My summaryThis page of converters and calculators section covers microstrip line impedance calculator. Yes, any dielectric above will have an effect, although not a large one since most of the field is below the microstrip. This calculator will help you calculate the guided wavelength, provided the dimensions of the microstrip are given as well as the velocity of propagation, the microstrip material's dielectric constant, and the input frequency. [z0,eff_ep] = getZ0 (txline) returns the characteristic impedance and effective epsilon without dispersion for a microstrip or coplanar waveguide (CPW) transmission line. The characteristic impedance (Z o) of a microstrip transmission line can be calculated using the active calculator or the equations at the bottom of the page. One 50 Ohm, while the next 68 Ohm. The full structure of the transmission line in microstrip_rlc. To use the calculator, place values in either the velocity of propagation field or the dielectric constant field. Large selection of online interactive calculators for RF design, including attenuators, capacitance, resonance, RF traps, and microstrip impedance. Use lineleng to calculate the phase shift of a reflection coefficient for line lengths of d=0, 1/8, 1/4, and ½ wavelengths. Differential Microstrip Impedance Calculators Giving Conflicting Answers. Need Help to calculate input and output impedance of this amplifier: Homework Help: 11: May 26, 2023: How to calculate the input current through my buck converter? General Electronics Chat: 5: Dec 20, 2018: Can You Calculate The Input Impedance? General Science, Physics & Math: 27: Dec 3, 2018: A: How to calculate. This value was. Wire Microstrip Impedance Calculator. There should be a solid ground in the layer underneath the trace. Using this formula, you can calculate the characteristic impedance of a. The microstrip antenna can also be matched to a transmission line of characteristic impedance Z0 by using a quarter-wavelength transmission line of characteristic impedance Z1 as shown in Figure 2. Matlab/Freemat file 1. As seen from the formula when D decreases, while keeping H constant, Zdiff decrease. Note that if the trace is longer than its critical length, it should be treated as a transmission line with a controlled impedance. Increasing t decreases Zo, although it has small effect on Zo. 671; thus Z 0 = 48. 2) * (1 + 0. Provide values for three of the four parameters h, t, w, Z 0 and the relative permittivity of the dielectric. The patch cutout for the feed inset should be > 2 times the microstrip width. Input Zo, and click on [ Synthesis ] button. 1. dual or asymmetric stripline microstrip calculator to find the impedance of printed circuit boards of a known dielectric constant of material, using javascript language. 37 mil), the deviation of the calculated. These two adjustments lead to: Equation DGB2: This equation is the same as, and reduces to, IPC’s Equation 5. Note that this defines the bandwidth given the operating frequency and wavelength in free space: Microstrip patch antenna bandwidth A Microstrip Patch Antenna CalculatorOverview. Track Thickness: mm. The input impedance, Zin, of the shorted microstrip line is shown in Figure 3. 5. Following equation or formula is used for Differential Microstrip Impedance Calculator. 2. The microstrip calculator determines the width and length of a microstrip line for a given characteristic impedance (Zo) and electrical length or vice versa. Enter the relative permitivity, width of the trace, the ground plane spacing, and the substrate thickness to calculate the characteristic impedance. microstrip target impedance: 50 Ω. b) The characteristic impedance of the line. There are four different types of impedance used in characterizing differential trace impedances. Nowadays, devices are more complex and delicate, so more appropriate calculations can increase the functionality of PCBs and devices. 6 ohms. Getting the Most Accurate Impedance Calculations. 5mm. 6. This is the same reason we have to consider spacing between traces in differential pairs: the two conductors interact with each other to determine the odd-mode (and differential) impedance . The trace resistance of a microstrip is important in determining how much power it dissipates. Most RF Coaxial Cables have an impedance of 50 ohms or 75 ohms. EEWeb - Electrical Engineering News and Resources. We know that ZL in this case is 50 ohms, due to the. A matching network optimizes the transfer of power from a source to a load by maximizing the power delivered to the load while meeting other performance specifications. The stepped impedance lowpass microstrip filters have a cascaded structure of alternating high- and low-impedance transmission lines. The length of the net is important for impedance matching and minimising propagation delay. dBm to Watt converter Stripline Impedance calculator Microstrip line impedance Antenna G/T Noise temp. USB traces must be 90 Ohms differential. ELECTROMAGNETIC COMPATIBILITY (EMC) CALCULATORS – Electromagnetic Compatibility Laboratory, Missouri University of Science & Technology VERY VERY VERY…EXTENSIVE. All About Circuits is the largest online electrical engineering communities in the world with over 700K engineers, who collaborate every day to. 6046 [ohm] Zodd = 47. High-quality circuit boards as prototype and series at reasonable prices. The IPC Formulas and Wadell’s Method. beammy. Following is the formula for differential impedance for a Microstrip. Include both the pcb dielectric thickness as well as the wire insulation in the height calculation. Coupled Microstrip Analysis/Synthesis Calculator. Wire Self Inductance. Coplanar wave guide with ground plane. Rho: Conductor resistivity relative to copper. This calculator requires symmetry in the trace widths and location between plane layers. dBm to Watt converter Stripline Impedance calculator Microstrip line impedance Antenna G/T Noise temp. Press Analyze to see the results. Microstrip impedance shall be calculated according to above Eq. 3. dBm to Watt converter Stripline Impedance calculator Microstrip line impedance Antenna G/T Noise temp. 4, loss tangent =. 0 Dimensional units: mm milsh is the height of the microstrip line above the ground plane. In this measurement, a voltage source is used to excite Port 1 and the received signal at. A solution to the problems of microstrip is coplanar waveguide (CPW) shown in Figure [Math Processing Error] 3. Just as a sanity check, we can quickly calculate the total inductance of a trace determined with this method and compare it with typical values. An example is shown. Input w, and click on [ Analyze ] button. Click here to see the user guide of our impedance. • Plotting 𝐸⃗ fields for magnitude and vector, in both linear and dB scale. I got the following question regarding the impedance of a grounded coplanar waveguide(gcw) and microstrip as shown in the image attached: If I increase the spacing w in the gcw to large values I am expecting getting a similar impedance results for the microstrip if the other parameters remain the same since both geometries equalise. The MWI-2017 Microwave Impedance Calculator software is able to calculate key parameters for most common microwave transmission lines, including microstrip, stripline, and coplanar-waveguide transmission lines. Microstrip patch antenna is used in mobile handset due to simple look, lower cost, small size and light in weight. 1. 5. 3 will accurately capture the dependence of Z0 on the parameters ϵr and h / W. Microstrip Impedance Calculator. For example, coupledMicrostripLine (Length. For an embedded (internal) microstrip, the formulas provided in paragraph 4. Input impedance (Ohms) Desired output impedance (Ohms) Note: This transformer cable should be electrically one quarter wavelength, or a multiple of an odd quarterwavelength. 32 and the equation shown in 5. 02 m Slotline Equation. Input Zo, and click on [ Synthesis ] button. Embedded Microstrip Impedance Calculator. Can anyone explain this discrepancy?1. Microstrip lines have three parameters that we can change to achieve 50 ohm impedance: Due to design constraints, there is only one parameter (track width,) left to achieve 50 ohm. Sorted by: 1. L-Match Topology. 1. Once you know the characteristic impedance, the differential. Based on the assessment in the Polar Instruments article, Wheeler’s method appears to be the most accurate method for calculating microstrip. For a case of dielectric constant of 4. (18) Topic 59: Input Impedance/Admittance The equation for input impedance can be defined as a function. Loop Inductance Calculator. As an important part of the electronic radio frequency device, such as microstrip antennas, 1,2 resonant antennas, 3 microstrip line is the carrier and the transmission tool of energy and information. 3): fHigher-Microstrip = c/(4h εr − 1− −−−−√) = 10. To use this calculator, enter the values for the wire diameter and substrate. This dipole antenna calculator determines the size of a simple dipole antenna for a given frequency and the dipole wire diameter. Coplanar waveguide characteristic impedance calculator. 0 (FR-4), it turns out that when W/H is 2/1, the resulting impedance will be close to 50 Ω (as in the first example, with W = 20 mils). Input w, and click on [ Analyze ] button. Additional benefits of patch antennas is that they are easily fabricated making them cost effective. Figure 5. Understanding coax can be helpful when working with it. 4. Going Forward with a Trace Impedance Calculator. Following is the list of useful converters and calculators. Impedance in Ohms. The thickness and width of the printed wire, the distance between the printed wire and the ground, and the dielectric constant of the dielectric determine the characteristic. z0_f = getZ0 (txline,freq) returns the characteristic impedance with dispersion for a transmission line at the specified frequency. Microstrip line impedance calculators are useful to some extent, but they have some of their downsides, so it is very necessary to use some up-to-date modern tools for calculations. 