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/* Physical Transmission Lines */
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== Understanding RF Circuit Analysis as an Analog Simulation ==
You can use [[RF.Spice A/D]] to simulate or design distributed analog and mixed-mode circuits at high frequencies. RF circuit analysis, by nature, is an AC analysis that you typically run at high frequencies ranging from tens of Megahertz to tens of Gigahertz. At such high frequencies, the dimensions of your circuit may become comparable in order of magnitude to the wavelength, when wave retardation effects start to appear. In other words, your circuit starts to act like a distributed structure rather than a lumped circuit where signals propagate instantaneously. In the analysis of a low frequency circuit, two nodes that are connected to each other through a wire are assumed to have equal potentials or identical voltages. In RF circuits, however, parts and devices are connected to one another using transmission line segments, which introduce additional phase shifts depending on their electrical lengths and may also alter the voltages and currents at different points of the circuit due to impedance mismatch.
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[[File:RFSpice_Screen.png|thumb|left|720px|RF simulation in RF.Spice A/D.]]
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[[RF.Spice A/D]] uses the same Berkeley SPICE and XSPICE simulation engines of its forerunner B2.Spice A/D. In other words, the high frequency AC analysis is carried out by the same analog and mixed-mode SPICE simulation engines based on nodal admittance analysis, which have been enhanced with additional RF simulation capabilities. As a result, you can mix the RF devices in your circuits with all the other analog and mixed-mode devices. You can also mix transmission-line-type RF devices with digital parts and perform mixed-mode time domain simulations.
The concepts of [[Transmission Lines|transmission lines]] and [[Multiport Networks|multiport networks]] are integral to any RF simulation. From a simulation point of view, an RF circuit is made up of a collection of [[Multiport Networks|multiport networks]] that are interconnected via [[Transmission Lines|transmission lines]] segments or components. If the input of your circuit is connected to a source and its output is connected to a load, then you can compute all the voltages and currents at all various circuit nodes, some of which may serve as external or internal ports of your circuit. Or you can calculate the port characteristics of the overall network by designating input and output ports to your RF circuit.
All the RF devices of [[RF.Spice A/D]] can be divided into two groups: devices based on transmission line models, and devices based on multiple networks. RF.Spice's transmission line models are enhanced versions of SPICE's standard LTRA model. The transmission-line-based devices typically utilize a combination of LTRA and passive RLC models. [[Multiport Networks|Multiport networks]] are characterized and modeled based on their frequency-domain scattering (S) parameters. The S-parameters are tabulated as a function of frequency, and their values are interpolated in between the frequency samples. [[RF.Spice A/D]] performs an AC analysis of these RF devices by converting their S-parameters to Y-parameters and using them in conjunction with SPICE’s nodal admittance matrix formalism. The S-parameter-based RF devices of [[RF.Spice A/D]] are primarily intended for use in two types of [[tests]]:
* AC Frequency Sweep Test
* Network Analysis Test
[[Image:Tutorial_icon.png|40px]] '''[[RF.Spice_A/D#RF_Tutorial_Lessons| RF.Spice A/D RF Tutorial Lessons Gateway]]'''
{{Note | S-parameter-based RF devices do not work with “Live Simulation” or Transient Test as their models typically contain S-parameters at high frequencies only.}}
The RF circuit analysis performed by [[RF.Spice A/D]] is based on the assumption that your distributed RF circuit can be modeled as an interconnected network of multiport devices and transmission line segments and components. This means that all the coupling or crosstalk effects must have been captured by the S-parameter-based models of devices or by the transmission line and discontinuity models used by [[RF.Spice A/D]]. Most of these models work satisfactorily at lower frequencies up to several Gigahertz. At these frequencies, a quasi-static regime may be able to represent the physics of your RF circuit to a good level of accuracy. In the quasi-static regime, the different parts of your circuits can be treated as multiport devices or components that are governed by the Kirchhoff circuit laws.
