How Long Is The Trace On The PCB To Be The Transmission Line?

The definition of a transmission line is a signal line with signal return (composed of two wires of a certain length, one is the signal propagation path, and the other is the signal return path). The most common transmission line is the trace on our PCB board. What are the transmission lines? As shown in the figure below, twisted pair cable, coaxial cable and so on.

So how long is the trace on the PCB to be the transmission line?

This is related to the propagation speed of the signal. The signal speed in the copper wire on the FR4 sheet is 6in/ns. Simply put, as long as the round-trip time of the signal on the trace is greater than the rise time of the signal, the trace on the PCB should be processed as a transmission line.

Let's see what happens when the signal propagates over a long trace. Suppose there is a 60-inch PCB trace, as shown in the figure, the return path is the ground plane of the inner layer of the PCB near the signal line, and the signal line and the ground plane are open at the far end.

The signal propagates forward on this trace, and it takes 10ns to transmit to the end of the trace, and another 10ns to return to the source, so the total round-trip time is 20ns. If the above signal round-trip path is regarded as an ordinary current loop, there should be no current in the return path, because it is open at the far end. But the actual situation is not the case, there is current for the first period of time after the return path is on the signal.

Add a signal with a rise time of 1 ns to this trace. In the first 1 ns, the signal has only traveled 6 inches on the line. I don't know if the far end is open or short. Then how big is the impedance felt by the signal? determine? If the signal round-trip path is regarded as an ordinary current loop, there will be contradictions, so it must be handled as a transmission line.

In fact, there is a parasitic capacitance between the signal line and the return ground plane, as shown in the figure below. When the signal propagates forward, the voltage at point A does not change continuously. For the parasitic capacitance, the changing voltage means that a current is generated, and the direction is shown by the dotted line in the figure. Therefore, the impedance felt by the signal is the impedance presented by the capacitance, and the parasitic capacitance constitutes the path of current return. The signal will feel an impedance at every point through which it propagates forward. This impedance is generated by the application of a varying voltage to the parasitic capacitance, which is usually called the transient impedance of the transmission line.

When the signal reaches the far end and the voltage at the far end rises to the final voltage of the signal, the voltage no longer changes. Although the parasitic capacitance still exists, there is no voltage change, and the capacitance is equivalent to an open circuit, which corresponds to the DC situation.

Therefore, the short-term performance of this signal path is different from the long-term performance. For a short period of time, the performance is the transmission line. Even if the remote end of the transmission line is open, during the signal transition period, the performance of the front section of the transmission line will be like a resistor with limited resistance.