34. 2. Microstrip Impedance. The nice part about coax is that it can be bent and flexible unlike most pcb transmission lines. Getting the Most Accurate Impedance Calculations. A coplanar waveguide calculator will operate in one of two ways. Note that if the wire is insulated, then the results of this calculator will just be an estimate. 96s/h )If you wanna confirm how good is the tool any of the two ways can be followed: 1. Yet I got a ZDiff CPW with ground capable calculator: Differential surface coplanar waveguide with ground calculations: *0. Apparently it. icrostrip line: H. Embedded Microstrip Trace. The characteristic impedance is an important parameter determining the power handling capacity of a waveguide, both average and peak powers. In fact, striplines often make components such as band-pass filter's more accurately, with more symmetric roll-off and no lower cutoff frequency. Figure 5. The embedded microstrip impedance formula is an approximation and the results are highly sensitive to the values of the variables. The new version includes: This software is intended to assist with microwave circuit design in predicting the impedance of a circuit made with Rogers High Frequency. Microstrip Traces and Controlled Impedance. This calculator provides accurate microstrip transmission line analysis and synthesis. Instructions are below the calculator and don’t forget we can make and test your controlled impedance printed circuit boards too. Rectangle Inductance Description. 8), the ratio of W/H for fifty-ohm microstrip is about 95%. 23. INPUT DATA. A. e. The substrate parameters (ε r and h) and the. a) The effective relative permittivity of the substrate. For example, microstrip = microstripLine (Length=0. ( 0. For example on 0. 2 of the Microstrip Calculator, h=H1 and b=H2-H1. Such a microstrip is constructed with two traces referenced to the same reference plane with a dielectric material between them. The differential signals have a differential characteristic impedance. I have been fiddling around with GPS antenna trace impedance matching. So, the dielectric at my 5-6GHz frequency range is 3. This tool helps you create a matching circuit so that optimal power transfer occurs between unmatched loads. Microstrip Impedance Calculator. Description. If the ratio (L/W) is close to unity, the radiation pattern will be symmetric but may not provide a resonable input impedance. The impedance bandwidth of the antenna is 2. Instructions are below the calculator and don’t forget we can make and test your controlled impedance printed circuit board too. Asymmetric Stripline. Output ⊕. to NF RF and Wireless tutorials WLAN 802. This calculator determines the impedance of a symmetric differential stripline pair. 1 to 3. Development Kits. This transmission line calculator was. Procedure: • We know the standard characteristics impedance of microstrip line to be of 50Ω. Each Port is matched to the characteristic impedance Z 0 of the single, isolated microstrip transmission line. fsp is composed of two metal traces and a lumped RLC element 2 mm long placed in between; the metal traces and the substrate have the same properties as in the FDE simulation. 1 er 15 Note that 1. Incidentally, the trace thickness parameter does have a. First, let’s use the “analyze” approach. EasyEDA directly supports controlled impedance designs for 4 and 6 layer PCBs only. The characteristic impedance is given by: Eq. Single-stub matching is a very common method for impedance matching using microstrip lines at frequences in the UHF band (300-3000 MHz) and above. PCB Structures / Discrete Structures / Signal Management. Typical realisation technologies are printed circuit board (PCB), alumina coated with a. Z diff = 2* Z o (1 - 0. 5. November 15, 2023 Maurizio Di Paolo Emilio. 8. Use the following equation to calculate the impedance of a microstrip trace layout. There are 3 types of microstrip models to choose from- uncoated, coated, and embedded. The IPC-2141 trace Impedance calculator will help make initial design easier by allowing the user to input basic parameters and get a calculated impedance according to the IPC-2141 standard. 0; 1 < ε r < 15). Visit to learn about our other electrical engineering tools & resources. Overview. By determining its trace resistance, the contribution of a microstrip to the overall circuit resistance can be evaluated. Ideally clk, mosi and miso tracks should be the same length, kept. 0. 