IMPEDANCE MATCHING & SMITH CHART

Impedance Matching of RF Transmission Lines : Basic requirements needed for a better transmission line High transmission efficiency Very small VSWR Can able to operate over a range of frequencies. All the above will be affected due to mismatch problems.

Effects of Mismatch : Power loss in feeder line. Transmission line may damage. Frequency stability problem in generator. Signal get reduced due to reduction of signal-to-noise ratio. In order to avoid the problems we need a Matching Network. Different types of impedance matching : Reflection less match Conjugate match Zo match

Reflection less match Conjugate match Zo match

Types of Matching Network : Impedance matching using L or C of a transmission line. Impedance matching using L- C of a transmission line. Impedance matching using quarter wave transformer. Impedance matching using half wave lines. Impedance matching using short circuit stubs. Stub Matching : [ Tuning Stubs] For high microwave frequencies, a section of a transmission line can be used as matching network at suitable distances. It can be connected in two ways (OC & SC) 1. Series (series reactance) 2. Parallel (Shunt reactance )

Types of Stubs : Single Stub Double stub Triple stub

Figure Reflection and transmission at the junction of two transmission lines with different characteristic impedances.

Figure (a) Voltage, (b) current, and Short-circuited line Figure (a) Voltage, (b) current, and (c) impedance (Rin = 0 or ) variation along a short-circuited transmission line.

Open-circuited line Figure (a) Voltage, (b) current, and (c) impedance (Rin = 0 or ) variation along an open-circuited transmission line.

Figure Voltage standing wave patterns (a) Standing wave for short-circuit load. (b) Standing wave for unknown load.

The Slotted Line A transmission line allowing the sampling of E field amplitude of a standing wave on a terminated line. With this device the SWR and the distance of the first voltage minimum from the load can be measured, from this data ZL can be determined. ZL is complex  2 distinct quantities must be measured. Replaced by vector network analyzer. Assume for a certain terminated line, we have measured the SWR on the line and lmin , the distance from the load to the first voltage minimum on the line.

An X-band waveguide slotted line.

Impedances, voltages, currents, etc. all repeat every half wavelength Smith Chart Impedances, voltages, currents, etc. all repeat every half wavelength The magnitude of the reflection coefficient, the standing wave ratio (SWR) do not change, so they characterize the voltage & current patterns on the line If the load impedance is normalized by the characteristic impedance of the line, the voltages, currents, impedances, etc. all still have the same properties, but the results can be generalized to any line with the same normalized impedances The Smith Chart is a clever tool for analyzing transmission lines The outside of the chart shows location on the line in wavelengths The combination of intersecting circles inside the chart allow us to locate the normalized impedance and then to find the impedance anywhere on the line

Smith Chart – Real Circles

Smith Chart – Imaginary Circles x=1/3 x=1 x=2.5 x=-1/3 x=-1 x=-2.5 Smith Chart – Imaginary Circles

Smith Chart