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2.9 Transmission Lines Applied to High Frequency Circuits 99 So far we have only looked at voltage waveforms but of course there will also be currents and they too will create standing waves which will have maxima and minima. The minima will repeat every half wavelength and so will the maxima, however the phase of current and voltage standing waves will be different. We will see the rigorous mathematical equations that describe this phase relationship in section 2.14 but let us first of all look at it from a more intuitive viewpoint. Figure 2.9-10 Voltage and Current Profiles along short-circuited quarter-wave line, V S is 1V peak and 1GHz in frequency The quarter-wave line in Figure 2.9-10 is terminated with a short circuit hence the voltage at point β must be zero. The current on the other hand will be maximum since the low impedance seen at β allows maximum current flow. At point α instead, a large impedance (equation (2.9-2)) will be seen and hence no current should flow through. The current is therefore at a minimum while the voltage is at a maximum. The existence of a phase difference between voltage and current standing waves, which in the case of open and short circuits happens to be 90⁰, may also be understood intuitively from Figure 2.3-4 (section 2.3). The figure is shown below for the reader's convenience. This figure shows how lossless transmission lines may be modelled by large networks of series inductors and shunt capacitors. As demonstrated by equations (1.4-1) and (1.5-7) these elements introduce a phase shift between voltage and current, hence some degree of difference between voltage and current along a transmission line is also to be expected. I would like to reiterate at this stage that this phase difference is not always 90⁰ as in the case of open and short circuits. There are of course perfectly rigorous expressions which describe voltages and currents along a transmission line, which we will illustrate in section 2.14. β RF short circuit α Conquer Radio Frequency 99 www.cadence.com/go/awr