2 Low Impedance; The formulas developed in Section 4. microstrip = microstripLine (Name=Value) sets properties using one or more name value pair arguments. WILKINSON POWER DIVIDER CALCULATOR. The variation in impedance of microstrip with frequency is at least partly (I think mainly) due to the wave in microstrip not being TEM. This coupling is one of the features of differential traces. Microstrip Impedance Calculator Enter the Height, Width and Permittivity to get the Impedance of the Microstrip Note : The unit of the height and width entered must be the same. The Microstrip Differential Impedance Calculator simplifies the process of determining the differential impedance of a microstrip transmission line. Microstrip is a type of electrical transmission line which can be fabricated with any technology where a conductor is separated from a ground plane by a dielectric layer known as "substrate". . Inductance of microstrip lines Microstrip lines used as shunt inductors Application Note AN258, Rev. Modeling approximation can be used to design the microstrip trace. Hello. If the ratio of line width to substrate thickness is w/h = 4. Characteristic Impedance of the System (Z0) Ohms. The effective dielectric constant drives the length of the taper, this effect was not. To start, select the type of PCB conductor, fill in the geometric measurements of your circuit board, and it will automatically give you the relevant. Minimum PCB Trace width with SMD components and. Total Capacitance in pf. We invite you to voice your opinions. I would like to know how to compute the impedance at the edge of a microstrip patch in CST. These are considered to be standardized impedance values with cables readily available. 8. 7. Microstrip Patch Antenna Calculator Formula. This tool is designed to calculate the resistance of a microstrip trace with a copper conductor. 1mm FR4 in between yealds about 50 ohms. Please see Disclaimer below. The impedance of a differential via pair cannot be treated with a single via impedance calculator unless the vias are spaced far apart. VSWR, Return Loss and Reflection Coefficient. The microstrip patch antenna calculator determines the length (L) and width (W) of a rectangular microstrip patch antenna for a given resonant frequency or vice versa. to NFThe coaxial cable, along with the balanced two-wire, is the most common type of transmission line used in RF communications. to NF. Calculating the Differential impedance is a two-step process, first Calculate the single ended impedance Zo and then use this value to calculate the differential impedance. Such a stripline is constructed with two traces referenced to the same reference planes above and below the traces with a dielectric material between them. The Sierra Circuits Impedance Calculator uses the 2D numerical solution of Maxwell’s equations for PCB transmission lines. Characteristic impedance calculator for a 4-layer board. An edge couple differential microstrip transmission line is constructed with two traces referenced to the same reference plane. In microstrip, the width of the conductor and thickness of. All calculators are approximations for general purpose use only and are not to be used for high degree of accuracy purposes. Enter the values of trace width (w), trace thickness. What is a Microstrip Impedance Calculator? This is a calculator used for determining the characteristic impedance of a microstrip. The new version includes: This software is intended to assist with microwave circuit design in predicting the impedance of a circuit made with Rogers High Frequency circuit materials. 0. Note: All dimensions are in mils. Some of them include Microstrip, Stripline and Coplanar Waveguide. It actually depends upon the D/H ratio. 0, medical, smart city, and other applications that are impractical or impossible with other wired and wireless technologies, providing twice the bandwidth and three times the speed of Wi-Fi 6, deterministic network support, and more…. 71. This calculator is designed to determine the magnitude of the crosstalk on a stripline if its dimensions and source voltage is provided. Visit to learn more about our other electrical engineering tools and resources. The quarterwave impedance transformation calculator is used to match an input and an output impedance at a given frequency for maximum power transfer. The calculator allows you to make an approximate calculation of the characteristic impedance of a microstrip transmission line, provided that the line operates at a frequency below the critical one. Perhaps the most common type of transmission line is the coax. LC Impedance matching network designer Enter the input and output impedances to be matched and the centre frequency. An example of a wire microstrip might most often be found in prototypes or reworked boards where a wire is used over the top of pcb or copper clad material. The plots show the magnitude and phase of the input impedance. 2. Embedded Microstrip Impedance Calculator. Where a Microstrip Line Calculator Fails. I can't quite get it when microstrip starts to behave more like a coplanar waveguide. 0; 1 < ε r < 15 ) Select the units for all dimensions: mm mils. The result of a Schwarz-Christoffel mapping is used to find the radial gap capacitor. To use the calculator, place values in either the velocity of propagation field or the dielectric constant field. The phase is mostly + 90 ∘ or − 90 ∘, indicating that Zin is mostly reactive. Don’t forget to check out our other. This online microstrip impedance calculator calculates the characteristic impedance of the microstrip (Ω), W/H ratio, and effective dielectric constant (εe) by entering the value of dielectric material relative. *The structure may propagate in 3 modes: coplanar waveguide, coupled slot lines and microstrip. 