As the frequency increases, more complex wave radiation and propagation effects start to appear and affect the performance of your circuit. At much higher frequencies and in the millimeter wave region of the spectrum, the coupling between adjacent [[Transmission Lines|transmission lines]] may no longer be neglected. In such cases, a full-wave electromagnetic analysis of portions of the circuit might become inevitable. This might be especially true for junction areas and vertical interconnects that join transmission line traces on two sides of a board and across different substrate layers. For accurate analysis of structures of this type you need a full-wave electromagnetic (EM) modeling tool. [[EM.Cube]] is a modular suite of EM simulation tools for this very purpose. Among its computational modules are time domain full-wave simulators like [[EM.Tempo]] based on the Finite Different Time Domain (FDTD) method as well as frequency domain full-wave simulators like [[EM.Picasso]] and [[EM.Libera]] based on different variations of the Method of Moments (MoM).
{{Note | You can analyze a complex passive multiport device in [[EM.Cube]] and import its simulated S-parameter data into [[RF.Spice A/D]] as a new custom device in your parts database.}}
== Multiport Networks ==
A multiport network is a frequency-domain “black-box” block that is modeled by its S-[[parameters]] as a function of frequency. [[RF.SpiceA/D]] currently offers the following models:
* Complex Impedance (a two-pin device)
Each pair of pins form a port of the device. In other words, an N-port device has 2N pins or terminals. In most cases, the negative pin of a port is grounded, while its positive pin is connected to the other parts of your circuit. It is very important that all the pins of a multiport device are properly connected to ensure a successful simulation.
An N-port device is characterized by a complex-valued NxN scattering (S) matrix. A one-port has only one S-parameter, i.e. s11. A two-port has four S-[[parameters]]: s11, s21, s12 and s22. A Complex Impedance is a special type of one-port that is defined by its complex-valued z11 parameter rather than by s11. [[Multiport Networks|Multiport networks]] can be connected to one another through their ports. For example, you can cascade two two-ports as shown in the opposite figure. Note how the negative pins of the two devices have been grounded.
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[[File:twoport1.png|thumb|400pxleft|480px| Cascading two two-port network devices.]]
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{{Note | Multipart Network devices do not work with “Live Simulation” or Transient Test as their models normally contain S-[[parameters]] at high frequencies only.}}
=== Defining S-Parameters ===
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[[File:twoport2.png|thumb|400pxleft|550px| The property dialog of a multiport network device.]]
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Among RF.Spice's multiport network device, the one-port, two-port, three-port and four-port are all defined based on their S-parameters. All multiport network devices have a "Port Reference Impedance" parameter. The default value of the reference impedance is 50 Ohms for the one-port, two-port, three-port and four-port. For most RF circuits, you do not have to touch the 50Ω default value.
Besides entering the S-parameter values manually using in the parameter table, you can directly import these values from a text file with a ".TXT" file extension. For this purpose, click the button labeled "Load from File..." in the property dialog. This opens up the standard [[Windows]] Open dialog, with the file type set to text files. Browse your folders and select the text file to load the data from. The S-parameters you import to [[RF.Spice A/D]] can come from manufacturer data sheets or they can be generated by electromagnetic simulation suites such as [[EM.Cube]]. For example, among [[EM.Cube]]'s computational modules, the FDTD, Planar MoM, Wire MoM and Surface MoM simulation engines all generate S-parameter text files for structures with port definitions. These files can directly be loaded into [[RF.Spice A/D]].
===The Complex Impedance Device ===
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[[File:twoport3.png|thumb|400pxleft|550px| The property dialog of the Complex Impedance device.]]
