High-frequency interconnects require special consideration because they often behave not as ordinary wires but rather as transmission lines.
In low-frequency systems, components are connected by wires or PCB traces. The resistance of these conductive elements is low enough to be negligible in most situations.
This aspect of circuit design and analysis changes dramatically as frequency increases. RF signals do not travel along wires or PCB traces in the straightforward fashion that we expect based on our experience with low-frequency circuits.
The behavior of RF interconnects is very different from that of ordinary wires carrying low-frequency signals—so different, in fact, that additional terminology is used: a transmission line is a cable (or simply a pair of conductors) that must be analyzed according to the characteristics of high-frequency signal propagation.
First, let’s clarify two things:
“Cable” is a convenient but imprecise word in this context. The coaxial cable is certainly a classic example of a transmission line, but PCB traces also function as transmission lines. The “microstrip” transmission line consists of a trace and a nearby ground plane, as follows:
The “stripline” transmission line consists of a PCB trace and two ground planes:
PCB transmission lines are particularly important because their characteristics are controlled directly by the designer. When we buy a cable, its physical properties are fixed; we simply gather the necessary information from the datasheet. When laying out an RF PCB, we can easily customize the dimensions—and thus the electrical characteristics—of the transmission line according to the needs of the application.
Not every high-frequency interconnect is a transmission line; this term refers primarily to the electrical interaction between signal and cable, not to the frequency of the signal or the physical characteristics of the cable. So when do we need to incorporate transmission-line effects into our analysis?
The general idea is that transmission-line effects become significant when the length of the line is comparable to or greater than the wavelength of the signal. A more specific guideline is one-fourth of the wavelength:
Recall that wavelength is equal to propagation velocity divided by frequency:
If we assume a propagation velocity of 0.7 times the speed of light, we have the following wavelengths:
|1 kHz||210 km|
|1 MHz||210 m|
|1 GHz||210 mm|
|10 GHz||21 mm|
The corresponding transmission-line thresholds are the following:
|1 kHz||52.5 km|
|1 MHz||52.5 m|
|1 GHz||52.5 mm|
|10 GHz||5.25 mm|
So for very low frequencies, transmission-line effects are negligible. For medium frequencies, only very long cables require special consideration. However, at 1 GHz many PCB traces must be treated as transmission lines, and as frequencies climb into the tens of gigahertz, transmission lines become ubiquitous.
The most important property of a transmission line is the characteristic impedance (denoted by Z0). Overall this is a fairly straightforward concept, but initially it can cause confusion.
First, a note on terminology: “Resistance” refers to opposition to any flow of current; it is not dependent on frequency. “Impedance” is used in the context of AC circuits and often refers to a frequency-dependent resistance. However, we sometimes use “impedance” where “resistance” would theoretically be more appropriate; for example, we might refer to the “output impedance” of purely resistive circuit.
Thus, it’s important to have a clear idea of what we mean by “characteristic impedance.” It is not the resistance of the signal conductor inside the cable—a common characteristic impedance is 50 Ω, and a DC resistance of 50 Ω for a short cable would be absurdly high. Here are some salient points that help to clarify the nature of characteristic impedance:
The impedance of a transmission line is not intended to restrict current flow in the way that an ordinary resistor would. Characteristic impedance is simply an unavoidable result of the interaction between a cable composed of two conductors in close proximity. The importance of characteristic impedance in the context of RF design lies in the fact that the designer must match impedances in order to prevent reflections and achieve maximum power transfer. This will be discussed in the next page.
by Jake Hertz
In Partnership with Rohde & Schwarz
In Partnership with Analog Devices
by Robert Keim