0; 1 < εr < 15 ) Select the units for all dimensions: mm mils. The Calculator has the following tools: Regulators. 6. eu. Be aware that there are many microstrip impedance calculators on the Internet that give sometimes widely varying results. 1 (a). A certain microstrip line has fused quartz (ϵr = 3. In both cases, you’ll need to enter your stackup information into the calculator to get accurate results. trace is typically quoted as being 5 to. In both cases, you’ll need to enter your stackup information into the calculator to get accurate results. The impedance of microstrip is inversely proportional to the thickness of the signal track, but the difference for 0. This calculator is designed to compute the maximum allowable current that can flow through a stripline. There are many demands placed on PCB stackup design. *PCB vendors can use controlled impedances and will vary any designated trace width at mask level to hit impedance targets. Method: Designing an impedance matching network is a central. The substrate parameters (ε r and h) are required. Tuning for your traces to the desired impedance value occurs by adjusting trace width and distance from the reference plane. There are a lot of online trace impedance calculators specifically designed for differential traces. Electronics and Electrical Engineering Tools. could someone point me towards reliable and proven method to calculate impedances for edge coupled differential microstrip?From here, we can see that there are specific stack-ups where a CPW and a microstrip/stripline will have 50 Ohm impedance and the same trace width, even though the ground clearance is quite close clearance to the trace in the CPW. Most RF Coaxial Cables have an impedance of 50 ohms or 75 ohms. The source for formulas used in this calculator (except where otherwise noted) is the Design Guide for Electronic Packaging Utilizing High-Speed Techniques (4th Working Draft, IPC-2251, February 2001. Microstrip Characteristic Impedance Calculator Using a Formula by Brian C. It shows the minimum trace-to-ground spacing required to. Where: Z 0 is the characteristic impedance of the microstrip; ε r is the relative permittivity (dielectric constant) of the substrate material; h is the height of the microstrip above the ground plane; W is the width of the microstrip trace; By knowing the values of the dielectric constant, height, and width, you can use this formula to calculate the characteristic. A great example is the surface microstrip which forms on the outer layers of the PCB. Not all calculators will explicitly state this. 98 * 1 / 2) / sqrt(4. The impedance Z 0 of a transmission line consisting of a circular signal conductor having a diameter d and centered between parallel ground planes separated by a distance h is given by: Eq. The PCB Impedance Calculator in Altium Designer. The edge couple differential symmetric stripline transmission line is a common technique for routing differential traces. The microstrip a. This technique doesn’t work for wide band requirements, but is a simple way to achieve this at a specific. Push the CALCULATE button. Microstrip Trace Impedance Calculator;. 6 Ω and ε e = 6. I have only Saturn PCB SW to make some calculations. 60. Based. 9, h = 0. Just enter the given values for trace thickness, substrate heights, trace width and subtrate dielectric in the calculator above and press the "calculate. 3: Normalized characteristic impedance and normalized effective permittivity of a microstrip line as a function of u = w / h. 2 Effective Permittivity and Characteristic Impedance; 4. Following is the list of useful converters and calculators. (1) When the characteristic impedance (Zo) of the line width (w) is calculated. These tools seamlessly integrate with the rest of your design tools in a. Antenna Tutorial Antenna Gain vs Effective Area Types of antenna TV Antenna TV Antenna Booster Satellite Dish Antenna Mobile Antenna Antenna Installation Antenna Suppliers. Note that the "h", for dielectric thickness in this formula is omitted in some other Polar publications. com Microstrip Impedance Calculator. For example, going from 10 mil to 20 mil alumina, or two-mil to four-mil GaAs. 19. This can be achieved by regulating the inner and outer diameter of the coaxial cable, along with the. 8. Just enter the given values for trace thickness. 352278 [-] coupling =-9. Following equation or formula is used for Microstrip Mitred Bend Calculator. including microstrip and stripline designs. 