Issue link: https://iconnect007.uberflip.com/i/1190860
DECEMBER 2019 I DESIGN007 MAGAZINE 19 The distributed system model is more accurate but also more complex than the lumped element model. The selection of the model is dependent on the accura- cy required in a specific ap- plication. There is no clear- cut demarcation in the fre- quency at which these mod- els should be used, although the changeover is usually somewhere in the 100–500- MHz range. An often-quot- ed rule of thumb is that traces longer than one-tenth (0.1) wavelength will usual- ly need to be analyzed as a distributed system, which is about where the two curves start to deviate noticeably in the example of Figure 3. The technology employed and the physical scale of the design is also significant as minia- turized circuits can use the lumped model at a higher frequency. PCBs using plated through- hole technology are larger than equivalent de- signs using surface-mount technology. Hybrid integrated circuits are smaller than PCB tech- nologies, and monolithic integrated circuits are smaller again. ICs can use lumped designs at higher frequencies than printed circuits, and this is done in some radio-frequency devices. This choice is particularly significant for hand- held devices because lumped element designs generally result in a smaller product. To illustrate the difference between the re- gimes of the analytical treatment of the trans- mission line, the two models are compared in a simulation for increasing lengths of transmis- sion line (Figure 3). The analysis shows the be- havior of the load voltage (V L ) using lumped and distributed element calculations for a loss- less transmission line. The frequency depen- dence is shown in the form of the trace length being a multiple of the wavelength. Depending on the signal rise time, the dis- tributed model for transmission lines starts de- viating from the simplified lumped element model between a trace length of 0.01 and 0.1 of the wavelength of the signal. This simula- tion uses a load impedance that is matched to the impedance of the transmission line, so the reflections are negligible. Although a lossless distributed model is a good representation of a typical low-frequen- cy transmission line, at high frequencies the conductor and dielectric losses also need to be considered. Key Points • The lumped element model assumes that the attributes of the circuit are concen- trated into idealized electrical components connected by a network of perfectly conducting wires • As the frequency and rise time increase, these elements become distributed continuously through the substrate along the entire length of the trace • Electromagnetic energy radiates into the surrounding dielectric material and couples to nearby structures creating a distributed system of parasitic elements • The distributed model is used, at high frequencies, when the wavelength becomes comparable to the physical dimensions of the circuit • The lumped element model completely fails at one-quarter wavelength (a 90° phase change) Figure 3: Lumped vs. distributed element analysis of a transmission line.