I measure L1 to be 0.122λ and L2 to be 0.377λ This point for y1 is L1, and likewise for y2 and L2 measuring these lengths is easy, start from the short circuit edge and simply read the WTG scale at L1 and L2. Follow this point on the reactive axis as it curves outward toward the edge of the chart and draw a line normal (perpendicular) to the edge of the chart. To get the possible lengths of our stub we will look at the reactive axis of y1 and y2. The second solution, d2, is measured from yL to y2 WTG. The arc between yL and y1 (wavelength toward generator- WTG) is d1, our first solution for the distance from the load to the stub. Draw line from the center through y1 and y2 outward to the edge of the chart. Use a ruler to draw a line from zL through the center of the circle to the far edge of the chart the intersection point with the SWR circle should be marked yL for the admittance component we will need to cancel out the inductive reactance.
For shunt stubs we will use the Smith chart as an admittance chart, so mark the inductive reactance component (upper side) y1 and the capacitive reactance component (lower side) as y2. This circle will intersect with the 1+j b circle at two points. Plot this zL on the Smith chart and use a compass to create an SWR circle. Like the name implies, a shunt stub of some unknown length will be placed in parallel with the transmission line at some point near the load, the parameters of which we will generate using a Smith chart.īegin by normalizing the impedance parameters: Shunt stubs are by far the most common arrangement, so we will look at these first. Say we have a 75Ω line but our load is 100+j80Ω we will need to add a stub to match these lines, adding a length of transmission line to cancel out the reactive j80 from the unmatched load. That being said, we will take a look at each of the stub tuning configurations using sample problems solved using the Smith chart. For the purposes of this article we will assume that the reader is already familiar with using a Smith chart and the focus of this article will be the application of the Smith chart to stub tuning. The design specifications for stub tuners can be found analytically, but an engineer has a tool at his disposal that can be used to solve these problems much faster: the Smith chart. Special stub circuits can help increase this otherwise narrow bandwidth which we will discuss later on. The goal that stubs are designed to accomplish is to cancel out the reactive component of the load to be matched, thus they will only work at a specific frequency. The stub can simply be fabricated onto the PCB along with the rest of the circuit. Because of this, one of the primary places an engineer will encounter stub tuners is in printed circuit boards using microstrip-line waveguides. Stub tuners are simple to implement and cheap to manufacture: they only require more of the same material used to make the transmission line. The image below depicts the basic layout of stub tuners from Pozar's Microwave Design: This occurs by placing a specific length of stub a specific distance away from the load.
Stub tuning is one method that satisfies both of these criteria stub tuning is simply the process of adding a length of transmission line to the existing length in either series, shunt, open circuit, or short circuit configuration to match the line to the load. This can be accomplished using a variety of different methods and components, each suited towards specific applications. This of course leads to the inevitable and age-old dilemma of the engineer where we will have to balance the best possible solution with the cheapest possible implementation. In RF engineering, it is critical to have a waveguide line matched to its load this minimizes signal loss, maximizes power handling, and ultimately will give the best performance out of any given RF circuit.
Learn the secrets to becoming a stub tuning wizard.
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