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== List of Standard Imported RF Devices ==
{| class="wikitable"
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! Device Type !! Symbol Name !! Model Type !! Schematic Symbol
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| RF Capacitor || capacitor || one-port || [[File:G6a.png]]
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| RF Inductor || inductor || one-port || [[File:G7a.png]]
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| RF Diode || diode || one-port || [[File:G9.png]]
|-
| RF BJT || bjt_npn_2port <br /> bjt_pnp_2port || two-port || [[File:G11A.png]]
|-
| RF JFET || jfet_n <br /> jfet_p || two-port || [[File:G12.png]]
|-
| RF MOSFET || mosfet_n <br /> mosfet_p || two-port || [[File:G13a.png]]
|-
| RF MESFET || mesfet_n <br /> mesfet_p || two-port || [[File:G14.png]]
|-
| One-Port|| one-port || one-port || [[File:G60.png]]
|-
| Two-Port|| two-port || two-port || [[File:G61.png]]
|-
| Three-Port|| three-port || three-port || [[File:G62.png]]
|-
| Four-Port|| four-port || four-port || [[File:G63.png]]
|-
| Open End || open_end || one-port || [[File:G64.png]]
|-
| Bend || bend_junction || two-port || [[File:G65.png]]
|-
| Step Junction || step_junction || two-port || [[File:G66.png]]
|-
| Tee Junction || tee_junction || three-port || [[File:G67.png]]
|-
| Cross Junction || cross_junction || four-port || [[File:G68.png]]
|-
|}
== Generic Transmission Lines ==
The standard SPICE provides two types of general-purpose transmission line models: lossless (TRA) and lossy (LTRA). These models are primarily intended for transient analysis. The lossless transmission line model is characterized by either its delay in seconds or by its normalized length at a given frequency. On the other hand, the lossy transmission line model is characterized by distributed RLCG [[parameters]]: resistance per unit length (R), inductance per unit length (L), capacitance per unit length (C), and conductance per unit length (G). Both [[B2.Spice A/D]] and [[RF.SpiceA/D]] offer the native SPICE transmission line models TRA and LTRA as passive devices.
However, [[RF.SpiceA/D]] also offers a number of other transmission line models specifically intended for use in RF circuit analysis. These include the generic T-Line, the generic coupled T-lines, and a variety of physical transmission line models.
=== The Generic T-Line ===
* Z0: Characteristic Impedance in Ohms
The default parameters of the Generic T-Line are Z0 = 50 Ohms, eeff = 1, alpha = 0, and len = 10mm. A unit effective permittivity implies a TEM transmission line because √ε<sub>eff</sub> = β / k<sub>0</sub>, where β is the propagation constant of the transmission line and k<sub>0</sub> = 2πf/c is the free space propagation constant, with f being the frequency in Hertz and c = 3e8 m/s being the speed of light. A zero attenuation constant represents a lossless transmission line. The Generic T-Line device is indeed a two-port network with a 2×2 scattering matrix or four S-parameters: s11, s21, s12 and s22. Obviously, this is a reciprocal and symmetric network, i.e., s11 = s22, and s21 = s12.
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[[File:tline.png|thumb|left|360px| The schematic symbol of the Generic T-Line device.]]
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Note that N-port networks in [[RF.Spice A/D]] have schematic symbols with 2N pins. Each pair of pins represents a port. In a similar way, the generic T-line has two ports and four pins. The pins are marked with plus and minus signs. For example, in the figure above, the pins P1+ and P1- together form Port 1. Normally, the negative pins are grounded, and the positive pins are connected to the other parts of the circuit.
=== Open and Short Stubs ===
The Generic Open Stub and Generic Short Stub are two one-port devices based on the Generic T-Line device. They represent terminated generic transmission line segments. In the open stub case, the termination load is Z<sub>L</sub> → ∞, and in the short stub case, the termination load is Z<sub>L</sub> = 0. The [[parameters]] of both open and short stub devices are the same as those of the generic T-line device.
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[[File:tline2.png|thumb|400pxleft|480px| The schematic symbols of the Generic Open Stub (left) and Generic Short Stub (right) devices.]]
