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CHAPTER 3 - Foundations of RF & Microwave Circuit Characterisation 126 Remember how in section 2.9 we expressed the physical length of the line in terms of fractions of the wavelength ? Well, since the reflection coefficient is a complex quantity which may be plotted on a polar plot, expressing the length of a transmission line in a form which helps visualising its location on this type of plot may be very useful. We therefore define a measure, , termed electrical length, which is expressed in degrees or radians. Its definition is shown in equation (3.2-5). With this measure, we are effectively scaling the ratio between and by a or 360ι angle. We will see shortly how this can be very useful when using polar plots to represent the reflection coefficient. Let's see what correspondence there is between the physical length of a line (in fractions of a wavelength) and its electrical length. Let us start with a line long (Figure 3.2-1). From (3.2-5) we get . Figure 3.2-1 Physical and electrical lengths for a line, =50Ω =100Ω Now remember that the reflection coefficient measures reflections so, if the transmission line between measurement point and load has an electrical length of or 180ι, by the time the incident signal reaches the load, gets reflected and comes back to the measurement point, it will have travelled twice the length of the line i.e. or 360ι. This is why the electrical length is multiplied by 2 in the exponent of the exponential in equation (3.2-4)! This means that an electrical length of 180ι, gets the reflection coefficient to rotate by 360ι and hence takes us all the way around the polar plot thereby making travel back to the starting point. It is just as if the line was invisible! This was also shown in section 2.9 and is further illustrated in Figure 3.2-2 and Figure 3.2-3. θൌͳͺͲι (3.2-5) Conquer Radio Frequency 126 www.cadence.com/go/awr

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