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22 DESIGN007 MAGAZINE I APRIL 2020 them in a factory environment yielding repeat- able results. Hence, from a cost and practical- ity perspective, the TDR is the de facto stan- dard impedance measurement instrument in the PCB fabrication industry. A TDR applies a very fast pulse (<100 ps) to an impedance test coupon via a controlled im- pedance cable and matching impedance probe (Figure 3). Whenever there is a change in im- pedance, part of the signal energy is reflected back to the TDR and is measured by the in- strument. The magnitude of the reflected sig- nal is related to the value of the discontinu- ity. Changes in the cross-sectional area of the trace, distance to the plane(s), and return path or proximity to other pads and traces will also cause a change in the impedance and cause a reflection. From this data, it is possible to graph the impedance and its variation over dis- tance or time. If a signal propagates from a region with im- pedance Z1, and enters a region with an im- pedance Z2, the incident waveform will re- flect. The reflection coefficient—defined as the ratio of the reflected to the incident voltage—is related to the two impedances by the reflection coefficient : Equation 1 By measuring the reflected signal and know- ing the incident signal and the impedance of the source, the impedance of the transmission line can be extracted. When measured, in the time domain by a TDR, the incident waveform is a fast-rising step edge, and the impedance profile of the trace is measured as: Equation 2 When measured, in the frequency domain by a VNA, the incident waveform is a sine wave, and the reflected amplitude and phase is mea- sured at each frequency value. The reflection coefficient, usually referred to as S-parameter (S 11 ), is related to the total, integrated overall impedance of the transmission line at each fre- quency by: Equation 3 The key attribute of a TDR to consider is the pulse rise time, as this determines the measured resolution. The faster the rising edge, the short- er the impedance discontinuity, which can be detected. If you are characterizing a connector or other very short type of interconnect, then a faster rise time will allow you to see anomalies that would be missed with a slower rise time. Most of the energy of the pulse will be in the first harmonic, and it is this frequency that is used to calculate the impedance. Fortunately, impedance does not vary much with frequency although insertion loss does. Impedance test coupons are generally 150 mm long (see IPC standard IPC-2141A Design Guide for High-Speed Controlled Impedance Figure 3: TDR measurement overview.

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