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=== Generic T-Line Discontinuities ===
In real practical RF circuits, you often need to transition from one transmission line to another or connect two or more [[Transmission Lines|transmission lines]] together. These transitions can be modeled as [[Multiport Networks|multiport networks]]. [[RF.SpiceA/D]] currently offers five generic T-Line discontinuity devices as follows:
* Generic Open End (a one-port)
* Generic Cross Junction (a four-port)
The schematic symbols of these devices are shown in the opposite figure. Similar to other RF devices or [[Multiport Networks|multiport networks]], the negative pins of the ports must always be grounded. Unlike the T-line device described earlier which have models based on or derived from the standard SPICE LTRA, the generic T-line discontinuities have S-parameter-based models.
When you first place these discontinuity parts on your circuit, they have default S-parameter values. The default values have been chosen to be very general and may not necessarily represent the physics of your specific circuit. You must enter your own S-parameter values over the desired frequency range and replace the default values. These data can easily be generated in and imported from an electromagnetic simulation suite like [[EM.Cube]]. Unlike physical [[Transmission Lines|transmission lines]] like microstrip or coaxial line (to be discussed later) that have particular geometries and physical structures, the Generic T-Line device and Generic T-Line Discontinuities are very general by definition and do not have physical, material or dimensional [[parameters]]. You can model and simulate very complicated transmission line structures as well as open end, bend, step, tee or cross junctions based on those structures using [[EM.Cube]] and then import their S-parameter data into the corresponding discontinuity parts.
For more information about generic transmission line discontinuity devices, please refer to [[Glossary_of_Generic_RF_Devices | Glossary of Generic RF Devices]].
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[[File:tline4.png|thumb|480pxleft|720px| The schematic symbols of the Generic T-Line Discontinuity devices: (a) Open End, (b) Bend, (c) Step Junction, (d) Tee Junction and (e) Cross Junction.]]
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=== The Variety of Physical Transmission Line Types ===
In addition to the Generic T-Line, [[RF.Spice A/D]] also offers a large number of physical [[Transmission Lines|transmission lines]] as follows:
* Microstrip Line
The physical transmission line types are characterized by their physical dimensions and material properties.
=== Physical Line Calculators and Designers ===
When you place a generic T-line part in your circuit, you have to specify its characteristic impedance (Z0), effective permittivity (eeff) and attenuation constant (alpha). In the case of physical transmission line parts like mircostrip, coaxial line or CPW, you specify the physical parameters of the line such as various dimensions and material properties. [[RF.Spice A/D]] then automatically calculates the necessary transmission line parameters at the time of simulation based on your physical data.
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[[File:tline6.png|thumb|left|480px| Microstrip Line Calculator.]]
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For every physical transmission line type listed above, the '''Device Manager''' of [[RF.Spice A/D]] provides a corresponding '''Line Calculator'''. The line calculators are accessible form the '''Tools Menu''' of the Device Manager. The line calculators take the substrate properties and the physical dimensions of a line types and calculate its characteristic impedance (Z0) and effective permittivity (eeff). The Line Calculator dialog also has an "Operational Frequency" input with a default frequency of 1GHz, which is used to calculate the guide wavelength of the transmission line at that frequency. In many practical applications, you need quarter-wavelength line segments. In that case, you must first calculate the guide wavelength of the transmission line as defined by λ<sub>g</sub> = λ<sub>0</sub> / √ε<sub>eff</sub>, where λ<sub>0</sub> = c/f is the free space wavelength at the operational frequency.
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[[File:tline10.png|thumb|350pxleft|480px| CPW Line Calculator.]]
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[[File:tline12.png|thumb|350pxlrft|480px| Coaxial Line Calculator.]]
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You often need to design a 50Ω transmission line of a certain type. [[RF.Spice A/D]] provides ten physical transmission line design tools for:
* Twin-Lead Line
* Twisted-Pair Line
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[[File:tline7.png|thumb|left|480px| Microstrip Line Designer.]]
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The above line designers ignore the conductor and dielectric losses and calculate the physical dimensions of the line for a given value of the characteristic impedance Z0. For example, given a substrate with thickness h and relative permittivity ε<sub>r</sub>, the "Microstrip Designer" calculates the microstrip width in mm for a given value of Z0 (50 Ohms by default). Some line type like CPW and coaxial line have more than one dimensional parameter that can be varied. For example, CPW has slot width (w) and center strip width (s), while coaxial line has inner and outer conductor radii. In such cases, the line designer dialog provides radio button options to fix one parameter and vary the other.
