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the rule of thumb to prevent higher order mode is that the substrate height is less than lambda/10 at the highest operating frequency (I think also that the line width should be smaller than lambda/2, but I am not sure of this)
To check this I use the port solver of CST or HFSS to determine the higher order modes and if they will be excited by your ms line feed (e.g. SMA connector)
Do you know there is a software similar to Agilent ADS LineCalc for the determination of the frequency where high order mode exist when designing the microstrip?
I think that you should consider to microstrip line's cut-off frequency. Each mode, itself has a cut-off frequency and you can calculate yourself.
To illustrate,use HFSS or another simulation tool, simulate with the number of modes that you're interested in. After finishing, creat propagation constant report, you will have what you want to see.
You should keep the line narrower than 1/2 lambda. However, for practical design, a better guideline is to make sure that it is narrower than 1/4 lambda. This means that you need to watch both your highest frequency and your lowest impedance line, since it is the widest.
I saw a similar thread here: **broken link removed**
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