Issue link: https://iconnect007.uberflip.com/i/1174596
46 DESIGN007 MAGAZINE I OCTOBER 2019 drawn in LTSPICE: a lossless 45-ohm T-line section between a 50-ohm source and load 50- ohm termination. Figure 3 shows the resulting frequency response. With 2V source voltage, if we had all matched conditions (Z 0 = Z 01 = Z 02 = 50 ohms), we would expect to get—and would get—1V across the load regardless of frequency. That is the signal level we get at very low frequencies in the example too. As frequency goes up, we notice that both the input voltage (the voltage across the input of the transmission line af- ter the source resistance) and the Vout start to drop but at different rates. At 50 MHz, both curves reach their mini- mum values. Vin voltage drops approximate- ly 10%, but the Vout drops only 5.5 mV—much less than the 5% what we would expect from lumped-circuit assumptions. The variation continues peri- odically with frequency. The traces reach a 1V maximum at 100 MHz, and then the be- havior repeats. With a 5-ns de- lay through the transmission line, the first minimum at 50 MHz corresponds to the quar- ter-wave condition at the maxi- mum points of 100 MHz and its multiples, and we have the half- wavelength (and its multiples) condition. Note the logarithmic frequency scale, which visually distorts the plots, making the linear phase lines looked curved; however, at the same time, it allows us to observe a several- decade wide frequency range with good reso - lution throughout the entire range. With the linear frequency scale, the phase curve would be a straight line sloping downwards, follow- ing Equation 1: Equation 1 In Equation 1, j is the phase angle in radi- ans, w is the radian frequency, and t pd is the propagation delay through the transmission line. Also note the delay readout in the cur- Figure 2: LTSPICE simulation circuit with impedance mismatch. Figure 3: Frequency response of circuit in Figure 2. Voltage magnitudes are solid lines referencing the left vertical axis, and phase is the dotted line referencing the right vertical axis.