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[[File:tline11.png|thumb|350pxleft|480px| CPW Line Designer.]]
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[[File:tline13.png|thumb|350pxleft|480px| Coaxial Line Designer.]]
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=== Physical Transmission Line Discontinuities ===
Besides the Generic T-Line Discontinuity devices described earlier, [[RF.Spice A/D]] also offers a large number of physical transmission line discontinuity devices based on some of the transmission line types listed above. Among these, the microstrip components are more widely used and have more variety. Unlike the generic T-line components which require that you supply the S-parameter data, the physical components are parameterized based on their geometrical and material properties. As a result, you simply enter the physical dimensions and other [[parameters]] and their S-[[parameters]] are automatically calculated by [[RF.Spice A/D]] during the circuit simulation. In other words, the property dialog of these components contains their physical [[parameters]] only and does not show the values of their S-[[parameters]] as a function of frequency.
[[Image:Info_icon.png|40px]] For more information about physical transmission line discontinuity devices, please refer to '''[[Glossary_of_Physical_Transmission_Lines_and_Components|Glossary of Physical Transmission Lines and Components]]'''.
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[[File:tline5.png|thumb|480pxleft|720px| The schematic symbols of the some Physical Transmission Line Discontinuity devices. (Top Row) microstrip components: right-angled bend, mitered bend, tee and cross junctions, (Bottom Row) CPW components: open end, short end, gap and step junction.]]
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== List of Physical Transmission Line Types ==
{| class="wikitable"
|-
! Line Type !! Model Name !! Parameters !! Image !! Schematic Symbol
|-
| Microstrip Line || microstrip-line || len: line segment length in mm <br /> w: microstrip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity <br /> sigma: microstrip conductivity in S/m <br /> tand: substrate dielectric loss tangent <br /> t: metallization thickness in mm || [[File:microstrip.png]] || [[File:microstrip1.png|120px]]
|-
| Coupled Microstrips || coupled-microstrips || len: line segment length in mm <br /> w: strip width in mm <br /> s: microstrip spacing in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity || [[File:coupled_microstrips.png]] || [[File:coupled_microstrips1.png|120px]]
|-
| Covered Microstrip Line || microstrip-covered || len: line segment length in mm <br /> w: microstrip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity <br /> hc: cover height in mm || [[File:microstrip_cover.png]] || [[File:CoveredMS1.png|120px]]
|-
| Suspended Microstrip Line || microstrip-suspended || len: line segment length in mm <br /> w: microstrip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity <br /> b: height of substrate above ground in mm || [[File:SUSPMS.png]] || [[File:SuspMS1.png|120px]]
|-
| Inverted Microstrip Line || microstrip-inverted || len: line segment length in mm <br /> w: microstrip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity <br /> b: microstrip height above ground in mm || [[File:INVMS.png]] || [[File:InvMS1.png|120px]]
|-
| Coplanar Strips (CPS) Line || cps-line || len: line segment length in mm <br /> w: strip width in mm <br /> s: strip spacing in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity || [[File:CPS.png]] || [[File:CPS1.png|120px]]
|-
| Stripline || stripline || len: line segment length in mm <br /> w: strip width in mm <br /> b: parallel plate spacing in mm <br /> er: substrate relative permittivity <br /> sigma: strip conductivity in S/m <br /> tand: substrate dielectric loss tangent <br /> t: strip thickness in mm || [[File:stripline.png]] || [[File:stripline1.png|120px]]
|-
| Coupled Striplines || coupled-striplines || len: line segment length in mm <br /> w: strip width in mm <br /> s: strip spacing in mm <br /> b: parallel plate spacing in mm <br /> er: substrate relative permittivity || [[File:coupled_striplines.png]] || [[File:coupled_striplines1.png|120px]]
