/12-fundamentals/post/1665-what-is-differential-impedance-and-why-do-we-care.