Designing a Microstrip Impedance Matching Circuit for 50Ω-j500Ω @900MHz

[VinnyCee]

I need to make an impedance matching circuit using microstrip lines.

Zin --> MATCHING CIRCUIT --> ZL

The input impedance (Zin) is 50Ω. The impedance at the load is 50 - j 500Ω. Design frequency of 900MHz.

The board I am required to use is the Taconic RF-35. It has a thickness of d = 1.524mm, dielectric constant ξr = 3.5 and loss tangent σ = 0.002.

The magnitude of S11 at the design frequency must be less than -10dB. The size of the circuit is of particular importance. How can I make the microstrip impedance matching circuit smaller?

To start, I got the normalized load impedance of 1 - j 10Ω and plotted that on a Smith chart.

Now I have to use the Smith chart to find what inductance and/or capacitance I should use to match the two ports. After I get those numbers, I could used lumped elements to do the matching, but I must use microstrip lines instead.

After finding the required matching numbers, I will use an open stub to do the matching, I think. My questions are:

1) How do I improve the bandwidth (resonant frequency of 900MHz)? Maybe 875MHz - 925MHz?
2) How do I reduce the physical size of the impedance matching circuit? <---- MOST IMPORTANT
3) How do I increase the voltage sensitivity of the impedance matching circuit?

 

[uWave_Matt]

Do you need the bandwidth to be 900MHz, or the center/resonant frequency to be 900MHz?

Typically, device dimensions are limited by wavelengths corresponding to the frequency of operation...

 

[VinnyCee]

Resonant is 900MHz. So maybe make bandwidth 875MHz to 925MHz?

I know if I do the simplest matching circuit, it will be large (about 5 to 10 cm^2) but if I do a more intricate one I can reduce that size. I'd like it to be as small as possible. What type of microstrip geometry does matching but is also space-saving?

 

[skeptic2]

Have you already figured out how to match with stubs?

I calculate the electrical length at 900 MHz to be about 4.45 cm so I don't see any problem in doing this in 5 cm^2. To reduce the size further, have you considered folding both the transmission line and the stub?

Do you have access to any microstrip design software?

 

[VinnyCee]

Yup - I can do the matching with an open shunt stub, but I want it to be even smaller!

I have Sonnet in the lab and an old copy of AWR Microwave Office 2002 at home. I can't figure out how to place a 50Ohm input impedance (Zin) at port 1.

What do you mean by "folding both the transmission line and the stub"? What is folding?

 

[skeptic2]

The obvious way of matching 50-j500 ohms to 50 ohms is to insert an inductor with a reactance of 500 ohms in series with the load. However we must use a microstrip which is a shunt matching component, not a series one. we can use a 1/4 λ transmission line to rotate the load impedance 180 deg on the Smith Chart. To really appreciate what is happening you need to look at it on an immitance chart which is just a Smith Chart with an admittance chart overlaid on it.

The normalized impedance of 1-j10 ohms get transformed to 1+j10 mhos of admittance. At the source end of the transmission line we can now add a suseptance of -j500 mhos for a match which is an open stub thta is just shorter than a 1/4 λ. Is this what you got?

One way to broaden the matched range is to put a shunt, parallel resonant element at a 50 ohm point. Since the stub is just barely less than a 1/4 λ, it may serve that purpose. You may need to try it out on Sonnet to see if it improves the matched range.

Neither the transmission line nor the stub have to be straight. You can make zig zags or change the route in order to save space. I would only be careful not to get the stub and the transmission line so close to each other that there might be mutual coupling. If you make right angled corners you need to cut the outside corner of the transmission line off with a diagonal of length about equal to the root 2 times the transmission line width. You could also reduce the area somewhat more by going to a higher dielectric substrate like alumina if that's an option.