|-
| Off-Center Stripline || coupled-striplines || len: line segment length in mm <br /> w: strip width in mm <br /> s: offset from centerline in mm <br /> t: strip thickness in mm <br /> b: parallel plate spacing in mm <br /> er: substrate relative permittivity || [[File:OffCenter.png]] || [[File:OffStrp1.png|120px]]
|-
| Coplanar Waveguide Line || cpw-line || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity || [[File:cpw.png]] || [[File:cpw1.png|120px]]
|-
| Conductor-Backed CPW Line || cbcpw-line || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity || [[File:cbcpw.png]] || [[File:cbcpw1.png|120px]]
|-
| Covered CPW Line || cpw-covered || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> h: substrate thickness in mm <br /> hc: cover height in mm <br /> er: substrate relative permittivity || [[File:cpw_cover.png]] || [[File:CovCPW1.png|120px]]
|-
| Covered Conductor-Backed CPW Line || cbcpw-covered || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> h: substrate thickness in mm <br /> hc: cover height in mm <br /> er: substrate relative permittivity || [[File:cbcpw_cover.png]] || [[File:CovCBCPW1.png|120px]]
|-
| Finite-Ground CPW Line || fgcpw-line || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> g: ground strip width <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity || [[File:fgcpw.png]] || [[File:fgcpw1.png|120px]]
|-
| CPW Line with a Superstrate || cpw-super || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> g: ground strip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity <br /> hs: superstrate height in mm <br /> ers: superstrate relative permittivity || [[File:SuperCPW.png]] || [[File:SuperCPW1.png|120px]]
|-
| Double-Layer CPW Line || cpw-doublelayer || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> h1: lower substrate layer thickness in mm <br /> er1: lower substrate layer relative permittivity <br /> h2: upper substrate layer thickness in mm <br /> er2: upper substrate layer relative permittivity || [[File:DoubleCPW.png]] || [[File:DoubleCPW1.png|120px]]
|-
| Coaxial Line || coaxial-line || len: line segment length in mm <br /> r_in: inner conductor radius in mm <br /> r_out: outer conductor radius in mm <br /> er: dielectric core relative permittivity <br /> sigma: metal conductivity in S/m <br /> tand: dielectric core loss tangent || [[File:coax.png]] || [[File:coax1.png|120px]]
|-
| Twin-Lead Line || twin-lead || len: line segment length in mm <br /> r: wire radius in mm <br /> s: wire spacing in mm <br /> er: dielectric medium relative permittivity <br /> sigma: wire conductivity in S/m <br /> tand: dielectric medium loss tangent || [[File:twin.png]] || [[File:twin1.png|120px]]
|-
| Twisted-Pair Line || twisted-pair || len: line segment length in mm <br /> r: wire radius in mm <br /> s: wire spacing in mm <br /> T: number of twists per length in 1/m <br /> erc: dielectric cover relative permittivity <br /> erm: dielectric medium relative permittivity <br /> sigma: wire conductivity in S/m <br /> tand: dielectric cover loss tangent || [[File:twisted.png]] || [[File:twisted1.png|120px]]
|-
|}
== Working with Coupled Transmission Line Devices ==
[[RF.Spice A/D]] provides three coupled line devices, all of which assumes lossless [[Transmission Lines|transmission lines]]:
# Generic Coupled T-Lines
# Coupled Striplines
The Generic Coupled T-Lines device has the following [[parameters]]:
* Z0e: Even Mode Characteristic Impedance in Ohms
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[[File:tline8.png|thumb|320pxleft|480px| Coupled Microstrips Calculator.]]
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[[File:tline14tline9.png|thumb|320pxleft|480px| Coupled Striplines CalculatorMicrostrips Designer.]]
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[[File:tline9tline14.png|thumb|320pxleft|480px| Coupled Microstrips DesignerStriplines Calculator.]]
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[[File:tline15.png|thumb|320pxleft|480px| Coupled Striplines Designer.]]
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