Issue link: https://iconnect007.uberflip.com/i/701250
32 The PCB Magazine • July 2016 lines, ν g will depend on frequency. In the fre- quency domain, the change in phase with fre- quency is defined as group delay (τ g ) and can be measured and expressed as a time delay. Given the fields within the microstrip are propagat- ing within a dielectric, the group velocity and group delay are necessary functions of the di- electric properties of the PCB on which the mi- crostrip is constructed. Therefore, the relation- ship between group velocity/delay and the PCB dielectric properties allows for calculation of ɛ r once the group delay of a particular microstrip transmission line is known. The same microstrip lines utilized in the im- pedance extraction method of this paper were utilized here. The only difference is that data was measured in the frequency domain instead of the time domain. The group delay method utilizes the described dispersive properties of microstrip transmission lines and the swept frequency source of a vector network analyzer (VNA) to calculate frequency dependent nor- mal ɛ r. Fortunately, group delay is easily mea- sured with a VNA using the simple relationship in the following equation [7]: where and The phase data collected on a VNA must be unwrapped before this calculation can be fully accomplished. If the phase is not unwrapped and the difference in frequency corresponds to a 360-degree phase wrap, the calculated val- ue will not provide a correct group delay. The wrapped and unwrapped phase can be seen in Figure 4. The group delay can be calculated lo- cally if the phase is not unwrapped. Once the group delay is obtained the effec- tive dielectric constant (K eff ) can be calculated using the following equation: where and With the effective dielectric constant (K eff ) of the microstrip transmission line now known, the frequency dependent ɛ r can be calculated. The effective dielectric constant of a microstrip transmission line is not the same as the PCB ROUND ROBIN OF HIGH-FREQUENCY TEST METHODS BY IPC-D24C TASK GROUP (PART 1) Figure 4: Wrapped vs. unwrapped phase for group delay calculation.