6.2: Step
6.2 Step
Stepped microstrip components are often found in microstrip integrated circuits. They act as impedance transformers [e.g., in input and output matching networks of (high power) microwave transistor amplifiers], as compensating elements in microstrip power dividers, or as filter circuits comprised of lumped inductive and capacitive elements [22 25].
6.2.1 Quasi-Static Equivalent Circuit
An abrupt impedance step is established when two microstrip transmission lines with different characteristic impedances are cascaded. Figure 6.21 illustrates a symmetric structure of an impedance step. The capital letters T 1 and T 2 denote the reference planes on either side of the step. As Figure 6.22 shows, modeling of the step is usually in terms of an equivalent parallel capacitance C p and a total series inductance L s, both frequency independent. The shunted capacitance considers the stored excess charge and the electric fringing field at the front end of the partially open-ended wider microstrip transmission line of width w 1. The total series inductance accounts for current density crowding at the narrowing of the wider line to the smaller one.
Figure 6.21: Symmetric impedance step.
Figure 6.22: Equivalent circuit of the symmetric impedance step.
Figure 6.23 shows a T-type network of an impedance step. The total inductance may be split into the partial inductances L 1 and L 2 (as a first-order approximation) as follows [26]
(6.45) | |
(6.46) | |
with ( ? = 1,2) the inductance per unit length of a microstrip line of width w