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22 The PCB Design Magazine • October 2017 monics cancel. The high-frequency content of a square wave is significantly affected by the rise time of the waveform. Also, as the frequency increases, the amplitude decreases. In the real world, one needs to consider the maximum bandwidth of a signal, including harmonics, rather than assume the perfect square wave fun- dament frequency model. Surprisingly, even at very low frequency, an old-fashioned telegraph line is a transmission line simply because the wire length is compa- rable to the signal rise time. In recent years, edge rates have become much faster, to the point where short traces, on a PCB, are a small multiple of the edge rates propagating through them. As such, one should consider these PCB traces to be transmission lines and analyze their signal integrity. In general, all drivers whose trace length (in inches) is equal to or greater than the rise time (in nanoseconds) should be considered critical and treated as high-speed transmission lines. It is the signal rise/fall time, rather than the sig- nal clock frequency, that determines the criti- cal signal speed. However, a steep rise/fall time may be slowed by loading the signal line with a damping/back-matching resistor close to the source. Impedance is the key factor that controls the stability of a design—it is the core issue of both the signal and power integrity methodol- ogy. At low frequencies, a PCB trace is almost an ideal circuit with little resistance, and with- out capacitance or inductance. Current follows the path of least resistance. But at high frequen- cies, alternating current circuit characteristics dominate causing inductance and capacitance to become prevalent. Current then follows the path of least inductance. The impedance of an ideal, lossless transmission line is related to the capacitance and inductance: But this is very simplistic and the imped- ance should be simulated by a field solver to obtain accurate values, of impedance, for each signal layer of the substrate. The impedance of the trace is extremely important, as any mis- match along the transmission path will result in a reduction in quality of the signal and pos- sibly radiation of noise. For perfect transfer of energy, the impedance at the source must equal the impedance at the load. However, this is not usually the case and terminations are generally required, at fast edge rates, to limit ringing. 50 to 60 ohms characteristic impedance is often used in high-speed designs. Lower im- pedance values cause excessive dI/dt crosstalk and can double the power consumed to create a heat dissipation problem. Higher impedances not only produce high crosstalk, but also pro- duce circuits with greater electromagnetic emis- sions and sensitivity. However as core voltages drop, rise times become faster and frequency increases, and a lower impedance is more desir- able. For example, DDR3/4 memory buses use 40 ohm characteristic and 80 ohm differential impedance. Figure 3 details the actual input impedance measured with a vector network analyzer (VNA), looking into a one inch transmission line with the other end open. This looks remarkably simi- lar to the AC impedance of a plane cavity's res- onance, which also has no termination. How- ever, the plane pair has more area and therefore much more capacitance and less inductance than a trace, making the resonance lower in frequency and providing a very low impedance path. So, planes simply act as big, fat, untermi- nated transmission lines. This transmission line was designed to have a characteristic impedance of 50Ω but the fre- quency dependant losses impact on the quality of the signal. The frequency domain transmit- ted and reflected data is respectively referred to as insertion and return loss. The characteristic impedance (Zo), that is commonly used to spec- ify trace impedance, is defined as the instanta- neous impedance of a lossless transmission line. The most fundamental signal integrity analysis involves defining the board stackup, including appropriate dielectric constants and layer thicknesses, and determining the appro- priate trace width (and clearance for differential signals) that corresponds with the target char- acteristic and differential impedance for the traces. However, selecting the right impedance, and other transmission line characteristics, are essential to generating accurate results. WHEN DO TRACES BECOME TRANSMISSION LINES?

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