QWMatch (Quarter-Wave Match)

Symbol

Parameters

Name	Description	Unit	Default
Subst	Microstrip substrate name	None	MSub1
F	Center frequency	GHz	1
DeltaF	Total frequency bandwidth	GHz	0.5
Zo	Desired input impedance	Ohm	50
Rload	Load impedance to match	Ohm	100
ResponseType	Type of frequency response	None	Uniform
N	Number of quarter-wave sections; set N=0 to compute N	None	0
Rmax	Maximum voltage reflection coefficient	None	0.1
Delta	Length added to transformer sections for tuning performance	mil	0

Notes

1. A quarter-wave matching network matches a real load impedance (Rload) to a desired real input impedance (Zo) using multiple quarter wavelength sections. A specified frequency response can be realized by proper design of the individual sections.
2. DeltaF is defined as the total bandwidth centered at the design center frequency.
3. If the number of sections N is set to zero, the Design Assistant chooses N such that the reflection coefficient is less that Rmax over the bandwidth DeltaF. The resulting bandwidth may be broader than that specified. Otherwise, Rmax and DeltaF are ignored.
4. The ResponseType specifies the distribution of the partial reflection coefficients seen at each section interface - Uniform, Binomial, and Chebyshev distributions are available. These in turn specify the shape of the reflection coefficient versus frequency.
5. A single-section quarter-wave matching transformer can be designed by setting N = 1.
6. Since the reflection coefficient may not be at its minimum value at the design center frequency, the optimization centers the variation of S11 (referenced to the value of Zo) versus frequency at the center frequency by changing the length of each quarter-wave section. All sections are tuned by the same length during the optimization.
7. A SmartComponent subnetwork is empty until the Design Assistant is used to generate the design. Refer to Design Assistant.

For a more detailed discussion of this device, see: D. M. Pozar, Microwave Engineering, 2nd Edition, John Wiley & Sons: New York, 1998, pp. 275-288; R. S. Elliott, An Introduction to Guided Waves and Microwave Circuits, Prentice Hall, John Wiley, New Jersey, 1993, pp. 218-224.

Example

A quarter-wave matching network was designed to match a load impedance of 100 Ohms to a 50 Ohm line at a center frequency of 4 GHz. Specifying a Chebyshev frequency response for which the reflection coefficient remains below 0.1 over a 3 GHz bandwidth dictates 3 quarter-wave sections. Tuning using the Optimization Assistant yielded a value of Delta =-2.284 mil.