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# microstrip resonator simulation question

#### yefj

##### Advanced Member level 4
Hello, a resonator which is an open circuit stripline was built as shown bellow exactly as described in the example bellow.
Smith chart and S-params and E-field are as shown bellow.
I am used to think that at resonance our S-params is supposed to very low.
Where did i go wrong?
Maybe resonance and being impedance matched is no the same thing?
Thanks.

S11 Smith chart looks as expected, |S11| magnitude plot is also plausible but useless, it simply hides resonator behaviour.

Hello FVM,Shown bellow real and imag of S11,what should i see in here that says there is resosnance?
why its acting accordingly.

Plot Z1 rather than S11 to see the resonance.

Hello FVM, Why Z11 peaks at resonance according to this expression?
Why Z11 is Zin?
Thanks.

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UPDATE: i see that at 4.866GHZ my input impedance is purely resistive.
How do i also make it perfectly matched?
I need to lower the width of the strip line?

Real impedance represents losses and to a small extent radiation. Why do you want to match it?

Hello, FVM as you can see my resonator no matter what line width my input impedance .
for L=25mm we have resonance at f=4.33GHz
i am trying to see why my input impedance is getting purley resistive at f=4.33GHz.
I have an expression as shown bellow.
What is my L and C for my open circuit microstrip.

-Parallel Resonance Circuit exhibits OPEN Circuit @ resonance as you have in your simulation charts.
-$Z_{in}=Z_{11}$ Because you have only ONE Port
-The resonance Frequency of the resonator is esentially defined by the Length, NOT much by Width ( interpret hyperbolic function in the equation )

You got a resonator that works @ Peak Frequency of $Z_{11}$. What else you wanna see ?

Hello , i have tried to simulate a halfwave microstrip by this example.
the end of the microstrip is open circuit.
the substrate height and width are tested for 50ohm as shown bellow.

but when i simulate this transmitiion line i get the impedance going around the open circuit circumference on the right side as you can see on the smith chart bellow..
how do i match this transmition line to 50 ohms?
is there a way?
thanks.

[Merged with previous same topic thread]
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How do i match it to 50 ohms?
Thanks
--- Updated ---

-Parallel Resonance Circuit exhibits OPEN Circuit @ resonance as you have in your simulation charts.
-$Z_{in}=Z_{11}$ Because you have only ONE Port
-The resonance Frequency of the resonator is esentially defined by the Length, NOT much by Width ( interpret hyperbolic function in the equation )

You got a resonator that works @ Peak Frequency of $Z_{11}$. What else you wanna see ?
How do i match it to 50 ohms?
Thanks

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Considering the wide tolerances on e_R , TDR electrical testing is a wise choice.

H=1.59mm, W = 5.4 mm Zo = 50 Er = 1.80 @ 5MHz = 1.83 @ 5GHz
18 um base Cu. using Saturn PCB

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S11 of an ideal transmission with open or shorted end is located on the unit circle, |S11|=1, corresponding to purely reactive Z11. A real microstrip line has a certain amount of losses, Z11 exposes a certain real Z11 component, respectively S11 locus is shifted towards the center.

Theoretically, Z11 of a lossy line could be matched to 50 ohms, but why would you? The question has been already asked before but wasn't yet answered.

This question has me puzzled as a 50 ohm half-wave open-ended stub will be high impedance at the source , s11. which will not produce much gain unless you have a current source. It would make more sense to define a 1/4 wave open-ended short cct resonance or a 1/2 wave shorted end stub to achieve a high Q for s11 on voltage rather than z11. However it would make sense with a 0 ohm driver with a peak on z11 .

However it would make sense as s21 with an "unloaded" output resonant gain from a low impedance source. then impedance magnitude is less important than the phase response of resonance to match the 2x delay time..

Hello,FVM i want to build a dielectric resonator which is fed by microstrip line.
So matching is important because we want out energy to be delivered to the resonator.
Why it not logical to match the micrdtrip fed resonator?
What methods are the best to match such structure?
Thanks.
S11 of an ideal transmission with open or shorted end is located on the unit circle, |S11|=1, corresponding to purely reactive Z11. A real microstrip line has a certain amount of losses, Z11 exposes a certain real Z11 component, respectively S11 locus is shifted towards the center.

Theoretically, Z11 of a lossy line could be matched to 50 ohms, but why would you? The question has been already asked before but wasn't yet answered.

A resonator does not exhibit 50 Ohm. Instead, it exhibits Open Circuit ( ideally) @ Resonance Frequency.
You can imagine that Parallel resonance Circuit @ Resonance Frequency. Therefore Impedance Curve moves on along Smith Chart Circumference and when its length arrives lambda/4 it will exibits Short Circuit/Open Circuit.
But it does never exhibit 50 Ohm.

