Why Impedance Matching is Important in a Transmission Line
Do you know the transmission line critical length for these traces?
Whether you are working with digital or analog signals, you’ll most likely need to match impedances between a source, transmission line, and load. The reason impedance matching is important in a transmission line is to ensure that a 5 V signal sent down the line is seen as a 5 V signal at the receiver. If you understand why transmission line matching is important, you can start to understand when you need to do this, either at the driver or receiver ends of the line.
When we talk about impedance matching, we are referring to setting the driver, transmission line, and receiver impedances to the same value. This is usually 50 Ohms for single-ended transmission lines, although differential signalling standards may specify different values for impedance matching. Here’s why impedance matching is important in a transmission line and how to implement consistent impedance in PCB interconnects.
How an Interconnect is Impedance Matched: 3 Cases
The goal of impedance matching in a transmission line is to set a consistent impedance throughout an interconnect. When the impedances of the driver, receiver, and transmission line are matched, a few important things happen, which will be discussed below. The following cases should be addressed when discussing why impedance matching is important in a transmission line:
The driver, line, and receiver are matched to the same impedance. This can be considered a case with perfect matching. In this case, there are no reflections along the line (either at the input to the line or output), and maximum power is transferred downstream to the receiver. The voltage in the signal only decreases due to scattering losses, absorption, and DC and skin effect losses.
The driver and receiver are matched, but the line is mismatched. In this case, there will be some reflection as soon as the signal is launched into the transmission line. In other words, when the line is not matched to the driver, some of the sourced signal is reflected back into the driver. This effectively prevents some power from transmitting into the transmission line. Similarly, there will be a reflection at the receiver end, and the signal will travel back to the driver.
The input impedance will determine whether maximum power is transferred from the driver to the receiver. In the case of a short transmission line, the transmission line impedance will look like the load’s impedance when the transmission line is very short. The question of this critical length is addressed in another article. You can determine the exact input impedance (defined as the impedance of the transmission line after the first signal reflection) with the following equations:
Input impedance for lossy and lossless transmission lines
The driver, receiver, and line are all mismatched. In this case, it doesn’t matter what the length of the transmission line is; there will be continuous reflections as the signal travels along the line, producing an undesirable stair-step increase in the voltage seen by the receiver. You won’t transfer maximum power from the driver to the receiver, even if the line is very short, because the driver and receiver are mismatched.
Why Impedance Matching is Important in a Transmission Line: Reflections
When the driver and the transmission line are matched, you suppress a reflection at the input of the transmission line. However, when the line is not matched to the receiver in this case, you still have a reflection at the receiver. Similarly, if the line is mismatched from the driver and receiver, you effectively lose some signal due to reflection. Setting the impedance of the line, driver, and receiver to the same power ensures you transfer maximum power to the receiver. Note that some signalling standards do not rely on maximum power transfer and instead rely on high input impedance to sense a signal at the input (e.g., LVDS).
Impedance matching at an interface between two portions of an interconnect prevents reflections at that interface. Anytime there is a reflection at an impedance discontinuity (i.e., the driver-line interface, or the driver-source interface), there is an abrupt change in the signal level, which produces a transient response in the interconnect. The resulting reflection appears as ringing (i.e., overshoot/undershoot) that is superimposed on top of the desired signal level as well as a possible stair-step response (in digital signals). Reflections create another problem, depending on whether we are working with digital or analog signals.
Reflections with Digital Signals
Repeated back-and-forth reflections on a mismatched transmission line can produce a stair-step response in the voltage seen at the receiver and the source. This stair-step response can appear as a gradual increase in the signal level (see below for an example) or an up-and-down stair-step style response, both of which interfere with subsequent incoming signals. As a result, the voltage seen at the receiver can vary over time, as shown in the example below. Note that the typical transient response on top of the voltage change produced at each reflection has been omitted for clarity.
Example stair-step response for a high-speed digital signal on a mismatched transmission line
Reflections with Analog Signals
Just as digital signals can reflect repeatedly on a transmission line when the receiver is mismatched with the line, the same applies to analog signals. There are certain frequencies that will form standing wave resonances on a line when driven with an analog signal. These frequencies will be some integer multiple of some lowest fundamental frequency. This causes strong radiation from a transmission line at particular frequencies. Note that, in the case of very short transmission lines, this will still occur when the driver and receiver are mismatched, the relevant frequencies will just be much larger to accommodate the shorter wavelength on the transmission line.
Standing waves on a transmission line mean your traces will appear to act like these antennas
Even if the line is short, you still need to impedance match the driver and receiver to prevent repeated reflections and ringing on a transmission line. Also, the exact length that defines when a line is short is not set in stone; it depends on the allowed impedance mismatch along an interconnect. As more devices run at lower levels and faster edge rates, allowed mismatches are becoming ever-more razor thin. This necessitates more accurate impedance-controlled routing during the design phase.
We’ve implicitly described single-ended signalling here, but the exact same discussion applies to differential signalling; just replace the term “characteristic impedance” with “differential impedance, and the same concepts will apply, albeit the math is a bit different. We’ll continue looking at these issues in upcoming articles in order to help designers quickly make the right decisions with more advanced interconnect architectures, signalling standards, and modulation schemes.
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