Common Mode vs Differential Mode Signals
Even mode propagation refers to the way signal propagates on differential pair (P & N traces), where signals have equal in magnitude and polarity.
Odd mode propagation refers to way signal propagates on differential pair (P & N traces), where signals have equal in magnitude but inverted polarity.
Even mode impedance (Zeven): it is defined as the impedance on a single trace of the differential pair when driven by a common mode voltage (i.e symmetric voltage excitation between P/N trace).
Odd mode (Zodd): it is defined as the impedance on a single trace of the differential pair when driven by a differential mode voltage (i.e anti-symmetric voltage excitation between P/N trace)
Differential impedance (Zdiff):it is what the differential driver sees across the differential pair.
Common mode impedance (Zcom): it is what the common mode voltage driver sees across the differential pair.
Characteristic impedance (Zo): it is the impedance of a single trace on seen by a single ended driver, which is also commonly know as Single Ended (SE) trace.
It's a function of transmission line inductance and capacitance.
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
How do even mode impedance relate to characteristic impedance of each differential pair line?
Zeven= Zo (P/N)+Mutual Impedance (P&N)
How do odd mode impedance relate to characteristic impedance of each differential pair line?
Zodd= Zo (P/N)-Mutual Impedance (P&N)
How do differential impedance Zdiff relates to odd mode impedance in an ideal differential pair?
Zdiff = 2 x Zodd
When does Zodd equal to Zo?
The odd-mode impedance of the loosely coupled pair equals the characteristic impedance of the SE (single ended) trace, which is what generally seen in the PCB design for coupled trace. For tightly coupled trace (i.e differential P and N are routed closer to each other), mutual impedance is higher, so the Zodd will be lower.
Reference and Further Reading:
"The basics of Time Domain reflectometry", https://hvtechnologies.com/blog/basics-time-domain-reflectometry-tdr
"What is Differential Impedance and Why do We Care?", https://www.signalintegrityjournal.com/blogs/12-fundamentals/post/1665-what-is-differential-impedance-and-why-do-we-care