For antennas, a reflection coefficient expresses how much signal voltage is used in exciting the antenna and how much signal voltage is reflected back to the source. The reflection coefficient is a very important metric. The reflection coefficient is defined as: So, from this, we have determined that the impedance of the “load” represented by the blue dot is:īy using this method, it is simple to find the impedance represented by any point on the Smith Chart! Useful Smith Chart RelationsĪs mentioned before, a Smith Chart is really just a 1:1 mapping between a value of load impedance and a value of, the reflection coefficient of a load. The blue dot is also along the red arc marked “0.5,” so the imaginary part of the impedance must be:.The blue dot is along the yellow circle marked “2.0,” so the real part of the impedance must be:.What is the impedance for the load represented on the Smith Chart by the blue dot? This is easy to determine, because: For instance, notice the following Smith Chart: This is very handy for displaying complex impedance values. for any point along the red arc marked “0.5,” the imaginary part of the impedance is: Similarly, the red arcs represent contours where the Imaginary part of the impedance magnitude is the same, e.g. Where is the impedance the chart was normalized from. for any point along the yellow circle marked “2.0,” the real part of the impedance is: The yellow circles represent contours of where the Real part of the impedance magnitude is the same, e.g. The chart consists of yellow circles and red arcs. Each point on the chart represents an impedance, and the numbers marked on the chart represent different coefficients needed to multiply by the original load value (from which the chart was normalized from – If this is confusing, don’t worry about it – the “original load value” will almost always be known). What is seen here is the generic, normalized Smith Chart. To begin, observe the basic “format” of any Smith Chart: Because these impedances may very well be complex in nature, a Smith Chart is designed such that each point on it represents both the real and imaginary parts of the load’s impedance. Smith Charts provide a graphical representation of the impedance of any load – whether that load be an antenna or simply an open-circuited transmission line, such as a coax cable. One way of simplifying the analytical problems communication engineers typically face is by using a Smith Chart. Another reason determining load impedances is important is because of the 1:1 mapping between a value of load impedance and a corresponding value of, the reflection coefficient (a ratio of how much a signal is reflected versus how much a signal is radiated for a given load). Indeed, being able to calculate and measure the impedances of antennas, transmission lines, etc is very important within RF design, which are almost always complex numbers. attach an antenna whose impedance matches that of the signal source – this maximizes the transmitting-antenna’s power dissipation (and “reflects” back zero power). But even with lossless transmission lines, it is important in communications to “match impedances,” i.e. Eventually, the frequency of operation can become so high that the transmission line itself – no longer a simple wire – will exhibit significant signal-loss. However, as one approaches RF frequencies, these real-world effects become much more pronounced in cheap components. This highly non-ideal behavior occurs because, in reality, no true resistor, capacitor, inductor, or wire exists rather they are all processed and manufactured to operate within a certain frequency range – at frequencies where the real-world effects are quantitatively insignificant. This means a normal resistor can become a capacitor, a capacitor can become an inductor, and a normal wire can become a distributed network of inductors and capacitors. In the world of RF (Radio Frequency) electronics, normal “bench-top” circuit components cease to operate the way they were designed to.
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