Legend has it that opera singers can break champagne flutes just by wailing at the right note. From opera singers to the Tacoma Narrows Bridge, and the high tide in the Bay of Fundy in Canada, resonance can be a beautiful and simultaneously destructive phenomenon.
The terms “transmission delay” and “propagation delay” are sometimes used interchangeably. In analog systems, both terms can refer to the time required for a signal to travel between the ends of an interconnect. The same is true in digital systems. However, propagation delay is also sometimes used in place of rise and fall time when referring to logic gates. Obviously, this can create significant confusion. Electrical signals travel with a definite speed can cause resonance when they interfere.
Transmission Delay and Impedance Matching
Impedance matching of lower frequency analog signals is required when the impedance mismatch at the ends of an interconnect is large. In a PCB, mismatch is usually small (about 10 Ohms), but signal drivers can have much higher impedance mismatch (30 Ohms or more). So we need to consider how transmission delay and impedance mismatch affects both high and low frequencies signals.
When the transmission delay between the signal source and its destination on a PCB is very short compared to one-quarter of the oscillation period, the wave effectively spans across the entire interconnect. In other words, the speed of the propagation speed signal needs to be very fast compared to the oscillation period. In such a low-speed scenario, any transmission delay problems or transmission line reflections can be ignored.
When working with higher frequency signals, the transmission delay time is now comparable to one-quarter of the oscillation period. Transmission delay on a PCB interconnect cannot be ignored in this case. Therefore, it is not possible to analyze the behavior of such high-speed signals on PCB interconnects using ordinary network analysis techniques. The interconnects need to be considered as transmission lines and analyzed accordingly.
Resonance and Return Loss
When dealing with transmission lines in a PCB or your standard electrical lines carrying AC power, the transmission delay and any impedance discontinuities determine which signals can act as standing waves. Resonance on a transmission line depends on the transmission delay time and the signal frequency.
Try as we might, impedance matching is almost never perfect. Minor impedance mismatches as small as 1 Ohm can lead to analog signal resonance in an interconnect. Reflection at the ends of the interconnect causes interference between the transmitted and reflected signal. This leads to a return loss spectrum with a periodic structure.
Setting the length of the interconnect to specific multiples of one quarter the signal wavelength will set the signal return loss at either a maximum or minimum. The exact trace length required also depends on whether the reflection coefficient is positive or negative, as a negative reflection coefficient creates a 180 degree phase shift in the reflected signal.
Series interconnects tend to have a neat, periodic return loss spectrum. Parallel interconnects can have a complicated return loss spectrum, and the trace length required for a minimum return loss will no longer occur at specific integer multiples of the signal wavelength. Simulation tools can be very useful for tuning traces to just the right length in order to minimize insertion loss.
Ideally, your waves aren’t as unpredictable as this.
In digital circuits, ringing can occur due to resonance in short traces or due to signal reflection in long traces. Ringing can cause EMI and interference in nearby components, as well as a host of other effects. In short traces, where the transmission delay is much less than one-quarter of the oscillation frequency, the best way to reduce ringing is to increase the damping in the circuit with a series resistor or reduce the value of the natural frequency by changing the LC product.
An antenna fabricated from copper traces, microstrips, or another conductor can be thought of as an impedance mismatched transmission line. The input port of the antenna should always be impedance matched with the signal line. However, the output port is in contact with free space, and there is an obvious impedance discontinuity at the boundary of the antenna and with the substrate.
Although there can be many resonance frequencies that are defined by the antenna geometry, impedance matching using inductors and capacitors will only match the impedance to 50 Ohms at a particular signal frequency. With this in mind, it makes sense that an antenna operates best when it is supplied with a signal that is equal to the impedance-matched resonant frequency.
The impedance matching mentioned above should always be performed at the input port of the antenna, regardless of the emission frequency. The situation becomes more complicated with dual-band antennas, where both frequencies need to be matched simultaneously. The resulting resonance within the antenna itself needs to be determined either by manual calculation or by simulation.
A great piece of PCB layout software like Altium Designer makes it easy to layout your next high-speed design. The ActiveRoute tool, xSignals tool, and the integrated component libraries can help you avoid problems from propagation delay and transmission delay.
Talk to an Altium expert today if you are interested in learning more about Altium Designer.
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