Hello BigBoss, thank you for your reply.
My open circuit microstrip line excites a dielectric resonator.
So i think i could do matching to my open circuit transmission line.
my Zref=50 ohms line impedance is 43.5 ohms.
wave impedance 280 ohms.
So i need basicly match 5 ohms to 280?
How do i know what load i got at the end of the microstrip?
Thanks.

A resonator does not exhibit 50 Ohm. Instead, it exhibits Open Circuit ( ideally) @ Resonance Frequency.
You can imagine that Parallel resonance Circuit @ Resonance Frequency. Therefore Impedance Curve moves on along Smith Chart Circumference and when its length arrives lambda/4 it will exibits Short Circuit/Open Circuit.
But it does never exhibit 50 Ohm.

Hello BigBoss, thank you for your reply,

A resonator does not exhibit 50 Ohm. Instead, it exhibits Open Circuit ( ideally) @ Resonance Frequency.
You can imagine that Parallel resonance Circuit @ Resonance Frequency. Therefore Impedance Curve moves on along Smith Chart Circumference and when its length arrives lambda/4 it will exibits Short Circuit/Open Circuit.
But it does never exhibit 50 Ohm.
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update:
quarter wave trannsformer is no helping much.
Any idia what could help?
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UPDATE:
they get -30dB how they plane the microstrip line?

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Do you understand that you need a transfer function s21 as I showed many for 1/4 and 1/2 wave resonators using delay lines if you want to make use of one. This defines the source and the output. Here they just ask for the stub resonator unloaded. But a half-wave resonator does not make a high Q band-pass filter unless you used a current source or some high R source with the output unloaded

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So matching is important because we want out energy to be delivered to the resonator.
The purpose is still unclear.
1. Do you want the resonator to act as an antenna (radiating the power)?
2. Or act as a dielectric heater?
The microstrip line isn't well suited for either purpose.

Your 1st graph s11 shows the exact resonance when the reactive impedance is exactly on the half-wave boundary of a 100 ps delay line 5 GHz and in this configuration , it will be 0 degrees at both low frequency at the resonance. (s)

The characteristic impedance is always 50 ohms = sqrt { L/C } but resonances may occur depending on source and load impedance but the s21 response naturally changes with matching at source and load.

Here I made a s21 simulator for you to understand. to focus on the amplitude AND the phase response. Use the cursor over the plot to display the frequency and result.

You can use Z11 maximum or s11 where IM(f)=0 or the phase is 0 deg (series resonance) of lumped LC's) but to understand how to gain from resonance , you use s21.

When you are done with that, move the OUT line and attach to input of delay line.

I made a dummy 3 position switch to prevent disconnecting or moving the switch with your clicking on it to rotate as an ideal switch. The purpose was to show how mismatching the source impedance affects the response. If it messes up, just refresh the URL.

Your resonance is too low because your effective dielectric constant must be too high. This also happens in real-life from experience my watching expert PhD RF design students in a job designing band pass filters with dielectric resonators made of solid PTFE coax. But I won't say how to fix it and let you try.

Note this simulator uses ideal delay lines (lossless) with ideal resistors (no ESL, or Cp) and ideal wires ( 0 delay, 0 ESL, 0 ESR ohms)
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I asked chatGPT to improve my writing style.

The first graph, labeled s11, depicts the precise resonance when the reactive impedance coincides with the half-wave boundary of a 100 ps delay line operating at 5 GHz. In this particular configuration, the phase angle will be 0 degrees both at low frequencies and at the resonance.

The characteristic impedance is always 50 ohms, determined by the square root of the ratio of inductance (L) to capacitance (C). However, resonances may occur depending on the impedance of the source and load. The response of s21 naturally changes when there is mis-matching between the source and load impedances.

To help you understand the amplitude and phase response, I have created an s21 simulator. You can use the cursor to hover over the plot, which will display the corresponding frequency and result.

For analyzing resonance, you can use either the maximum Z11 or the s11 value at 0 degrees (which represents series resonance of lumped LC elements). However, to comprehend how to benefit from resonance, you should focus on s21.

Once you have finished with that, move the OUT line and connect it to the input of the delay line.

I have included a dummy 3-position switch to prevent accidental disconnections or movement caused by clicking. It rotates as an ideal switch would. The purpose of this switch is to demonstrate how mismatching the source impedance affects the response. If any issues occur, simply refresh the URL.

It appears that your resonance frequency is too low, possibly due to a high effective dielectric constant. This is a common occurrence in real-life scenarios, as observed when expert PhD RF design students design band pass filters using dielectric resonators made of solid PTFE coax. However, I will not provide guidance on how to rectify this issue and encourage you to try different approaches.

Please note that this simulator assumes ideal conditions, including lossless delay lines, ideal resistors (without ESL or Cp), and ideal wires with zero delay, ESL, and ESR ohms.

Also NOTE that this delay line uses air or vacuum dielectric so the length is longer. but still 50 Ohm.
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Apologies for verbose text and coarse plots, this one zooms in a bit more

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