29 mm width traces to obtain 100 Ohms ZDiff while using 0. To use this calculator, enter the values for the wire diameter and substrate dielectric and press the "calculate" button. Figure 2. Using online calculators, I figured out the width of the PCB trace to create an impedance of 50 Ohms is 2. Hallmark Circuits, Inc. The input impedance depends upon the. An embedded microstrip can be constructed using a microstrip with a solder mask. EEWeb offers a free online microstrip crosstalk calculator. Figure 5. It is a useful tool in the design and analysis of microwave circuits, particularly in the fields of communication, radar, and satellite systems. Correct track impedance is the first point usually made in various online sources I've found on the subject, so I tried to get the microstrip impedance calculator to get as close the desired 100 Ohm. 04 in the ε eff. This tool is valuable for engineers, hobbyists, and anyone working with microstrip. This calculator is designed to calculate the characteristic impedance of an embedded microstrip - a flat conductor suspended over a ground plane with a dielectric between it and another dielectric material above the. Rectangle Loop Inductance Calculator. In the next page we will see what factor effect the differential impedance and how to calculate it. Our RF and microwave calculators and converters will provide the figures you need for your radio frequency engineering needs. The quality of an impedance match can be expressed mathematically by the reflection coefficient (Γ). This calculator helps you calculate the characteristic impedance of a coaxial cable given its dimensions. 0 mm and L (line length) to 100 mm and click on the Analyze button. The characteristic impedance of “narrow” ( W ≪ h) microstrip line can be roughly approximated by Equation 7. 37 mil, H = 30 mil and T = 1. The edge couple differential symmetric stripline transmission line is a common technique for routing differential traces. Stripline vs. Microstrip Length (L) in inches. Radar Calculators. New Online Microwave Impedance Calculator. Visit to learn more about the EEWeb communit. To use this calculator, simply input your microstrip geometry and Dk value, and the tool will return the differential impedance value for a pair of microstrip traces. Visit to learn more about our other electrical engineering tools. This allows you to double check the calculator and make sure that it selected appropriate values, by making sure the impedance correctly matches the input impedance. 39 for the effective dielectric constant. Thickness: Thickness of the microstrip conductor. 6 Band Resistor. Index Terms-Microstrip patch antenna, MATLAB calculator, CST, 2. 4. 1 er. 6 mils line width, and the effective dielectric constant is 6. The calculator then uses a formula to calculate the width and spacing of the trace or transmission line required to achieve the desired characteristic impedance. The default units for all given values, except the subtrate. 37mm for a 50 ohm. As with other microstrip devices, the conductor and the ground plane are separated by a dielectric. [1] This paper constructs a simple formula of distribute conductance of a microstrip line and then of the dielectric attenuation with only one arbitrary constant, p = 1. Reference: R. Edge-Coupled Traces. 635 mm, W = 0. This Mantaro calculator tells me. Noise Conversion Calculator. That means on ten mil (254 micron) alumina, the width for fifty ohm microstrip will be about 9. Modeling approximation can be used to understand the impedance of. INPUT DATA. Line Thickness (T) in mils. Broadside Trace Inductance Calculator. ZigBee. Calculates with the characteristic impedance of the system and ratio of the power at the output to get the impedance of the various transmission lines that make up the Wilkinson Power Divider. To avoid microstrip modes, have h >> (w+2g) and extend component side ground away from the trace by > (w+2g). The differential impedance will be a bit less than 2x the single-ended impedance. since a number of factors can affect impedance. dBm to Watt converter. Coil Inductance Calculator. The amplitude of this crosstalk is what this tool calculates. Assuming that there is no loss in the transmission process, the characteristic impedance of the antenna can be expressed by the distributed capacitance C per unit length and the phase velocity Vp:Overview. The Smith Chart graphically maps S11=reflection coefficient= (ZL-Z0)/ (ZL+Z0) to Load Impedance (ZL), normalized to Z0 (source impedance = center of chart). Description. Table 1 shows some free impedance calculators on the internet. 4. -> Go to some fabricator's websites like sierra circuit where they have their own calculator which they share online (After registration) and compare the results. 1< W/H < 3. They are useful at design time and for training purposes, both of which stimulated. Coplanar Waveguide Calculator. One of the features of this type of microstrip is the coupling between lines. Symmetric Stripline Impedance Calculators and Formulas; To really see how the trace widths for these transmission lines compare, we need to plot the characteristic impedance vs. 6 ohms and Z even = 110 ohms for your geometry, very close to your result.